GNU Octave
A high-level interactive language for numerical computations
Edition 3 for Octave version 2.1.x
February 1997
John W. Eaton
Copyright c 1996, 1997 John W. Eaton.
This is the third edition of the Octave documentation, and is consistent with version 2.1.x
of Octave.
Permission is granted to make and distribute verbatim copies of this manual provided the
copyright notice and this permission notice are preserved on all copies.
Permission is granted to copy and distribute modified versions of this manual under the conditions
for verbatim copying, provided that the entire resulting derived work is distributed
under the terms of a permission notice identical to this one.
Permission is granted to copy and distribute translations of this manual into another language,
under the same conditions as for modified versions.
Portions of this document have been adapted from the gawk, readline, gcc, and C library
manuals, published by the Free Software Foundation, 59 Temple Place—Suite 330, Boston,
MA 02111–1307, USA.
i
Table of Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
How You Can Contribute to Octave . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1 A Brief Introduction to Octave . . . . . . . . . . . . . 5
1.1 Running Octave. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Simple Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Creating a Matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Matrix Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Solving Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Integrating Differential Equations . . . . . . . . . . . . . . . . . . . . . . 6
Producing Graphical Output . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Editing What You Have Typed. . . . . . . . . . . . . . . . . . . . . . . . . 7
Help and Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.1 Fonts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.2 Evaluation Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.3 Printing Notation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.4 Error Messages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.5 Format of Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.5.1 A Sample Function Description . . . . . . . . . 9
1.3.5.2 A Sample Command Description . . . . . . . 10
1.3.5.3 A Sample Variable Description . . . . . . . . . 11
2 Getting Started. . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1 Invoking Octave. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 Command Line Options . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.2 Startup Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Quitting Octave. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Commands for Getting Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4 Command Line Editing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.1 Cursor Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.2 Killing and Yanking . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4.3 Commands For Changing Text . . . . . . . . . . . . . . . . . 19
2.4.4 Letting Readline Type For You . . . . . . . . . . . . . . . . . 20
2.4.5 Commands For Manipulating The History . . . . . . . 20
2.4.6 Customizing readline . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.7 Customizing the Prompt . . . . . . . . . . . . . . . . . . . . . . . 23
2.4.8 Diary and Echo Commands . . . . . . . . . . . . . . . . . . . . 24
2.5 How Octave Reports Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.6 Executable Octave Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.7 Comments in Octave Programs. . . . . . . . . . . . . . . . . . . . . . . . . . 26
ii GNU Octave
3 Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1 Built-in Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.1 Numeric Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.2 String Objects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.3 Data Structure Objects . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 User-defined Data Types. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3 Object Sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4 Numeric Data Types. . . . . . . . . . . . . . . . . . . . . . 31
4.1 Matrices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.1.1 Empty Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 Ranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3 Logical Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.4 Predicates for Numeric Objects. . . . . . . . . . . . . . . . . . . . . . . . . . 36
5 Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.1 Creating Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.2 Searching and Replacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.3 String Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.4 Character Class Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
6 Data Structures . . . . . . . . . . . . . . . . . . . . . . . . . . 45
7 Containers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
7.1 Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
7.2 Cell Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
8 I/O Streams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
9 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
9.1 Global Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
9.2 Status of Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
9.3 Summary of Built-in Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 56
9.4 Defaults from the Environment. . . . . . . . . . . . . . . . . . . . . . . . . . 61
iii
10 Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
10.1 Index Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
10.2 Calling Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
10.2.1 Call by Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
10.2.2 Recursion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
10.3 Arithmetic Operators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
10.4 Comparison Operators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
10.5 Boolean Expressions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
10.5.1 Element-by-element Boolean Operators. . . . . . . . . 70
10.5.2 Short-circuit Boolean Operators . . . . . . . . . . . . . . . 71
10.6 Assignment Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
10.7 Increment Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
10.8 Operator Precedence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
11 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
12 Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
12.1 The if Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
12.2 The switch Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
12.3 The while Statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
12.4 The do-until Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
12.5 The for Statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
12.5.1 Looping Over Structure Elements . . . . . . . . . . . . . . 84
12.6 The break Statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
12.7 The continue Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
12.8 The unwind_protect Statement. . . . . . . . . . . . . . . . . . . . . . . . 87
12.9 The try Statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
12.10 Continuation Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
13 Functions and Script Files. . . . . . . . . . . . . . . . 91
13.1 Defining Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
13.2 Multiple Return Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
13.3 Variable-length Argument Lists . . . . . . . . . . . . . . . . . . . . . . . . 95
13.4 Variable-length Return Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
13.5 Returning From a Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
13.6 Function Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
13.7 Script Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
13.8 Dynamically Linked Functions . . . . . . . . . . . . . . . . . . . . . . . . 101
13.9 Organization of Functions Distributed with Octave . . . . . 104
14 Error Handling . . . . . . . . . . . . . . . . . . . . . . . . . 107
iv GNU Octave
15 Input and Output . . . . . . . . . . . . . . . . . . . . . . 109
15.1 Basic Input and Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
15.1.1 Terminal Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
15.1.2 Terminal Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
15.1.3 Simple File I/O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
15.2 C-Style I/O Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
15.2.1 Opening and Closing Files . . . . . . . . . . . . . . . . . . . 116
15.2.2 Simple Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
15.2.3 Line-Oriented Input . . . . . . . . . . . . . . . . . . . . . . . . . 118
15.2.4 Formatted Output. . . . . . . . . . . . . . . . . . . . . . . . . . . 118
15.2.5 Output Conversion for Matrices . . . . . . . . . . . . . . 119
15.2.6 Output Conversion Syntax . . . . . . . . . . . . . . . . . . . 120
15.2.7 Table of Output Conversions . . . . . . . . . . . . . . . . . 120
15.2.8 Integer Conversions. . . . . . . . . . . . . . . . . . . . . . . . . . 121
15.2.9 Floating-Point Conversions . . . . . . . . . . . . . . . . . . . 122
15.2.10 Other Output Conversions . . . . . . . . . . . . . . . . . . 123
15.2.11 Formatted Input . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
15.2.12 Input Conversion Syntax . . . . . . . . . . . . . . . . . . . . 124
15.2.13 Table of Input Conversions . . . . . . . . . . . . . . . . . . 125
15.2.14 Numeric Input Conversions. . . . . . . . . . . . . . . . . . 126
15.2.15 String Input Conversions. . . . . . . . . . . . . . . . . . . . 126
15.2.16 Binary I/O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
15.2.17 Temporary Files. . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
15.2.18 End of File and Errors . . . . . . . . . . . . . . . . . . . . . . 128
15.2.19 File Positioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
16 Plotting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
16.1 Two-Dimensional Plotting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
16.2 Specialized Two-Dimensional Plots . . . . . . . . . . . . . . . . . . . . 136
16.3 Three-Dimensional Plotting . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
16.4 Plot Annotations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
16.5 Multiple Plots on One Page. . . . . . . . . . . . . . . . . . . . . . . . . . . 140
16.6 Multiple Plot Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
16.7 Interaction with gnuplot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
17 Matrix Manipulation . . . . . . . . . . . . . . . . . . . 143
17.1 Finding Elements and Checking Conditions . . . . . . . . . . . . 143
17.2 Rearranging Matrices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
17.3 Special Utility Matrices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
17.4 Famous Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
v
18 Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
18.1 Utility Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
18.2 Complex Arithmetic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
18.3 Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
18.4 Sums and Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
18.5 Special Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
18.6 Coordinate Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . 161
18.7 Mathematical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
19 Linear Algebra . . . . . . . . . . . . . . . . . . . . . . . . . 165
19.1 Basic Matrix Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
19.2 Matrix Factorizations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
19.3 Functions of a Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
20 Nonlinear Equations . . . . . . . . . . . . . . . . . . . . 173
21 Quadrature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
21.1 Functions of One Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
21.2 Orthogonal Collocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
22 Differential Equations. . . . . . . . . . . . . . . . . . . 177
22.1 Ordinary Differential Equations . . . . . . . . . . . . . . . . . . . . . . . 177
22.2 Differential-Algebraic Equations . . . . . . . . . . . . . . . . . . . . . . . 178
23 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
23.1 Quadratic Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
23.2 Nonlinear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
23.3 Linear Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
24 Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
24.1 Basic Statistical Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
24.2 Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
24.3 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
24.4 Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
25 Financial Functions . . . . . . . . . . . . . . . . . . . . . 203
26 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
27 Polynomial Manipulations. . . . . . . . . . . . . . . 207
vi GNU Octave
28 Control Theory. . . . . . . . . . . . . . . . . . . . . . . . . 211
28.1 System Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
28.1.1 Variables common to all OCST system formats
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
28.1.2 tf format variables . . . . . . . . . . . . . . . . . . . . . . . . . . 212
28.1.3 zp format variables . . . . . . . . . . . . . . . . . . . . . . . . . . 213
28.1.4 ss format variables . . . . . . . . . . . . . . . . . . . . . . . . . . 213
28.2 System Construction and Interface Functions. . . . . . . . . . . 213
28.2.1 Finite impulse response system interface functions
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
28.2.2 State space system interface functions . . . . . . . . . 214
28.2.3 Transfer function system interface functions . . . 217
28.2.4 Zero-pole system interface functions. . . . . . . . . . . 218
28.2.5 Data structure access functions . . . . . . . . . . . . . . . 219
28.2.6 Data structure internal functions . . . . . . . . . . . . . 223
28.3 System display functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
28.4 Block Diagram Manipulations. . . . . . . . . . . . . . . . . . . . . . . . . 224
28.5 Numerical Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
28.6 System Analysis-Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
28.7 System Analysis-Time Domain . . . . . . . . . . . . . . . . . . . . . . . . 240
28.8 System Analysis-Frequency Domain . . . . . . . . . . . . . . . . . . . 243
28.9 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
28.10 Miscellaneous Functions (Not yet properly
filed/documented) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
29 Signal Processing . . . . . . . . . . . . . . . . . . . . . . . 259
30 Image Processing . . . . . . . . . . . . . . . . . . . . . . . 267
31 Audio Processing . . . . . . . . . . . . . . . . . . . . . . . 271
32 Quaternions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
33 System Utilities . . . . . . . . . . . . . . . . . . . . . . . . 275
33.1 Timing Utilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
33.2 Filesystem Utilities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
33.3 Controlling Subprocesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
33.4 Process, Group, and User IDs . . . . . . . . . . . . . . . . . . . . . . . . . 287
33.5 Environment Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
33.6 Current Working Directory . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
33.7 Password Database Functions . . . . . . . . . . . . . . . . . . . . . . . . . 288
33.8 Group Database Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
33.9 System Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
vii
Appendix A Tips and Standards . . . . . . . . . . . 293
A.1 Writing Clean Octave Programs . . . . . . . . . . . . . . . . . . . . . . . 293
A.2 Tips for Making Code Run Faster. . . . . . . . . . . . . . . . . . . . . . 293
A.3 Tips for Documentation Strings. . . . . . . . . . . . . . . . . . . . . . . . 294
A.4 Tips on Writing Comments. . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
A.5 Conventional Headers for Octave Functions . . . . . . . . . . . . . 295
Appendix B Known Causes of Trouble. . . . . . 299
B.1 Actual Bugs We Haven’t Fixed Yet . . . . . . . . . . . . . . . . . . . . 299
B.2 Reporting Bugs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
B.3 Have You Found a Bug?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
B.4 Where to Report Bugs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
B.5 How to Report Bugs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
B.6 Sending Patches for Octave. . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
B.7 How To Get Help with Octave . . . . . . . . . . . . . . . . . . . . . . . . . 303
Appendix C Installing Octave . . . . . . . . . . . . . . 305
C.1 Installation Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
C.2 Binary Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
C.2.1 Installing Octave from a Binary Distribution . . . 310
C.2.2 Creating a Binary Distribution . . . . . . . . . . . . . . . . 311
Appendix D Emacs Octave Support . . . . . . . . 313
D.1 Installing EOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
D.2 Using Octave Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
D.3 Running Octave From Within Emacs. . . . . . . . . . . . . . . . . . . 317
D.4 Using the Emacs Info Reader for Octave. . . . . . . . . . . . . . . . 318
Appendix E Grammar . . . . . . . . . . . . . . . . . . . . . 321
E.1 Keywords . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
Appendix F GNU GENERAL PUBLIC
LICENSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
F.1 Preamble. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
F.2 TERMS AND CONDITIONS FOR COPYING,
DISTRIBUTION AND MODIFICATION . . . . . . . . . . . . . . . 324
F.3 Appendix: How to Apply These Terms to Your New
Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
Concept Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
Variable Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
Function Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
Operator Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
viii GNU Octave
Preface 1
Preface
Octave was originally intended to be companion software for an undergraduate-level
textbook on chemical reactor design being written by James B. Rawlings of the University
of Wisconsin-Madison and John G. Ekerdt of the University of Texas.
Clearly, Octave is now much more than just another ‘courseware’ package with limited
utility beyond the classroom. Although our initial goals were somewhat vague, we knew
that we wanted to create something that would enable students to solve realistic problems,
and that they could use for many things other than chemical reactor design problems.
There are those who would say that we should be teaching the students Fortran instead,
because that is the computer language of engineering, but every time we have tried that, the
students have spent far too much time trying to figure out why their Fortran code crashes
and not enough time learning about chemical engineering. With Octave, most students pick
up the basics quickly, and are using it confidently in just a few hours.
Although it was originally intended to be used to teach reactor design, it has been used in
several other undergraduate and graduate courses in the Chemical Engineering Department
at the University of Texas, and the math department at the University of Texas has been
using it for teaching differential equations and linear algebra as well. If you find it useful,
please let us know. We are always interested to find out how Octave is being used in other
places.
Virtually everyone thinks that the name Octave has something to do with music, but it
is actually the name of a former professor of mine who wrote a famous textbook on chemical
reaction engineering, and who was also well known for his ability to do quick ‘back of the
envelope’ calculations. We hope that this software will make it possible for many people to
do more ambitious computations just as easily.
Everyone is encouraged to share this software with others under the terms of the GNU
General Public License (see Appendix F [Copying], page 323) as described at the beginning
of this manual. You are also encouraged to help make Octave more useful by writing and
contributing additional functions for it, and by reporting any problems you may have.
Acknowledgements
Many people have already contributed to Octave’s development. In addition to John
W. Eaton, the following people have helped write parts of Octave or helped out in various
other ways.
• Thomas Baier baier@ci.tuwien.ac.at wrote the original versions of popen, pclose,
execute, sync_system, and async_system.
• Karl Berry karl@cs.umb.edu wrote the kpathsea library that allows Octave to recursively
search directory paths for function and script files.
• Georg Beyerle gbeyerle@awi-potsdam.de contributed code to save values in Matlab’s
‘.mat’-file format, and has provided many useful bug reports and suggestions.
• John Campbell jcc@bevo.che.wisc.edu wrote most of the file and C-style input and
output functions.
• Brian Fox bfox@gnu.org wrote the readline library used for command history editing,
and the portion of this manual that documents it.
2 GNU Octave
• Klaus Gebhardt gebhardt@crunch.ikp.physik.th-darmstadt.de ported Octave to
OS/2.
• A. Scottedward Hodel A.S.Hodel@eng.auburn.edu contributed a number of functions
including expm, qzval, qzhess, syl, lyap, and balance.
• Kurt Hornik Kurt.Hornik@ci.tuwien.ac.at provided the corrcoef, cov, fftconv,
fftfilt, gcd, lcd, kurtosis, null, orth, poly, polyfit, roots, and skewness functions,
supplied documentation for these and numerous other functions, rewrote the
Emacs mode for editing Octave code and provided its documentation, and has helped
tremendously with testing. He has also been a constant source of new ideas for improving
Octave.
• Phil Johnson johnsonp@nicco.sscnet.ucla.edu has helped to make Linux releases
available.
• Friedrich Leisch leisch@ci.tuwien.ac.at provided the mahalanobis function.
• Ken Neighbors wkn@leland.stanford.edu has provided many useful bug reports and
comments on Matlab compatibility.
• Rick Niles niles@axp745.gsfc.nasa.gov rewrote Octave’s plotting functions to add
line styles and the ability to specify an unlimited number of lines in a single call. He
also continues to track down odd incompatibilities and bugs.
• Mark Odegard meo@sugarland.unocal.com provided the initial implementation of
fread, fwrite, feof, and ferror.
• Tony Richardson arichard@stark.cc.oh.us wrote Octave’s image processing functions
as well as most of the original polynomial functions.
• R. Bruce Tenison btenison@dibbs.net wrote the hess and schur functions.
• Teresa Twaroch twaroch@ci.tuwien.ac.at provided the functions gls and ols.
• Andreas Weingessel Andreas.Weingessel@ci.tuwien.ac.at wrote the audio functions
lin2mu, loadaudio, mu2lin, playaudio, record, saveaudio, and setaudio.
• Fook Fah Yap ffy@eng.cam.ac.uk provided the fft and ifft functions and valuable
bug reports for early versions.
Special thanks to the following people and organizations for supporting the development
of Octave:
• The National Science Foundation, through grant numbers CTS-0105360, CTS-9708497,
CTS-9311420, and CTS-8957123.
• The industrial members of the Texas-Wisconsin Modeling and Control Consortium
(TWMCC (http://www.che.utexas.edu/twmcc)).
• The Paul A. Elfers Endowed Chair in Chemical Engineering at the University of
Wisconsin-Madison.
• Digital Equipment Corporation, for an equipment grant as part of their External Research
Program.
• Sun Microsystems, Inc., for an Academic Equipment grant.
• International Business Machines, Inc., for providing equipment as part of a grant to
the University of Texas College of Engineering.
• Texaco Chemical Company, for providing funding to continue the development of this
software.
Preface 3
• The University of Texas College of Engineering, for providing a Challenge for Excellence
Research Supplement, and for providing an Academic Development Funds grant.
• The State of Texas, for providing funding through the Texas Advanced Technology
Program under Grant No. 003658-078.
• Noel Bell, Senior Engineer, Texaco Chemical Company, Austin Texas.
• James B. Rawlings, Professor, University of Wisconsin-Madison, Department of Chemical
Engineering.
• Richard Stallman, for writing GNU.
This project would not have been possible without the GNU software used in and used
to produce Octave.
How You Can Contribute to Octave
There are a number of ways that you can contribute to help make Octave a better system.
Perhaps the most important way to contribute is to write high-quality code for solving new
problems, and to make your code freely available for others to use.
If you find Octave useful, consider providing additional funding to continue its development.
Even a modest amount of additional funding could make a significant difference in
the amount of time that is available for development and support.
If you cannot provide funding or contribute code, you can still help make Octave better
and more reliable by reporting any bugs you find and by offering suggestions for ways to
improve Octave. See Appendix B [Trouble], page 299, for tips on how to write useful bug
reports.
Distribution
Octave is free software. This means that everyone is free to use it and free to redistribute
it on certain conditions. Octave is not in the public domain. It is copyrighted and there are
restrictions on its distribution, but the restrictions are designed to ensure that others will
have the same freedom to use and redistribute Octave that you have. The precise conditions
can be found in the GNU General Public License that comes with Octave and that also
appears in Appendix F [Copying], page 323.
Octave is available on CD-ROM with various collections of other free software, and
from the Free Software Foundation. Ordering a copy of Octave from the Free Software
Foundation helps to fund the development of more free software. For more information,
write to
Free Software Foundation
59 Temple Place—Suite 330
Boston, MA 02111–1307
USA
Octave is also available on the Internet from ftp://ftp.che.wisc.edu/pub/octave,
and additional information is available from http://www.che.wisc.edu/octave.
4 GNU Octave
Chapter 1: A Brief Introduction to Octave 5
1 A Brief Introduction to Octave
This manual documents how to run, install and port GNU Octave, and how to report
bugs.
GNU Octave is a high-level language, primarily intended for numerical computations.
It provides a convenient command line interface for solving linear and nonlinear problems
numerically, and for performing other numerical experiments. It may also be used as a
batch-oriented language.
GNU Octave is also freely redistributable software. You may redistribute it and/or modify
it under the terms of the GNU General Public License as published by the Free Software
Foundation. The GPL is included in this manual in Appendix F [Copying], page 323.
This document corresponds to Octave version 2.1.x.
1.1 Running Octave
On most systems, the way to invoke Octave is with the shell command ‘octave’. Octave
displays an initial message and then a prompt indicating it is ready to accept input. You
can begin typing Octave commands immediately afterward.
If you get into trouble, you can usually interrupt Octave by typing Control-C (usually
written C-c for short). C-c gets its name from the fact that you type it by holding down
CTRL and then pressing c . Doing this will normally return you to Octave’s prompt.
To exit Octave, type quit, or exit at the Octave prompt.
On systems that support job control, you can suspend Octave by sending it a SIGTSTP
signal, usually by typing C-z.
1.2 Simple Examples
The following chapters describe all of Octave’s features in detail, but before doing that,
it might be helpful to give a sampling of some of its capabilities.
If you are new to Octave, I recommend that you try these examples to begin learning
Octave by using it. Lines marked with ‘octave:13>’ are lines you type, ending each with
a carriage return. Octave will respond with an answer, or by displaying a graph.
Creating a Matrix
To create a new matrix and store it in a variable so that it you can refer to it later, type
the command
octave:1> a = [ 1, 1, 2; 3, 5, 8; 13, 21, 34 ]
Octave will respond by printing the matrix in neatly aligned columns. Ending a command
with a semicolon tells Octave to not print the result of a command. For example
octave:2> b = rand (3, 2);
will create a 3 row, 2 column matrix with each element set to a random value between zero
and one.
To display the value of any variable, simply type the name of the variable. For example,
to display the value stored in the matrix b, type the command
octave:3> b
6 GNU Octave
Matrix Arithmetic
Octave has a convenient operator notation for performing matrix arithmetic. For example,
to multiply the matrix a by a scalar value, type the command
octave:4> 2 * a
To multiply the two matrices a and b, type the command
octave:5> a * b
To form the matrix product aT
a, type the command
octave:6> a’ * a
Solving Linear Equations
To solve the set of linear equations ax = b, use the left division operator, ‘\’:
octave:7> a \ b
This is conceptually equivalent to a−1
b, but avoids computing the inverse of a matrix
directly.
If the coefficient matrix is singular, Octave will print a warning message and compute a
minimum norm solution.
Integrating Differential Equations
Octave has built-in functions for solving nonlinear differential equations of the form
dx
dt
= f(x, t), x(t = t0) = x0
For Octave to integrate equations of this form, you must first provide a definition of the
function f(x, t). This is straightforward, and may be accomplished by entering the function
body directly on the command line. For example, the following commands define the right
hand side function for an interesting pair of nonlinear differential equations. Note that
while you are entering a function, Octave responds with a different prompt, to indicate that
it is waiting for you to complete your input.
octave:8> function xdot = f (x, t)
>
> r = 0.25;
> k = 1.4;
> a = 1.5;
> b = 0.16;
> c = 0.9;
> d = 0.8;
>
> xdot(1) = r*x(1)*(1 - x(1)/k) - a*x(1)*x(2)/(1 + b*x(1));
> xdot(2) = c*a*x(1)*x(2)/(1 + b*x(1)) - d*x(2);
>
> endfunction
Given the initial condition
Chapter 1: A Brief Introduction to Octave 7
x0 = [1; 2];
and the set of output times as a column vector (note that the first output time corresponds
to the initial condition given above)
t = linspace (0, 50, 200)’;
it is easy to integrate the set of differential equations:
x = lsode ("f", x0, t);
The function lsode uses the Livermore Solver for Ordinary Differential Equations, described
in A. C. Hindmarsh, ODEPACK, a Systematized Collection of ODE Solvers, in: Scientific
Computing, R. S. Stepleman et al. (Eds.), North-Holland, Amsterdam, 1983, pages 55–64.
Producing Graphical Output
To display the solution of the previous example graphically, use the command
plot (t, x)
If you are using the X Window System, Octave will automatically create a separate
window to display the plot. If you are using a terminal that supports some other graphics
commands, you will need to tell Octave what kind of terminal you have. Type the command
gset term
to see a list of the supported terminal types. Octave uses gnuplot to display graphics, and
can display graphics on any terminal that is supported by gnuplot.
To capture the output of the plot command in a file rather than sending the output
directly to your terminal, you can use a set of commands like this
gset term postscript
gset output "foo.ps"
replot
This will work for other types of output devices as well. Octave’s gset command is really
just piped to the gnuplot subprocess, so that once you have a plot on the screen that you
like, you should be able to do something like this to create an output file suitable for your
graphics printer.
Or, you can eliminate the intermediate file by using commands like this
gset term postscript
gset output "|lpr -Pname_of_your_graphics_printer"
replot
Editing What You Have Typed
At the Octave prompt, you can recall, edit, and reissue previous commands using Emacsor
vi-style editing commands. The default keybindings use Emacs-style commands. For
example, to recall the previous command, type Control-p (usually written C-p for short).
C-p gets its name from the fact that you type it by holding down CTRL and then pressing
p . Doing this will normally bring back the previous line of input. C-n will bring up the
next line of input, C-b will move the cursor backward on the line, C-f will move the cursor
forward on the line, etc.
A complete description of the command line editing capability is given in this manual
in Section 2.4 [Command Line Editing], page 18.
8 GNU Octave
Help and Documentation
Octave has an extensive help facility. The same documentation that is available in
printed form is also available from the Octave prompt, because both forms of the documentation
are created from the same input file.
In order to get good help you first need to know the name of the command that you
want to use. This name of the function may not always be obvious, but a good place to
start is to just type help. This will show you all the operators, reserved words, functions,
built-in variables, and function files. You can then get more help on anything that is listed
by simply including the name as an argument to help. For example,
help plot
will display the help text for the plot function.
Octave sends output that is too long to fit on one screen through a pager like less or
more. Type a RET to advance one line, a SPC to advance one page, and q to exit the
pager.
The part of Octave’s help facility that allows you to read the complete text of the printed
manual from within Octave normally uses a separate program called Info. When you invoke
Info you will be put into a menu driven program that contains the entire Octave manual.
Help for using Info is provided in this manual in Section 2.3 [Getting Help], page 17.
1.3 Conventions
This section explains the notational conventions that are used in this manual. You may
want to skip this section and refer back to it later.
1.3.1 Fonts
Examples of Octave code appear in this font or form: svd (a). Names that represent
arguments or metasyntactic variables appear in this font or form: first-number. Commands
that you type at the shell prompt sometimes appear in this font or form: ‘octave
--no-init-file’. Commands that you type at the Octave prompt sometimes appear in
this font or form: foo --bar --baz. Specific keys on your keyboard appear in this font or
form: ANY .
1.3.2 Evaluation Notation
In the examples in this manual, results from expressions that you evaluate are indicated
with ‘⇒’. For example,
sqrt (2)
⇒ 1.4142
You can read this as “sqrt (2) evaluates to 1.4142”.
In some cases, matrix values that are returned by expressions are displayed like this
[1, 2; 3, 4] == [1, 3; 2, 4]
⇒ [ 1, 0; 0, 1 ]
and in other cases, they are displayed like this
Chapter 1: A Brief Introduction to Octave 9
eye (3)
⇒ 1 0 0
0 1 0
0 0 1
in order to clearly show the structure of the result.
Sometimes to help describe one expression, another expression is shown that produces
identical results. The exact equivalence of expressions is indicated with ‘≡’. For example,
rot90 ([1, 2; 3, 4], -1)
≡
rot90 ([1, 2; 3, 4], 3)
≡
rot90 ([1, 2; 3, 4], 7)
1.3.3 Printing Notation
Many of the examples in this manual print text when they are evaluated. Examples in
this manual indicate printed text with ‘ ’. The value that is returned by evaluating the
expression (here 1) is displayed with ‘⇒’ and follows on a separate line.
printf ("foo %s\n", "bar")
foo bar
⇒ 1
1.3.4 Error Messages
Some examples signal errors. This normally displays an error message on your terminal.
Error messages are shown on a line starting with error:.
struct_elements ([1, 2; 3, 4])
error: struct_elements: wrong type argument ‘matrix’
1.3.5 Format of Descriptions
Functions, commands, and variables are described in this manual in a uniform format.
The first line of a description contains the name of the item followed by its arguments, if
any. The category—function, variable, or whatever—is printed next to the right margin.
The description follows on succeeding lines, sometimes with examples.
1.3.5.1 A Sample Function Description
In a function description, the name of the function being described appears first. It is
followed on the same line by a list of parameters. The names used for the parameters are
also used in the body of the description.
Here is a description of an imaginary function foo:
Functionfoo (x, y, ...)
The function foo subtracts x from y, then adds the remaining arguments to the result.
If y is not supplied, then the number 19 is used by default.
10 GNU Octave
foo (1, [3, 5], 3, 9)
⇒ [ 14, 16 ]
foo (5)
⇒ 14
More generally,
foo (w, x, y, ...)
≡
x - w + y + ...
Any parameter whose name contains the name of a type (e.g., integer, integer1 or matrix)
is expected to be of that type. Parameters named object may be of any type. Parameters
with other sorts of names (e.g., new file) are discussed specifically in the description of
the function. In some sections, features common to parameters of several functions are
described at the beginning.
Functions in Octave may be defined in several different ways. The catagory name for
functions may include another name that indicates the way that the function is defined.
These additional tags include
Built-in Function
The function described is written in a language like C++, C, or Fortran, and is
part of the compiled Octave binary.
Loadable Function
The function described is written in a language like C++, C, or Fortran. On
systems that support dynamic linking of user-supplied functions, it may be
automatically linked while Octave is running, but only if it is needed. See
Section 13.8 [Dynamically Linked Functions], page 101.
Function File
The function described is defined using Octave commands stored in a text file.
See Section 13.6 [Function Files], page 98.
Mapping Function
The function described works element-by-element for matrix and vector argu-
ments.
1.3.5.2 A Sample Command Description
Command descriptions have a format similar to function descriptions, except that the
word ‘Function’ is replaced by ‘Command. Commands are functions that may called without
surrounding their arguments in parentheses. For example, here is the description for
Octave’s cd command:
Commandcd dir
Commandchdir dir
Change the current working directory to dir. For example, cd ~/octave changes the
current working directory to ‘~/octave’. If the directory does not exist, an error
message is printed and the working directory is not changed.
Chapter 1: A Brief Introduction to Octave 11
1.3.5.3 A Sample Variable Description
A variable is a name that can hold a value. Although any variable can be set by the
user, built-in variables typically exist specifically so that users can change them to alter the
way Octave behaves (built-in variables are also sometimes called user options). Ordinary
variables and built-in variables are described using a format like that for functions except
that there are no arguments.
Here is a description of the imaginary variable do_what_i_mean_not_what_i_say.
Built-in Variabledo what i mean not what i say
If the value of this variable is nonzero, Octave will do what you actually wanted, even
if you have typed a completely different and meaningless list of commands.
Other variable descriptions have the same format, but ‘Built-in Variable’ is replaced by
‘Variable’, for ordinary variables, or ‘Constant’ for symbolic constants whose values cannot
be changed.
12 GNU Octave
Chapter 2: Getting Started 13
2 Getting Started
This chapter explains some of Octave’s basic features, including how to start an Octave
session, get help at the command prompt, edit the command line, and write Octave
programs that can be executed as commands from your shell.
2.1 Invoking Octave
Normally, Octave is used interactively by running the program ‘octave’ without any
arguments. Once started, Octave reads commands from the terminal until you tell it to
exit.
You can also specify the name of a file on the command line, and Octave will read and
execute the commands from the named file and then exit when it is finished.
You can further control how Octave starts by using the command-line options described
in the next section, and Octave itself can remind you of the options available. Type ‘octave
--help’ to display all available options and briefly describe their use (‘octave -h’ is a shorter
equivalent).
2.1.1 Command Line Options
Here is a complete list of all the command line options that Octave accepts.
--debug
-d Enter parser debugging mode. Using this option will cause Octave’s parser to
print a lot of information about the commands it reads, and is probably only
useful if you are actually trying to debug the parser.
--echo-commands
-x Echo commands as they are executed.
--exec-path path
Specify the path to search for programs to run. The value of path specified on
the command line will override any value of OCTAVE_EXEC_PATH found in the
environment, but not any commands in the system or user startup files that set
the built-in variable EXEC_PATH.
--help
-h
-? Print short help message and exit.
--info-file filename
Specify the name of the info file to use. The value of filename specified on
the command line will override any value of OCTAVE_INFO_FILE found in the
environment, but not any commands in the system or user startup files that set
the built-in variable INFO_FILE.
--info-program program
Specify the name of the info program to use. The value of program specified
on the command line will override any value of OCTAVE_INFO_PROGRAM found
in the environment, but not any commands in the system or user startup files
that set the built-in variable INFO_PROGRAM.
14 GNU Octave
--interactive
-i Force interactive behavior. This can be useful for running Octave via a remote
shell command or inside an Emacs shell buffer. For another way to run Octave
within Emacs, see Appendix D [Emacs], page 313.
--no-history
-H Disable command-line history.
--no-init-file
Don’t read the ‘~/.octaverc’ or ‘.octaverc’ files.
--no-line-editing
Disable command-line editing.
--no-site-file
Don’t read the site-wide ‘octaverc’ file.
--norc
-f Don’t read any of the system or user initialization files at startup. This is
equivalent to using both of the options --no-init-file and --no-site-file.
--path path
-p path Specify the path to search for function files. The value of path specified on the
command line will override any value of OCTAVE_PATH found in the environment,
but not any commands in the system or user startup files that set the built-in
variable LOADPATH.
--silent
--quiet
-q Don’t print the usual greeting and version message at startup.
--traditional
--braindead
Set initial values for user-preference variables to the following values for compatibility
with Matlab.
PS1 = ">> "
PS2 = ""
beep_on_error = 1
default_save_format = "mat-binary"
define_all_return_values = 1
do_fortran_indexing = 1
crash_dumps_octave_core = 0
empty_list_elements_ok = 1
implicit_str_to_num_ok = 1
ok_to_lose_imaginary_part = 1
page_screen_output = 0
prefer_column_vectors = 0
print_empty_dimensions = 0
treat_neg_dim_as_zero = 1
warn_function_name_clash = 0
whitespace_in_literal_matrix = "traditional"
Chapter 2: Getting Started 15
--verbose
-V Turn on verbose output.
--version
-v Print the program version number and exit.
file Execute commands from file.
Octave also includes several built-in variables that contain information about the command
line, including the number of arguments and all of the options.
Built-in Variableargv
The command line arguments passed to Octave are available in this variable. For
example, if you invoked Octave using the command
octave --no-line-editing --silent
argv would be a list of strings with the elements --no-line-editing and --silent.
If you write an executable Octave script, argv will contain the list of arguments
passed to the script. See Section 2.6 [Executable Octave Programs], page 26, for an
example of how to create an executable Octave script.
Built-in Variableprogram invocation name
Built-in Variableprogram name
When Octave starts, the value of the built-in variable program_invocation_name is
automatically set to the name that was typed at the shell prompt to run Octave, and
the value of program_name is automatically set to the final component of program_
invocation_name. For example, if you typed ‘/usr/local/bin/octave’ to start Octave,
program_invocation_name would have the value "/usr/local/bin/octave",
and program_name would have the value "octave".
If executing a script from the command line (e.g., octave foo.m) or using an executable
Octave script, the program name is set to the name of the script. See
Section 2.6 [Executable Octave Programs], page 26, for an example of how to create
an executable Octave script.
Here is an example of using these variables to reproduce Octave’s command line.
printf ("%s", program_name);
for i = 1:nargin
printf (" %s", nth (argv, i));
endfor
printf ("\n");
See Section 10.1 [Index Expressions], page 63, for an explanation of how to properly index
arrays of strings and substrings in Octave, and See Section 13.1 [Defining Functions],
page 91, for information about the variable nargin.
2.1.2 Startup Files
When Octave starts, it looks for commands to execute from the following files:
16 GNU Octave
octave-home/share/octave/site/m/startup/octaverc
Where octave-home is the directory in which all of Octave is installed (the
default is ‘/usr/local’). This file is provided so that changes to the default
Octave environment can be made globally for all users at your site for all versions
of Octave you have installed. Some care should be taken when making
changes to this file, since all users of Octave at your site will be affected.
octave-home/share/octave/version/m/startup/octaverc
Where octave-home is the directory in which all of Octave is installed (the
default is ‘/usr/local’), and version is the version number of Octave. This
file is provided so that changes to the default Octave environment can be made
globally for all users for a particular version of Octave. Some care should be
taken when making changes to this file, since all users of Octave at your site
will be affected.
~/.octaverc
This file is normally used to make personal changes to the default Octave envi-
ronment.
.octaverc
This file can be used to make changes to the default Octave environment for
a particular project. Octave searches for this file in the current directory after
it reads ‘~/.octaverc’. Any use of the cd command in the ‘~/.octaverc’ file
will affect the directory that Octave searches for the file ‘.octaverc’.
If you start Octave in your home directory, commands from from the file
‘~/.octaverc’ will only be executed once.
A message will be displayed as each of the startup files is read if you invoke Octave with
the --verbose option but without the --silent option.
Startup files may contain any valid Octave commands, including function definitions.
2.2 Quitting Octave
Built-in Functionexit (status)
Built-in Functionquit (status)
Exit the current Octave session. If the optional integer value status is supplied, pass
that value to the operating system as the Octave’s exit status.
Built-in Functionatexit (fcn)
Register a function to be called when Octave exits. For example,
function print_fortune ()
printf ("\n%s\n", system ("fortune"));
fflush (stdout);
endfunction
atexit ("print_fortune");
will print a message when Octave exits.
Chapter 2: Getting Started 17
2.3 Commands for Getting Help
The entire text of this manual is available from the Octave prompt via the command help
-i. In addition, the documentation for individual user-written functions and variables is
also available via the help command. This section describes the commands used for reading
the manual and the documentation strings for user-supplied functions and variables. See
Section 13.6 [Function Files], page 98, for more information about how to document the
functions you write.
Commandhelp
Octave’s help command can be used to print brief usage-style messages, or to display
information directly from an on-line version of the printed manual, using the GNU
Info browser. If invoked without any arguments, help prints a list of all the available
operators, functions, and built-in variables. If the first argument is -i, the help
command searches the index of the on-line version of this manual for the given topics.
For example, the command help help prints a short message describing the help
command, and help -i help starts the GNU Info browser at this node in the on-line
version of the manual.
Once the GNU Info browser is running, help for using it is available using the command
C-h.
The help command can give you information about operators, but not the comma and
semicolons that are used as command separators. To get help for those, you must type help
comma or help semicolon.
Built-in VariableINFO FILE
The variable INFO_FILE names the location of the Octave info file. The default value
is "octave-home/info/octave.info", in which octave-home is the directory where
all of Octave is installed.
Built-in VariableINFO PROGRAM
The variable INFO_PROGRAM names the info program to run. Its default initial value is
"octave-home/libexec/octave/version/exec/arch/info" in which octave-home is
the directory where all of Octave is installed, version is the Octave version number,
and arch is the system type (for example, i686-pc-linux-gnu). The default initial
value may be overridden by the environment variable OCTAVE_INFO_PROGRAM, or the
command line argument --info-program NAME, or by setting the value of INFO_
PROGRAM in a startup script
Built-in VariableMAKEINFO PROGRAM
The variable MAKEINFO_PROGRAM names the makeinfo program that Octave runs to
format help text that contains Texinfo markup commands. Its default initial value is
"makeinfo".
18 GNU Octave
Built-in Variablesuppress verbose help message
If the value of suppress_verbose_help_message is nonzero, Octave will not add
additional help information to the end of the output from the help command and
usage messages for built-in commands.
2.4 Command Line Editing
Octave uses the GNU readline library to provide an extensive set of command-line editing
and history features. Only the most common features are described in this manual. Please
see The GNU Readline Library manual for more information.
To insert printing characters (letters, digits, symbols, etc.), simply type the character.
Octave will insert the character at the cursor and advance the cursor forward.
Many of the command-line editing functions operate using control characters. For example,
the character Control-a moves the cursor to the beginning of the line. To type C-a,
hold down CTRL and then press a . In the following sections, control characters such as
Control-a are written as C-a.
Another set of command-line editing functions use Meta characters. On some terminals,
you type M-u by holding down META and pressing u . If your terminal does not have a
META key, you can still type Meta charcters using two-character sequences starting with
ESC. Thus, to enter M-u, you could type ESC u . The ESC character sequences are also
allowed on terminals with real Meta keys. In the following sections, Meta characters such
as Meta-u are written as M-u.
2.4.1 Cursor Motion
The following commands allow you to position the cursor.
C-b Move back one character.
C-f Move forward one character.
DEL Delete the character to the left of the cursor.
C-d Delete the character underneath the cursor.
M-f Move forward a word.
M-b Move backward a word.
C-a Move to the start of the line.
C-e Move to the end of the line.
C-l Clear the screen, reprinting the current line at the top.
C-_
C-/ Undo the last thing that you did. You can undo all the way back to an empty
line.
M-r Undo all changes made to this line. This is like typing the ‘undo’ command
enough times to get back to the beginning.
Chapter 2: Getting Started 19
The above table describes the most basic possible keystrokes that you need in order to
do editing of the input line. On most terminals, you can also use the arrow keys in place of
C-f and C-b to move forward and backward.
Notice how C-f moves forward a character, while M-f moves forward a word. It is a loose
convention that control keystrokes operate on characters while meta keystrokes operate on
words.
There is also a function available so that you can clear the screen from within Octave
programs.
Built-in Functionclc ()
Built-in Functionhome ()
Clear the terminal screen and move the cursor to the upper left corner.
2.4.2 Killing and Yanking
Killing text means to delete the text from the line, but to save it away for later use,
usually by yanking it back into the line. If the description for a command says that it ‘kills’
text, then you can be sure that you can get the text back in a different (or the same) place
later.
Here is the list of commands for killing text.
C-k Kill the text from the current cursor position to the end of the line.
M-d Kill from the cursor to the end of the current word, or if between words, to the
end of the next word.
M- DEL Kill from the cursor to the start of the previous word, or if between words, to
the start of the previous word.
C-w Kill from the cursor to the previous whitespace. This is different than M- DEL
because the word boundaries differ.
And, here is how to yank the text back into the line. Yanking means to copy the
most-recently-killed text from the kill buffer.
C-y Yank the most recently killed text back into the buffer at the cursor.
M-y Rotate the kill-ring, and yank the new top. You can only do this if the prior
command is C-y or M-y.
When you use a kill command, the text is saved in a kill-ring. Any number of consecutive
kills save all of the killed text together, so that when you yank it back, you get it in one
clean sweep. The kill ring is not line specific; the text that you killed on a previously typed
line is available to be yanked back later, when you are typing another line.
2.4.3 Commands For Changing Text
The following commands can be used for entering characters that would otherwise have
a special meaning (e.g., TAB, C-q, etc.), or for quickly correcting typing mistakes.
20 GNU Octave
C-q
C-v Add the next character that you type to the line verbatim. This is how to insert
things like C-q for example.
M- TAB Insert a tab character.
C-t Drag the character before the cursor forward over the character at the cursor,
also moving the cursor forward. If the cursor is at the end of the line, then
transpose the two characters before it.
M-t Drag the word behind the cursor past the word in front of the cursor moving
the cursor over that word as well.
M-u Uppercase the characters following the cursor to the end of the current (or
following) word, moving the cursor to the end of the word.
M-l Lowecase the characters following the cursor to the end of the current (or following)
word, moving the cursor to the end of the word.
M-c Uppercase the character following the cursor (or the beginning of the next word
if the cursor is between words), moving the cursor to the end of the word.
2.4.4 Letting Readline Type For You
The following commands allow Octave to complete command and variable names for
you.
TAB Attempt to do completion on the text before the cursor. Octave can complete
the names of commands and variables.
M-? List the possible completions of the text before the cursor.
Built-in Variablecompletion append char
The value of completion_append_char is used as the character to append to successful
command-line completion attempts. The default value is " " (a single space).
Built-in Functioncompletion matches (hint)
Generate possible completions given hint.
This function is provided for the benefit of programs like Emacs which might be
controlling Octave and handling user input. The current command number is not
incremented when this function is called. This is a feature, not a bug.
2.4.5 Commands For Manipulating The History
Octave normally keeps track of the commands you type so that you can recall previous
commands to edit or execute them again. When you exit Octave, the most recent commands
you have typed, up to the number specified by the variable history_size, are saved in a
file. When Octave starts, it loads an initial list of commands from the file named by the
variable history_file.
Here are the commands for simple browsing and searching the history list.
Chapter 2: Getting Started 21
LFD
RET Accept the line regardless of where the cursor is. If this line is non-empty, add
it to the history list. If this line was a history line, then restore the history line
to its original state.
C-p Move ‘up’ through the history list.
C-n Move ‘down’ through the history list.
M-< Move to the first line in the history.
M-> Move to the end of the input history, i.e., the line you are entering!
C-r Search backward starting at the current line and moving ‘up’ through the history
as necessary. This is an incremental search.
C-s Search forward starting at the current line and moving ‘down’ through the
history as necessary.
On most terminals, you can also use the arrow keys in place of C-p and C-n to move
through the history list.
In addition to the keyboard commands for moving through the history list, Octave
provides three functions for viewing, editing, and re-running chunks of commands from the
history list.
Commandhistory options
If invoked with no arguments, history displays a list of commands that you have
executed. Valid options are:
-w file Write the current history to the file file. If the name is omitted, use the
default history file (normally ‘~/.octave_hist’).
-r file Read the file file, replacing the current history list with its contents. If the
name is omitted, use the default history file (normally ‘~/.octave_hist’).
n Only display the most recent n lines of history.
-q Don’t number the displayed lines of history. This is useful for cutting and
pasting commands if you are using the X Window System.
For example, to display the five most recent commands that you have typed without
displaying line numbers, use the command history -q 5.
Commandedit history options
If invoked with no arguments, edit_history allows you to edit the history list using
the editor named by the variable EDITOR. The commands to be edited are first copied
to a temporary file. When you exit the editor, Octave executes the commands that
remain in the file. It is often more convenient to use edit_history to define functions
rather than attempting to enter them directly on the command line. By default, the
block of commands is executed as soon as you exit the editor. To avoid executing any
commands, simply delete all the lines from the buffer before exiting the editor.
The edit_history command takes two optional arguments specifying the history
numbers of first and last commands to edit. For example, the command
22 GNU Octave
edit_history 13
extracts all the commands from the 13th through the last in the history list. The
command
edit_history 13 169
only extracts commands 13 through 169. Specifying a larger number for the first
command than the last command reverses the list of commands before placing them
in the buffer to be edited. If both arguments are omitted, the previous command in
the history list is used.
Commandrun history [first] [last]
Similar to edit_history, except that the editor is not invoked, and the commands
are simply executed as they appear in the history list.
Built-in VariableEDITOR
A string naming the editor to use with the edit_history command. If the environment
variable EDITOR is set when Octave starts, its value is used as the default.
Otherwise, EDITOR is set to "emacs".
Built-in Variablehistory file
This variable specifies the name of the file used to store command history. The default
value is "~/.octave_hist", but may be overridden by the environment variable
OCTAVE_HISTFILE.
Built-in Variablehistory size
This variable specifies how many entries to store in the history file. The default value
is 1024, but may be overridden by the environment variable OCTAVE_HISTSIZE.
Built-in Variablesaving history
If the value of saving_history is nonzero, command entered on the command line
are saved in the file specified by the variable history_file.
2.4.6 Customizing readline
Built-in Functionread readline init file (file)
Read the readline library initialiazation file file. If file is omitted, read the default
initialization file (normally ‘~/.inputrc’.
Chapter 2: Getting Started 23
2.4.7 Customizing the Prompt
The following variables are available for customizing the appearance of the command-line
prompts. Octave allows the prompt to be customized by inserting a number of backslashescaped
special characters that are decoded as follows:
‘\t’ The time.
‘\d’ The date.
‘\n’ Begins a new line by printing the equivalent of a carriage return followed by a
line feed.
‘\s’ The name of the program (usually just ‘octave’).
‘\w’ The current working directory.
‘\W’ The basename of the current working directory.
‘\u’ The username of the current user.
‘\h’ The hostname, up to the first ‘.’.
‘\H’ The hostname.
‘\#’ The command number of this command, counting from when Octave starts.
‘\!’ The history number of this command. This differs from ‘\#’ by the number of
commands in the history list when Octave starts.
‘\$’ If the effective UID is 0, a ‘#’, otherwise a ‘$’.
‘\nnn’ The character whose character code in octal is nnn.
‘\\’ A backslash.
Built-in VariablePS1
The primary prompt string. When executing interactively, Octave displays the primary
prompt PS1 when it is ready to read a command.
The default value of PS1 is "\s:\#> ". To change it, use a command like
octave:13> PS1 = "\\u@\\H> "
which will result in the prompt ‘boris@kremvax> ’ for the user ‘boris’ logged in
on the host ‘kremvax.kgb.su’. Note that two backslashes are required to enter a
backslash into a string. See Chapter 5 [Strings], page 37.
Built-in VariablePS2
The secondary prompt string, which is printed when Octave is expecting additional
input to complete a command. For example, when defining a function over several
lines, Octave will print the value of PS1 at the beginning of each line after the first.
The default value of PS2 is "> ".
Built-in VariablePS4
If Octave is invoked with the --echo-input option, the value of PS4 is printed before
each line of input that is echoed. The default value of PS4 is "+ ". See Section 2.1
[Invoking Octave], page 13, for a description of --echo-input.
24 GNU Octave
2.4.8 Diary and Echo Commands
Octave’s diary feature allows you to keep a log of all or part of an interactive session by
recording the input you type and the output that Octave produces in a separate file.
Commanddiary options
Create a list of all commands and the output they produce, mixed together just as
you see them on your terminal. Valid options are:
on Start recording your session in a file called ‘diary’ in your current working
directory.
off Stop recording your session in the diary file.
file Record your session in the file named file.
Without any arguments, diary toggles the current diary state.
Sometimes it is useful to see the commands in a function or script as they are being
evaluated. This can be especially helpful for debugging some kinds of problems.
Commandecho options
Control whether commands are displayed as they are executed. Valid options are:
on Enable echoing of commands as they are executed in script files.
off Disable echoing of commands as they are executed in script files.
on all Enable echoing of commands as they are executed in script files and
functions.
off all Disable echoing of commands as they are executed in script files and
functions.
If invoked without any arguments, echo toggles the current echo state.
Built-in Variableecho executing commands
This variable may also be used to control the echo state. It may be the sum of the
following values:
1 Echo commands read from script files.
2 Echo commands from functions.
4 Echo commands read from command line.
More than one state can be active at once. For example, a value of 3 is equivalent to
the command echo on all.
The value of echo_executing_commands is set by the echo command and the command
line option --echo-input.
Chapter 2: Getting Started 25
2.5 How Octave Reports Errors
Octave reports two kinds of errors for invalid programs.
A parse error occurs if Octave cannot understand something you have typed. For example,
if you misspell a keyword,
octave:13> functon y = f (x) y = x^2; endfunction
Octave will respond immediately with a message like this:
parse error:
functon y = f (x) y = x^2; endfunction
^
For most parse errors, Octave uses a caret (‘^’) to mark the point on the line where it
was unable to make sense of your input. In this case, Octave generated an error message
because the keyword function was misspelled. Instead of seeing ‘function f’, Octave saw
two consecutive variable names, which is invalid in this context. It marked the error at y
because the first name by itself was accepted as valid input.
Another class of error message occurs at evaluation time. These errors are called runtime
errors, or sometimes evaluation errors because they occur when your program is being
run, or evaluated. For example, if after correcting the mistake in the previous function
definition, you type
octave:13> f ()
Octave will respond with
error: ‘x’ undefined near line 1 column 24
error: evaluating expression near line 1, column 24
error: evaluating assignment expression near line 1, column 22
error: called from ‘f’
This error message has several parts, and gives you quite a bit of information to help you
locate the source of the error. The messages are generated from the point of the innermost
error, and provide a traceback of enclosing expressions and function calls.
In the example above, the first line indicates that a variable named ‘x’ was found to be
undefined near line 1 and column 24 of some function or expression. For errors occurring
within functions, lines are counted from the beginning of the file containing the function
definition. For errors occurring at the top level, the line number indicates the input line
number, which is usually displayed in the prompt string.
The second and third lines in the example indicate that the error occurred within an
assignment expression, and the last line of the error message indicates that the error occurred
within the function f. If the function f had been called from another function, for example,
g, the list of errors would have ended with one more line:
error: called from ‘g’
These lists of function calls usually make it fairly easy to trace the path your program
took before the error occurred, and to correct the error before trying again.
26 GNU Octave
2.6 Executable Octave Programs
Once you have learned Octave, you may want to write self-contained Octave scripts,
using the ‘#!’ script mechanism. You can do this on GNU systems and on many Unix
systems1
For example, you could create a text file named ‘hello’, containing the following lines:
#! octave-interpreter-name -qf
# a sample Octave program
printf ("Hello, world!\n");
(where octave-interpreter-name should be replaced with the full file name for your Octave
binary). After making this file executable (with the chmod command), you can simply type:
hello
at the shell, and the system will arrange to run Octave as if you had typed:
octave hello
The line beginning with ‘#!’ lists the full file name of an interpreter to be run, and an
optional initial command line argument to pass to that interpreter. The operating system
then runs the interpreter with the given argument and the full argument list of the executed
program. The first argument in the list is the full file name of the Octave program. The
rest of the argument list will either be options to Octave, or data files, or both. The ‘-qf’
option is usually specified in stand-alone Octave programs to prevent them from printing
the normal startup message, and to keep them from behaving differently depending on
the contents of a particular user’s ‘~/.octaverc’ file. See Section 2.1 [Invoking Octave],
page 13. Note that some operating systems may place a limit on the number of characters
that are recognized after ‘#!’.
Self-contained Octave scripts are useful when you want to write a program which users
can invoke without knowing that the program is written in the Octave language.
If you invoke an executable Octave script with command line arguments, the arguments
are available in the built-in variable argv. See Section 2.1.1 [Command Line Options],
page 13. For example, the following program will reproduce the command line that is used
to execute it.
#! /bin/octave -qf
printf ("%s", program_name);
for i = 1:nargin
printf (" %s", argv(i,:));
endfor
printf ("\n");
2.7 Comments in Octave Programs
A comment is some text that is included in a program for the sake of human readers, and
that is not really part of the program. Comments can explain what the program does, and
how it works. Nearly all programming languages have provisions for comments, because
programs are typically hard to understand without them.
1
The ‘#!’ mechanism works on Unix systems derived from Berkeley Unix, System V Release 4, and some
System V Release 3 systems.
Chapter 2: Getting Started 27
In the Octave language, a comment starts with either the sharp sign character, ‘#’, or
the percent symbol ‘%’ and continues to the end of the line. The Octave interpreter ignores
the rest of a line following a sharp sign or percent symbol. For example, we could have put
the following into the function f:
function xdot = f (x, t)
# usage: f (x, t)
#
# This function defines the right hand
# side functions for a set of nonlinear
# differential equations.
r = 0.25;
...
endfunction
The help command (see Section 2.3 [Getting Help], page 17) is able to find the first
block of comments in a function (even those that are composed directly on the command
line). This means that users of Octave can use the same commands to get help for built-in
functions, and for functions that you have defined. For example, after defining the function
f above, the command help f produces the output
usage: f (x, t)
This function defines the right hand
side functions for a set of nonlinear
differential equations.
Although it is possible to put comment lines into keyboard-composed throw-away Octave
programs, it usually isn’t very useful, because the purpose of a comment is to help you or
another person understand the program at a later time.
28 GNU Octave
Chapter 3: Data Types 29
3 Data Types
All versions of Octave include a number of built-in data types, including real and complex
scalars and matrices, character strings, and a data structure type.
It is also possible to define new specialized data types by writing a small amount of C++
code. On some systems, new data types can be loaded dynamically while Octave is running,
so it is not necessary to recompile all of Octave just to add a new type. See Section 13.8
[Dynamically Linked Functions], page 101, for more information about Octave’s dynamic
linking capabilities. Section 3.2 [User-defined Data Types], page 30 describes what you
must do to define a new data type for Octave.
Built-in Functiontypeinfo (expr)
Return the type of the expression expr, as a string. If EXPR is omitted, return an
array of strings containing all the currently installed data types.
3.1 Built-in Data Types
The standard built-in data types are real and complex scalars and matrices, ranges,
character strings, and a data structure type. Additional built-in data types may be added
in future versions. If you need a specialized data type that is not currently provided as a
built-in type, you are encouraged to write your own user-defined data type and contribute
it for distribution in a future release of Octave.
3.1.1 Numeric Objects
Octave’s built-in numeric objects include real and complex scalars and matrices. All
built-in numeric data is currently stored as double precision numbers. On systems that use
the IEEE floating point format, values in the range of approximately 2.2251 × 10−308
to
1.7977 × 10308
can be stored, and the relative precision is approximately 2.2204 × 10−16
.
The exact values are given by the variables realmin, realmax, and eps, respectively.
Matrix objects can be of any size, and can be dynamically reshaped and resized. It is
easy to extract individual rows, columns, or submatrices using a variety of powerful indexing
features. See Section 10.1 [Index Expressions], page 63.
See Chapter 4 [Numeric Data Types], page 31, for more information.
3.1.2 String Objects
A character string in Octave consists of a sequence of characters enclosed in either
double-quote or single-quote marks. Internally, Octave currently stores strings as matrices
of characters. All the indexing operations that work for matrix objects also work for strings.
See Chapter 5 [Strings], page 37, for more information.
3.1.3 Data Structure Objects
Octave’s data structure type can help you to organize related objects of different types.
The current implementation uses an associative array with indices limited to strings, but
the syntax is more like C-style structures.
See Chapter 6 [Data Structures], page 45, for more information.
30 GNU Octave
3.2 User-defined Data Types
Someday I hope to expand this to include a complete description of Octave’s mechanism
for managing user-defined data types. Until this feature is documented here, you will have
to make do by reading the code in the ‘ov.h’, ‘ops.h’, and related files from Octave’s ‘src’
directory.
3.3 Object Sizes
The following functions allow you to determine the size of a variable or expression. These
functions are defined for all objects. They return −1 when the operation doesn’t make sense.
For example, Octave’s data structure type doesn’t have rows or columns, so the rows and
columns functions return −1 for structure arguments.
Function Filecolumns (a)
Return the number of columns of a.
Function Filerows (a)
Return the number of rows of a.
Built-in Functionlength (a)
Return the ‘lenghth’ of the object a. For matrix objects, the length is the number
of rows or columns, whichever is greater (this odd definition is used for compatibility
with Matlab).
Built-in Functionsize (a, n)
Return the number rows and columns of a.
With one input argument and one output argument, the result is returned in a 2
element row vector. If there are two output arguments, the number of rows is assigned
to the first, and the number of columns to the second. For example,
size ([1, 2; 3, 4; 5, 6])
⇒ [ 3, 2 ]
[nr, nc] = size ([1, 2; 3, 4; 5, 6])
⇒ nr = 3
⇒ nc = 2
If given a second argument of either 1 or 2, size will return only the row or column
dimension. For example
size ([1, 2; 3, 4; 5, 6], 2)
⇒ 2
returns the number of columns in the given matrix.
Built-in Functionisempty (a)
Return 1 if a is an empty matrix (either the number of rows, or the number of columns,
or both are zero). Otherwise, return 0.
Chapter 4: Numeric Data Types 31
4 Numeric Data Types
A numeric constant may be a scalar, a vector, or a matrix, and it may contain complex
values.
The simplest form of a numeric constant, a scalar, is a single number that can be an
integer, a decimal fraction, a number in scientific (exponential) notation, or a complex
number. Note that all numeric constants are represented within Octave in double-precision
floating point format (complex constants are stored as pairs of double-precision floating
point values). Here are some examples of real-valued numeric constants, which all have the
same value:
105
1.05e+2
1050e-1
To specify complex constants, you can write an expression of the form
3 + 4i
3.0 + 4.0i
0.3e1 + 40e-1i
all of which are equivalent. The letter ‘i’ in the previous example stands for the pure
imaginary constant, defined as
√
−1.
For Octave to recognize a value as the imaginary part of a complex constant, a space
must not appear between the number and the ‘i’. If it does, Octave will print an error
message, like this:
octave:13> 3 + 4 i
parse error:
3 + 4 i
^
You may also use ‘j’, ‘I’, or ‘J’ in place of the ‘i’ above. All four forms are equivalent.
4.1 Matrices
It is easy to define a matrix of values in Octave. The size of the matrix is determined
automatically, so it is not necessary to explicitly state the dimensions. The expression
a = [1, 2; 3, 4]
results in the matrix
a =
1 2
3 4
Elements of a matrix may be arbitrary expressions, provided that the dimensions all
make sense when combining the various pieces. For example, given the above matrix, the
expression
[ a, a ]
produces the matrix
32 GNU Octave
ans =
1 2 1 2
3 4 3 4
but the expression
[ a, 1 ]
produces the error
error: number of rows must match near line 13, column 6
(assuming that this expression was entered as the first thing on line 13, of course).
Inside the square brackets that delimit a matrix expression, Octave looks at the surrounding
context to determine whether spaces and newline characters should be converted
into element and row separators, or simply ignored, so commands like
[ linspace (1, 2) ]
and
a = [ 1 2
3 4 ]
will work. However, some possible sources of confusion remain. For example, in the expres-
sion
[ 1 - 1 ]
the ‘-’ is treated as a binary operator and the result is the scalar 0, but in the expression
[ 1 -1 ]
the ‘-’ is treated as a unary operator and the result is the vector [ 1, -1 ].
Given a = 1, the expression
[ 1 a’ ]
results in the single quote character ‘’’ being treated as a transpose operator and the result
is the vector [ 1, 1 ], but the expression
[ 1 a ’ ]
produces the error message
error: unterminated string constant
because to not do so would make it impossible to correctly parse the valid expression
[ a ’foo’ ]
For clarity, it is probably best to always use commas and semicolons to separate matrix
elements and rows. It is possible to enforce this style by setting the built-in variable
whitespace_in_literal_matrix to "ignore".
Built-in Variablewhitespace in literal matrix
Control auto-insertion of commas and semicolons in literal matrices.
Built-in Variablewarn separator insert
Print warning if commas or semicolons might be inserted automatically in literal
matrices.
Chapter 4: Numeric Data Types 33
When you type a matrix or the name of a variable whose value is a matrix, Octave
responds by printing the matrix in with neatly aligned rows and columns. If the rows of
the matrix are too large to fit on the screen, Octave splits the matrix and displays a header
before each section to indicate which columns are being displayed. You can use the following
variables to control the format of the output.
Built-in Variableoutput max field width
This variable specifies the maximum width of a numeric output field. The default
value is 10.
Built-in Variableoutput precision
This variable specifies the minimum number of significant figures to display for numeric
output. The default value is 5.
It is possible to achieve a wide range of output styles by using different values of output_
precision and output_max_field_width. Reasonable combinations can be set using the
format function. See Section 15.1 [Basic Input and Output], page 110.
Built-in Variablesplit long rows
For large matrices, Octave may not be able to display all the columns of a given row
on one line of your screen. This can result in missing information or output that
is nearly impossible to decipher, depending on whether your terminal truncates or
wraps long lines.
If the value of split_long_rows is nonzero, Octave will display the matrix in a series
of smaller pieces, each of which can fit within the limits of your terminal width. Each
set of rows is labeled so that you can easily see which columns are currently being
displayed. For example:
octave:13> rand (2,10)
ans =
Columns 1 through 6:
0.75883 0.93290 0.40064 0.43818 0.94958 0.16467
0.75697 0.51942 0.40031 0.61784 0.92309 0.40201
Columns 7 through 10:
0.90174 0.11854 0.72313 0.73326
0.44672 0.94303 0.56564 0.82150
The default value of split_long_rows is nonzero.
Octave automatically switches to scientific notation when values become very large or
very small. This guarantees that you will see several significant figures for every value in
a matrix. If you would prefer to see all values in a matrix printed in a fixed point format,
you can set the built-in variable fixed_point_format to a nonzero value. But doing so is
not recommended, because it can produce output that can easily be misinterpreted.
34 GNU Octave
Built-in Variablefixed point format
If the value of this variable is nonzero, Octave will scale all values in a matrix so that
the largest may be written with one leading digit. The scaling factor is printed on
the first line of output. For example,
octave:1> logspace (1, 7, 5)’
ans =
1.0e+07 *
0.00000
0.00003
0.00100
0.03162
1.00000
Notice that first value appears to be zero when it is actually 1. For this reason, you
should be careful when setting fixed_point_format to a nonzero value.
The default value of fixed_point_format is 0.
4.1.1 Empty Matrices
A matrix may have one or both dimensions zero, and operations on empty matrices are
handled as described by Carl de Boor in An Empty Exercise, SIGNUM, Volume 25, pages
2–6, 1990 and C. N. Nett and W. M. Haddad, in A System-Theoretic Appropriate Realization
of the Empty Matrix Concept, IEEE Transactions on Automatic Control, Volume
38, Number 5, May 1993. Briefly, given a scalar s, an m × n matrix Mm×n, and an m × n
empty matrix [ ]m×n (with either one or both dimensions equal to zero), the following are
true:
s · [ ]m×n = [ ]m×n · s = [ ]m×n
[ ]m×n + [ ]m×n = [ ]m×n
[ ]0×m · Mm×n = [ ]0×n
Mm×n · [ ]n×0 = [ ]m×0
[ ]m×0 · [ ]0×n = 0m×n
By default, dimensions of the empty matrix are printed along with the empty matrix
symbol, ‘[]’. The built-in variable print_empty_dimensions controls this behavior.
Built-in Variableprint empty dimensions
If the value of print_empty_dimensions is nonzero, the dimensions of empty matrices
are printed along with the empty matrix symbol, ‘[]’. For example, the expression
zeros (3, 0)
will print
ans = [](3x0)
Empty matrices may also be used in assignment statements as a convenient way to delete
rows or columns of matrices. See Section 10.6 [Assignment Expressions], page 72.
Chapter 4: Numeric Data Types 35
Octave will normally issue a warning if it finds an empty matrix in the list of elements
that make up another matrix. You can use the variable empty_list_elements_ok to suppress
the warning or to treat it as an error.
Built-in Variableempty list elements ok
This variable controls whether Octave ignores empty matrices in a matrix list.
For example, if the value of empty_list_elements_ok is nonzero, Octave will ignore
the empty matrices in the expression
a = [1, [], 3, [], 5]
and the variable a will be assigned the value [ 1, 3, 5 ].
The default value is "warn".
When Octave parses a matrix expression, it examines the elements of the list to determine
whether they are all constants. If they are, it replaces the list with a single matrix constant.
Built-in Variablepropagate empty matrices
If the value of propagate_empty_matrices is nonzero, functions like inverse and
svd will return an empty matrix if they are given one as an argument. The default
value is 1.
4.2 Ranges
A range is a convenient way to write a row vector with evenly spaced elements. A range
expression is defined by the value of the first element in the range, an optional value for the
increment between elements, and a maximum value which the elements of the range will
not exceed. The base, increment, and limit are separated by colons (the ‘:’ character) and
may contain any arithmetic expressions and function calls. If the increment is omitted, it
is assumed to be 1. For example, the range
1 : 5
defines the set of values ‘[ 1, 2, 3, 4, 5 ]’, and the range
1 : 3 : 5
defines the set of values ‘[ 1, 4 ]’.
Although a range constant specifies a row vector, Octave does not convert range constants
to vectors unless it is necessary to do so. This allows you to write a constant like ‘1
: 10000’ without using 80,000 bytes of storage on a typical 32-bit workstation.
Note that the upper (or lower, if the increment is negative) bound on the range is not
always included in the set of values, and that ranges defined by floating point values can
produce surprising results because Octave uses floating point arithmetic to compute the
values in the range. If it is important to include the endpoints of a range and the number of
elements is known, you should use the linspace function instead (see Section 17.3 [Special
Utility Matrices], page 148).
When Octave parses a range expression, it examines the elements of the expression to
determine whether they are all constants. If they are, it replaces the range expression with
a single range constant.
36 GNU Octave
4.3 Logical Values
Built-in Variabletrue
Logical true value.
Built-in Variablefalse
Logical false value.
4.4 Predicates for Numeric Objects
Built-in Functionisnumeric (x)
Return nonzero if x is a numeric object.
Built-in Functionisreal (x)
Return true if x is a real-valued numeric object.
Built-in Functionis complex (x)
Return true if x is a complex-valued numeric object.
Built-in Functionis matrix (a)
Return 1 if a is a matrix. Otherwise, return 0.
Function Fileis vector (a)
Return 1 if a is a vector. Otherwise, return 0.
Function Fileis scalar (a)
Return 1 if a is a scalar. Otherwise, return 0.
Function Fileis square (x)
If x is a square matrix, then return the dimension of x. Otherwise, return 0.
Function Fileis symmetric (x, tol)
If x is symmetric within the tolerance specified by tol, then return the dimension of x.
Otherwise, return 0. If tol is omitted, use a tolerance equal to the machine precision.
Built-in Functiois bool (x)
Return true if x is a boolean object.
Chapter 5: Strings 37
5 Strings
A string constant consists of a sequence of characters enclosed in either double-quote or
single-quote marks. For example, both of the following expressions
"parrot"
’parrot’
represent the string whose contents are ‘parrot’. Strings in Octave can be of any length.
Since the single-quote mark is also used for the transpose operator (see Section 10.3
[Arithmetic Ops], page 67) but double-quote marks have no other purpose in Octave, it is
best to use double-quote marks to denote strings.
Some characters cannot be included literally in a string constant. You represent them
instead with escape sequences, which are character sequences beginning with a backslash
(‘\’).
One use of an escape sequence is to include a double-quote (single-quote) character in
a string constant that has been defined using double-quote (single-quote) marks. Since a
plain double-quote would end the string, you must use ‘\"’ to represent a single doublequote
character as a part of the string. The backslash character itself is another character
that cannot be included normally. You must write ‘\\’ to put one backslash in the string.
Thus, the string whose contents are the two characters ‘"\’ may be written "\"\\" or ’"\\’.
Similarly, the string whose contents are the two characters ‘’\’ may be written ’\’\\’ or
"’\\".
Another use of backslash is to represent unprintable characters such as newline. While
there is nothing to stop you from writing most of these characters directly in a string
constant, they may look ugly.
Here is a table of all the escape sequences used in Octave. They are the same as those
used in the C programming language.
\\ Represents a literal backslash, ‘\’.
\" Represents a literal double-quote character, ‘"’.
\’ Represents a literal single-quote character, ‘’’.
\a Represents the “alert” character, control-g, ASCII code 7.
\b Represents a backspace, control-h, ASCII code 8.
\f Represents a formfeed, control-l, ASCII code 12.
\n Represents a newline, control-j, ASCII code 10.
\r Represents a carriage return, control-m, ASCII code 13.
\t Represents a horizontal tab, control-i, ASCII code 9.
\v Represents a vertical tab, control-k, ASCII code 11.
Strings may be concatenated using the notation for defining matrices. For example, the
expression
[ "foo" , "bar" , "baz" ]
produces the string whose contents are ‘foobarbaz’. See Chapter 4 [Numeric Data Types],
page 31, for more information about creating matrices.
38 GNU Octave
5.1 Creating Strings
Function Fileblanks (n)
Return a string of n blanks.
Function Fileint2str (n)
Function Filenum2str (x)
Convert a number to a string. These functions are not very flexible, but are provided
for compatibility with Matlab. For better control over the results, use sprintf (see
Section 15.2.4 [Formatted Output], page 118).
Function Filecom2str (zz, flg)
convert complex number to a string Inputs
zz complex number
flg format flag 0 (default): -1, 0, 1, 1i, 1 + 0.5i 1 (for use with zpout): -1, 0,
+ 1, + 1i, + 1 + 0.5i
Built-in Functionsetstr (x)
Convert a matrix to a string. Each element of the matrix is converted to the corresponding
ASCII character. For example,
setstr ([97, 98, 99])
⇒ "abc"
Function Filestrcat (s1, s2, ...)
Return a string containing all the arguments concatenated. For example,
s = [ "ab"; "cde" ];
strcat (s, s, s)
⇒ "ab ab ab "
"cdecdecde"
Built-in Variablestring fill char
The value of this variable is used to pad all strings in a string matrix to the same
length. It should be a single character. The default value is " " (a single space). For
example,
string_fill_char = "X";
[ "these"; "are"; "strings" ]
⇒ "theseXX"
"areXXXX"
"strings"
Chapter 5: Strings 39
Function Filestr2mat (s 1, ..., s n)
Return a matrix containing the strings s 1, . . ., s n as its rows. Each string is padded
with blanks in order to form a valid matrix.
Note: This function is modelled after Matlab. In Octave, you can create a matrix
of strings by [s 1; ...; s n] even if the strings are not all the same length.
Built-in Functionisstr (a)
Return 1 if a is a string. Otherwise, return 0.
5.2 Searching and Replacing
Function Filedeblank (s)
Removes the trailing blanks from the string s.
Function Filefindstr (s, t, overlap)
Return the vector of all positions in the longer of the two strings s and t where
an occurrence of the shorter of the two starts. If the optional argument overlap is
nonzero, the returned vector can include overlapping positions (this is the default).
For example,
findstr ("ababab", "a")
⇒ [ 1, 3, 5 ]
findstr ("abababa", "aba", 0)
⇒ [ 1, 5 ]
Function Fileindex (s, t)
Return the position of the first occurrence of the string t in the string s, or 0 if no
occurrence is found. For example,
index ("Teststring", "t")
⇒ 4
Note: This function does not work for arrays of strings.
Function Filerindex (s, t)
Return the position of the last occurrence of the string t in the string s, or 0 if no
occurrence is found. For example,
rindex ("Teststring", "t")
⇒ 6
Note: This function does not work for arrays of strings.
Function Filesplit (s, t)
Divides the string s into pieces separated by t, returning the result in a string array
(padded with blanks to form a valid matrix). For example,
split ("Test string", "t")
⇒ "Tes "
" s "
"ring"
40 GNU Octave
Function Filestrcmp (s1, s2)
Compares two strings, returning 1 if they are the same, and 0 otherwise.
Note: For compatibility with Matlab, Octave’s strcmp function returns 1 if the
strings are equal, and 0 otherwise. This is just the opposite of the corresponding C
library function.
Function Filestrrep (s, x, y)
Replaces all occurrences of the substring x of the string s with the string y. For
example,
strrep ("This is a test string", "is", "&%$")
⇒ "Th&%$ &%$ a test string"
Function Filesubstr (s, beg, len)
Return the substring of s which starts at character number beg and is len characters
long.
If OFFSET is negative, extraction starts that far from the end of the string. If LEN
is omitted, the substring extends to the end of S.
For example,
substr ("This is a test string", 6, 9)
⇒ "is a test"
Note: This function is patterned after AWK. You can get the same result
by s (beg : (beg + len - 1)).
5.3 String Conversions
Function Filebin2dec (s)
Return the decimal number corresponding to the binary number represented by the
string s. For example,
bin2dec ("1110")
⇒ 14
Function Filedec2bin (n)
Return a binary number corresponding the nonnegative decimal number n, as a string
of ones and zeros. For example,
dec2bin (14)
⇒ "1110"
Function Filedec2hex (n)
Return the hexadecimal number corresponding to the nonnegative decimal number
n, as a string. For example,
dec2hex (2748)
⇒ "abc"
Chapter 5: Strings 41
Function Filehex2dec (s)
Return the decimal number corresponding to the hexadecimal number stored in the
string s. For example,
hex2dec ("12B")
⇒ 299
hex2dec ("12b")
⇒ 299
Function Filestr2num (s)
Convert the string s to a number.
Mapping Functiontoascii (s)
Return ASCII representation of s in a matrix. For example,
toascii ("ASCII")
⇒ [ 65, 83, 67, 73, 73 ]
Mapping Functiontolower (s)
Return a copy of the string s, with each upper-case character replaced by the corresponding
lower-case one; nonalphabetic characters are left unchanged. For example,
tolower ("MiXeD cAsE 123")
⇒ "mixed case 123"
Built-in Functiontoupper (s)
Return a copy of the string s, with each lower-case character replaced by the corresponding
upper-case one; nonalphabetic characters are left unchanged. For example,
toupper ("MiXeD cAsE 123")
⇒ "MIXED CASE 123"
Built-in Functiondo string escapes (string)
Convert special characters in string to their escaped forms.
Built-in Functionundo string escapes (s)
Converts special characters in strings back to their escaped forms. For example, the
expression
bell = "\a";
assigns the value of the alert character (control-g, ASCII code 7) to the string variable
bell. If this string is printed, the system will ring the terminal bell (if it is possible).
This is normally the desired outcome. However, sometimes it is useful to be able to
print the original representation of the string, with the special characters replaced by
their escape sequences. For example,
octave:13> undo_string_escapes (bell)
ans = \a
replaces the unprintable alert character with its printable representation.
42 GNU Octave
Built-in Variableimplicit num to str ok
If the value of implicit_num_to_str_ok is nonzero, implicit conversions of numbers
to their ASCII character equivalents are allowed when strings are constructed using
a mixture of strings and numbers in matrix notation. Otherwise, an error message is
printed and control is returned to the top level. The default value is 0. For example,
[ "f", 111, 111 ]
⇒ "foo"
Built-in Variableimplicit str to num ok
If the value of implicit_str_to_num_ok is nonzero, implicit conversions of strings to
their numeric ASCII equivalents are allowed. Otherwise, an error message is printed
and control is returned to the top level. The default value is 0.
Built-in Variablewarn single quote string
Print warning if a signle quote character is used to introduce a string constant.
5.4 Character Class Functions
Octave also provides the following character class test functions patterned after the
functions in the standard C library. They all operate on string arrays and return matrices
of zeros and ones. Elements that are nonzero indicate that the condition was true for the
corresponding character in the string array. For example,
isalpha ("!Q@WERT^Y&")
⇒ [ 0, 1, 0, 1, 1, 1, 1, 0, 1, 0 ]
Mapping Functionisalnum (s)
Return 1 for characters that are letters or digits (isalpha (a) or isdigit (a) is
true).
Mapping Functionisalpha (s)
Return true for characters that are letters (isupper (a) or islower () is true).
Mapping Functionisascii (s)
Return 1 for characters that are ASCII (in the range 0 to 127 decimal).
Mapping Functioniscntrl (s)
Return 1 for control characters.
Mapping Functionisdigit (s)
Return 1 for characters that are decimal digits.
Mapping Functionisgraph (s)
Return 1 for printable characters (but not the space character).
Chapter 5: Strings 43
Mapping Functionislower (s)
Return 1 for characters that are lower case letters.
Mapping Functionisprint (s)
Return 1 for printable characters (including the space character).
Mapping Functionispunct (s)
Return 1 for punctuation characters.
Mapping Functionisspace (s)
Return 1 for whitespace characters (space, formfeed, newline, carriage return, tab,
and vertical tab).
Mapping Functionisupper (s)
Return 1 for upper case letters.
Mapping Functionisxdigit (s)
Return 1 for characters that are hexadecimal digits.
44 GNU Octave
Chapter 6: Data Structures 45
6 Data Structures
Octave includes support for organizing data in structures. The current implementation
uses an associative array with indices limited to strings, but the syntax is more like C-style
structures. Here are some examples of using data structures in Octave.
Elements of structures can be of any value type. For example, the three expressions
x.a = 1
x.b = [1, 2; 3, 4]
x.c = "string"
create a structure with three elements. To print the value of the structure, you can type its
name, just as for any other variable:
octave:2> x
x =
{
a = 1
b =
1 2
3 4
c = string
}
Note that Octave may print the elements in any order.
Structures may be copied.
octave:1> y = x
y =
{
a = 1
b =
1 2
3 4
c = string
}
Since structures are themselves values, structure elements may reference other structures.
The following statements change the value of the element b of the structure x to be a data
structure containing the single element d, which has a value of 3.
46 GNU Octave
octave:1> x.b.d = 3
x.b.d = 3
octave:2> x.b
ans =
{
d = 3
}
octave:3> x
x =
{
a = 1
b =
{
d = 3
}
c = string
}
Note that when Octave prints the value of a structure that contains other structures,
only a few levels are displayed. For example,
octave:1> a.b.c.d.e = 1;
octave:2> a
a =
{
b =
{
c = <structure>
}
}
This prevents long and confusing output from large deeply nested structures.
Built-in Variablestruct levels to print
You can tell Octave how many structure levels to display by setting the built-in
variable struct_levels_to_print. The default value is 2.
Functions can return structures. For example, the following function separates the real
and complex parts of a matrix and stores them in two elements of the same structure
variable.
octave:1> function y = f (x)
> y.re = real (x);
> y.im = imag (x);
> endfunction
When called with a complex-valued argument, f returns the data structure containing
the real and imaginary parts of the original function argument.
Chapter 6: Data Structures 47
octave:2> f (rand (2) + rand (2) * I);
ans =
{
im =
0.26475 0.14828
0.18436 0.83669
re =
0.040239 0.242160
0.238081 0.402523
}
Function return lists can include structure elements, and they may be indexed like any
other variable. For example,
octave:1> [ x.u, x.s(2:3,2:3), x.v ] = svd ([1, 2; 3, 4])
x.u =
-0.40455 -0.91451
-0.91451 0.40455
x.s =
0.00000 0.00000 0.00000
0.00000 5.46499 0.00000
0.00000 0.00000 0.36597
x.v =
-0.57605 0.81742
-0.81742 -0.57605
It is also possible to cycle through all the elements of a structure in a loop, using a
special form of the for statement (see Section 12.5 [The for Statement], page 84)
The following functions are available to give you information about structures.
Built-in Functionis struct (expr)
Return 1 if the value of the expression expr is a structure.
Built-in Functionstruct contains (expr, name)
Return 1 if the expression expr is a structure and it includes an element named name.
The first argument must be a structure and the second must be a string.
Built-in Functionstruct elements (struct)
Return a list of strings naming the elements of the structure struct. It is an error to
call struct_elements with an argument that is not a structure.
48 GNU Octave
Chapter 7: Containers 49
7 Containers
7.1 Lists
Built-in Functionlist (a1, a2, ...)
Create a new list with elements given by the arguments a1, a2, . . ..
Built-in Functionnth (list, n)
Return the n-th element of list.
Built-in Functionappend (list, a1, a2, ...)
Return a new list created by appending a1, a1, . . ., to list. If any of the arguments
to be appended is a list, its elements are appended individually. For example,
x = list (1, 2);
y = list (3, 4);
append (x, y);
results in the list containing the four elements ‘(1 2 3 4)’, not a list containing the
three elements ‘(1 2 (3 4))’.
Built-in Functionreverse (list)
Return a new list created by reversing the elements of list.
Built-in Functionsplice (list 1, offset, length, list 2)
Replace length elements of list 1 beginning at offset with the contents of list 2 (if
any). If length is omitted, all elements from offset to the end of list 1 are replaced.
As a special case, if offset is one greater than the length of list 1 and length is 0,
splice is equivalent to append (list 1, list 2).
Built-in Functionis list (x)
Return nonzero if x is a list.
7.2 Cell Arrays
Built-in Functioncell (x)
Built-in Functioncell (n, m)
Create a new cell array object. If invoked with a single scalar argument, cell returns
a square cell array with the dimension specified. If you supply two scalar arguments,
cell takes them to be the number of rows and columns. If given a vector with two
elements, cell uses the values of the elements as the number of rows and columns,
respectively.
Built-in Functioniscell (x)
Return true if x is a cell array object. Otherwise, return false.
50 GNU Octave
Chapter 8: I/O Streams 51
8 I/O Streams
Built-in Functionis stream (x)
Return true if x is a stream object. Otherwise, return false.
52 GNU Octave
Chapter 9: Variables 53
9 Variables
Variables let you give names to values and refer to them later. You have already seen
variables in many of the examples. The name of a variable must be a sequence of letters,
digits and underscores, but it may not begin with a digit. Octave does not enforce a limit
on the length of variable names, but it is seldom useful to have variables with names longer
than about 30 characters. The following are all valid variable names
x
x15
__foo_bar_baz__
fucnrdthsucngtagdjb
However, names like __foo_bar_baz__ that begin and end with two underscores are understood
to be reserved for internal use by Octave. You should not use them in code you write,
except to access Octave’s documented internal variables and built-in symbolic constants.
Case is significant in variable names. The symbols a and A are distinct variables.
A variable name is a valid expression by itself. It represents the variable’s current value.
Variables are given new values with assignment operators and increment operators. See
Section 10.6 [Assignment Expressions], page 72.
A number of variables have special built-in meanings. For example, ans holds the current
working directory, and pi names the ratio of the circumference of a circle to its diameter.
See Section 9.3 [Summary of Built-in Variables], page 56, for a list of all the predefined
variables. Some of these built-in symbols are constants and may not be changed. Others
can be used and assigned just like all other variables, but their values are also used or
changed automatically by Octave.
Variables in Octave do not have fixed types, so it is possible to first store a numeric
value in a variable and then to later use the same name to hold a string value in the same
program. Variables may not be used before they have been given a value. Doing so results
in an error.
9.1 Global Variables
A variable that has been declared global may be accessed from within a function body
without having to pass it as a formal parameter.
A variable may be declared global using a global declaration statement. The following
statements are all global declarations.
global a
global b = 2
global c = 3, d, e = 5
It is necessary declare a variable as global within a function body in order to access it.
For example,
global x
function f ()
x = 1;
endfunction
f ()
54 GNU Octave
does not set the value of the global variable x to 1. In order to change the value of the
global variable x, you must also declare it to be global within the function body, like this
function f ()
global x;
x = 1;
endfunction
Passing a global variable in a function parameter list will make a local copy and not
modify the global value. For example, given the function
function f (x)
x = 0
endfunction
and the definition of x as a global variable at the top level,
global x = 13
the expression
f (x)
will display the value of x from inside the function as 0, but the value of x at the top level
remains unchanged, because the function works with a copy of its argument.
initialize global variablesIf the value of this variable is nonzero, global variables are
given
the default initial value specified by the built-in variable default_global_variable_
value.
Built-in Variabledefault global variable value
The default for value for otherwise uninitialized global variables. Only used if the
variable initialize global variables is nonzero. If initialize_global_variables is
nonzero, the value of default_glbaol_variable_value is used as the initial value
of global variables that are not explicitly initialized. for example,
initialize_global_variables = 1;
default_global_variable_value = 13;
global foo;
foo
⇒ 13
the variable default_global_variable_value is initially undefined.
Built-in Functionis global (name)
Return 1 if name is globally visible. Otherwise, return 0. For example,
global x
is_global ("x")
⇒ 1
Chapter 9: Variables 55
9.2 Status of Variables
Commandclear [-x] pattern . . .
Delete the names matching the given patterns from the symbol table. The pattern
may contain the following special characters:
? Match any single character.
* Match zero or more characters.
[ list ] Match the list of characters specified by list. If the first character is !
or ^, match all characters except those specified by list. For example,
the pattern ‘[a-zA-Z]’ will match all lower and upper case alphabetic
characters.
For example, the command
clear foo b*r
clears the name foo and all names that begin with the letter b and end with the letter
r.
If clear is called without any arguments, all user-defined variables (local and global)
are cleared from the symbol table. If clear is called with at least one argument, only
the visible names matching the arguments are cleared. For example, suppose you
have defined a function foo, and then hidden it by performing the assignment foo
= 2. Executing the command clear foo once will clear the variable definition and
restore the definition of foo as a function. Executing clear foo a second time will
clear the function definition.
With -x, clear the variables that don’t match the patterns.
This command may not be used within a function body.
Commandwho options pattern . . .
Commandwhos options pattern . . .
List currently defined symbols matching the given patterns. The following are valid
options. They may be shortened to one character but may not be combined.
-all List all currently defined symbols.
-builtins
List built-in variables and functions. This includes all currently compiled
function files, but does not include all function files that are in the
LOADPATH.
-functions
List user-defined functions.
-long Print a long listing including the type and dimensions of any symbols.
The symbols in the first column of output indicate whether it is possible
to redefine the symbol, and whether it is possible for it to be cleared.
-variables
List user-defined variables.
56 GNU Octave
Valid patterns are the same as described for the clear command above. If no patterns
are supplied, all symbols from the given category are listed. By default, only user
defined functions and variables visible in the local scope are displayed.
The command whos is equivalent to who -long.
Built-in Functionexist (name)
Return 1 if the name exists as a variable, 2 if the name (after appending ‘.m’) is a
function file in the path, 3 if the name is a ‘.oct’ file in the path, 5 if the name is a
built-in function, or 6 is the name is a built-in constant. Otherwise, return 0.
This function also returns 2 if a regular file called name exists in Octave’s LOADPATH.
If you want information about other types of files, you should use some combination
of the functions file_in_path and stat instead.
Built-in Functiondocument (symbol, text)
Set the documentation string for symbol to text.
Commandtype options name . . .
Display the definition of each name that refers to a function.
Normally also displays if each name is user-defined or builtin; the -q option suppresses
this behaviour.
Currently, Octave can only display functions that can be compiled cleanly, because it
uses its internal representation of the function to recreate the program text.
Comments are not displayed because Octave’s parser currently discards them as it
converts the text of a function file to its internal representation. This problem may
be fixed in a future release.
Commandwhich name . . .
Display the type of each name. If name is defined from a function file, the full name
of the file is also displayed.
9.3 Summary of Built-in Variables
Here is a summary of all of Octave’s built-in variables along with cross references to
additional information and their default values. In the following table octave-home stands
for the root directory where all of Octave is installed (the default is ‘/usr/local’, version
stands for the Octave version number (for example, 2.1.x) and arch stands for the type of
system for which Octave was compiled (for example, i586-pc-linux-gnu).
DEFAULT_LOADPATH
See Section 13.6 [Function Files], page 98.
Default value: ".:octave-home/lib/version".
EDITOR See Section 2.4.5 [Commands For History], page 20.
Default value: "emacs".
Chapter 9: Variables 57
EXEC_PATH
See Section 33.3 [Controlling Subprocesses], page 283.
Default value: ":$PATH".
INFO_FILE
See Section 2.3 [Getting Help], page 17.
Default value: "octave-home/info/octave.info".
INFO_PROGRAM
See Section 2.3 [Getting Help], page 17.
Default value: "octave-home/libexec/octave/version/exec/arch/info".
LOADPATH See Section 13.6 [Function Files], page 98.
Default value: ":", which tells Octave to use the directories specified by the
built-in variable DEFAULT_LOADPATH.
OCTAVE_HOME
Default value: "/usr/local".
PAGER See Chapter 15 [Input and Output], page 109.
Default value: "less", or "more".
PS1 See Section 2.4.7 [Customizing the Prompt], page 23.
Default value: "\s:\#> ".
PS2 See Section 2.4.7 [Customizing the Prompt], page 23.
Default value: "> ".
PS4 See Section 2.4.7 [Customizing the Prompt], page 23.
Default value: "+ ".
automatic_replot
See Section 16.1 [Two-Dimensional Plotting], page 131.
Default value: 0.
beep_on_error
See Chapter 14 [Error Handling], page 107.
Default value: 0.
completion_append_char
See Section 2.4.4 [Commands For Completion], page 20.
Default value: " ".
default_eval_print_flag
See Chapter 11 [Evaluation], page 77.
Default value: 1.
default_return_value
See Section 13.2 [Multiple Return Values], page 93.
Default value: [].
58 GNU Octave
default_save_format
See Section 15.1.3 [Simple File I/O], page 113.
Default value: "ascii".
do_fortran_indexing
See Section 10.1 [Index Expressions], page 63.
Default value: 0.
crash_dumps_octave_core
See Section 15.1.3 [Simple File I/O], page 113.
Default value: 1.
define_all_return_values
See Section 13.2 [Multiple Return Values], page 93.
Default value: 0.
empty_list_elements_ok
See Section 4.1.1 [Empty Matrices], page 34.
Default value: "warn".
fixed_point_format
See Section 4.1 [Matrices], page 31.
Default value: 0.
gnuplot_binary
See Section 16.3 [Three-Dimensional Plotting], page 138.
Default value: "gnuplot".
history_file
See Section 2.4.5 [Commands For History], page 20.
Default value: "~/.octave_hist".
history_size
See Section 2.4.5 [Commands For History], page 20.
Default value: 1024.
ignore_function_time_stamp
See Section 13.6 [Function Files], page 98.
Default value: "system".
implicit_num_to_str_ok
See Section 5.3 [String Conversions], page 40.
Default value: 0.
implicit_str_to_num_ok
See Section 5.3 [String Conversions], page 40.
Default value: 0.
Chapter 9: Variables 59
max_recursion_depth
See Section 10.2.2 [Recursion], page 67.
Default value: 256.
ok_to_lose_imaginary_part
See Section 17.3 [Special Utility Matrices], page 148.
Default value: "warn".
output_max_field_width
See Section 4.1 [Matrices], page 31.
Default value: 10.
output_precision
See Section 4.1 [Matrices], page 31.
Default value: 5.
page_screen_output
See Chapter 15 [Input and Output], page 109.
Default value: 1.
prefer_column_vectors
See Section 10.1 [Index Expressions], page 63.
Default value: 1.
print_answer_id_name
See Section 15.1.1 [Terminal Output], page 110.
Default value: 1.
print_empty_dimensions
See Section 4.1.1 [Empty Matrices], page 34.
Default value: 1.
resize_on_range_error
See Section 10.1 [Index Expressions], page 63.
Default value: 1.
return_last_computed_value
See Section 13.5 [Returning From a Function], page 97.
Default value: 0.
save_precision
See Section 15.1.3 [Simple File I/O], page 113.
Default value: 17.
saving_history
See Section 2.4.5 [Commands For History], page 20.
Default value: 1.
60 GNU Octave
silent_functions
See Section 13.1 [Defining Functions], page 91.
Default value: 0.
split_long_rows
See Section 4.1 [Matrices], page 31.
Default value: 1.
struct_levels_to_print
See Chapter 6 [Data Structures], page 45.
Default value: 2.
suppress_verbose_help_message
See Section 2.3 [Getting Help], page 17.
Default value: 1.
treat_neg_dim_as_zero
See Section 17.3 [Special Utility Matrices], page 148.
Default value: 0.
warn_assign_as_truth_value
See Section 12.1 [The if Statement], page 79.
Default value: 1.
warn_comma_in_global_decl
See Section 9.1 [Global Variables], page 53.
Default value: 1.
warn_divide_by_zero
See Section 10.3 [Arithmetic Ops], page 67.
Default value: 1.
warn_function_name_clash
See Section 13.6 [Function Files], page 98.
Default value: 1.
warn_reload_forces_clear
See Section 13.8 [Dynamically Linked Functions], page 101.
Default value: 1.
warn_variable_switch_label
See Section 12.2 [The switch Statement], page 81.
Default value: 0.
whitespace_in_literal_matrix
See Section 4.1 [Matrices], page 31.
Default value: "".
Chapter 9: Variables 61
9.4 Defaults from the Environment
Octave uses the values of the following environment variables to set the default values
for the corresponding built-in variables. In addition, the values from the environment may
be overridden by command-line arguments. See Section 2.1.1 [Command Line Options],
page 13.
EDITOR See Section 2.4.5 [Commands For History], page 20.
Built-in variable: EDITOR.
OCTAVE_EXEC_PATH
See Section 33.3 [Controlling Subprocesses], page 283.
Built-in variable: EXEC_PATH. Command-line argument: --exec-path.
OCTAVE_PATH
See Section 13.6 [Function Files], page 98.
Built-in variable: LOADPATH. Command-line argument: --path.
OCTAVE_INFO_FILE
See Section 2.3 [Getting Help], page 17.
Built-in variable: INFO_FILE. Command-line argument: --info-file.
OCTAVE_INFO_PROGRAM
See Section 2.3 [Getting Help], page 17.
Built-in variable: INFO_PROGRAM. Command-line argument: --info-program.
OCTAVE_HISTSIZE
See Section 2.4.5 [Commands For History], page 20.
Built-in variable: history_size.
OCTAVE_HISTFILE
See Section 2.4.5 [Commands For History], page 20.
Built-in variable: history_file.
62 GNU Octave
Chapter 10: Expressions 63
10 Expressions
Expressions are the basic building block of statements in Octave. An expression evaluates
to a value, which you can print, test, store in a variable, pass to a function, or assign a new
value to a variable with an assignment operator.
An expression can serve as a statement on its own. Most other kinds of statements
contain one or more expressions which specify data to be operated on. As in other languages,
expressions in Octave include variables, array references, constants, and function calls, as
well as combinations of these with various operators.
10.1 Index Expressions
An index expression allows you to reference or extract selected elements of a matrix or
vector.
Indices may be scalars, vectors, ranges, or the special operator ‘:’, which may be used
to select entire rows or columns.
Vectors are indexed using a single expression. Matrices require two indices unless the
value of the built-in variable do_fortran_indexing is nonzero, in which case matrices may
also be indexed by a single expression.
Built-in Variabledo fortran indexing
If the value of do_fortran_indexing is nonzero, Octave allows you to select elements
of a two-dimensional matrix using a single index by treating the matrix as a single
vector created from the columns of the matrix. The default value is 0.
Given the matrix
a = [1, 2; 3, 4]
all of the following expressions are equivalent
a (1, [1, 2])
a (1, 1:2)
a (1, :)
and select the first row of the matrix.
A special form of indexing may be used to select elements of a matrix or vector. If
the indices are vectors made up of only ones and zeros, the result is a new matrix whose
elements correspond to the elements of the index vector that are equal to one. For example,
a = [1, 2; 3, 4];
a ([1, 0], :)
selects the first row of the matrix a.
This operation can be useful for selecting elements of a matrix based on some condition,
since the comparison operators return matrices of ones and zeros.
This special zero-one form of indexing leads to a conflict with the standard indexing
operation. For example, should the following statements
64 GNU Octave
a = [1, 2; 3, 4];
a ([1, 1], :)
return the original matrix, or the matrix formed by selecting the first row twice? Although
this conflict is not likely to arise very often in practice, you may select the behavior you
prefer by setting the built-in variable prefer_zero_one_indexing.
Built-in Variableprefer zero one indexing
If the value of prefer_zero_one_indexing is nonzero, Octave will perform zero-one
style indexing when there is a conflict with the normal indexing rules. See Section 10.1
[Index Expressions], page 63. For example, given a matrix
a = [1, 2, 3, 4]
with prefer_zero_one_indexing is set to nonzero, the expression
a ([1, 1, 1, 1])
results in the matrix [ 1, 2, 3, 4 ]. If the value of prefer_zero_one_indexing set
to 0, the result would be the matrix [ 1, 1, 1, 1 ].
In the first case, Octave is selecting each element corresponding to a ‘1’ in the index
vector. In the second, Octave is selecting the first element multiple times.
The default value for prefer_zero_one_indexing is 0.
Finally, indexing a scalar with a vector of ones can be used to create a vector the same
size as the index vector, with each element equal to the value of the original scalar. For
example, the following statements
a = 13;
a ([1, 1, 1, 1])
produce a vector whose four elements are all equal to 13.
Similarly, indexing a scalar with two vectors of ones can be used to create a matrix. For
example the following statements
a = 13;
a ([1, 1], [1, 1, 1])
create a 2 by 3 matrix with all elements equal to 13.
This is an obscure notation and should be avoided. It is better to use the function ones
to generate a matrix of the appropriate size whose elements are all one, and then to scale
it to produce the desired result. See Section 17.3 [Special Utility Matrices], page 148.
Built-in Variableprefer column vectors
If prefer_column_vectors is nonzero, operations like
for i = 1:10
a (i) = i;
endfor
(for a previously undefined) produce column vectors. Otherwise, row vectors are
preferred. The default value is 1.
If a variable is already defined to be a vector (a matrix with a single row or column),
the original orientation is respected, regardless of the value of prefer_column_
vectors.
Chapter 10: Expressions 65
Built-in Variableresize on range error
If the value of resize_on_range_error is nonzero, expressions like
for i = 1:10
a (i) = sqrt (i);
endfor
(for a previously undefined) result in the variable a being resized to be just large
enough to hold the new value. New elements that have not been given a value are
set to zero. If the value of resize_on_range_error is 0, an error message is printed
and control is returned to the top level. The default value is 1.
Note that it is quite inefficient to create a vector using a loop like the one shown in the
example above. In this particular case, it would have been much more efficient to use the
expression
a = sqrt (1:10);
thus avoiding the loop entirely. In cases where a loop is still required, or a number of values
must be combined to form a larger matrix, it is generally much faster to set the size of
the matrix first, and then insert elements using indexing commands. For example, given a
matrix a,
[nr, nc] = size (a);
x = zeros (nr, n * nc);
for i = 1:n
x(:,(i-1)*nc+1:i*nc) = a;
endfor
is considerably faster than
x = a;
for i = 1:n-1
x = [x, a];
endfor
particularly for large matrices because Octave does not have to repeatedly resize the result.
10.2 Calling Functions
A function is a name for a particular calculation. Because it has a name, you can ask
for it by name at any point in the program. For example, the function sqrt computes the
square root of a number.
A fixed set of functions are built-in, which means they are available in every Octave
program. The sqrt function is one of these. In addition, you can define your own functions.
See Chapter 13 [Functions and Scripts], page 91, for information about how to do this.
The way to use a function is with a function call expression, which consists of the function
name followed by a list of arguments in parentheses. The arguments are expressions which
give the raw materials for the calculation that the function will do. When there is more
than one argument, they are separated by commas. If there are no arguments, you can
omit the parentheses, but it is a good idea to include them anyway, to clearly indicate that
a function call was intended. Here are some examples:
66 GNU Octave
sqrt (x^2 + y^2) # One argument
ones (n, m) # Two arguments
rand () # No arguments
Each function expects a particular number of arguments. For example, the sqrt function
must be called with a single argument, the number to take the square root of:
sqrt (argument)
Some of the built-in functions take a variable number of arguments, depending on the
particular usage, and their behavior is different depending on the number of arguments
supplied.
Like every other expression, the function call has a value, which is computed by the
function based on the arguments you give it. In this example, the value of sqrt (argument)
is the square root of the argument. A function can also have side effects, such as assigning
the values of certain variables or doing input or output operations.
Unlike most languages, functions in Octave may return multiple values. For example,
the following statement
[u, s, v] = svd (a)
computes the singular value decomposition of the matrix a and assigns the three result
matrices to u, s, and v.
The left side of a multiple assignment expression is itself a list of expressions, and is
allowed to be a list of variable names or index expressions. See also Section 10.1 [Index
Expressions], page 63, and Section 10.6 [Assignment Ops], page 72.
10.2.1 Call by Value
In Octave, unlike Fortran, function arguments are passed by value, which means that
each argument in a function call is evaluated and assigned to a temporary location in
memory before being passed to the function. There is currently no way to specify that a
function parameter should be passed by reference instead of by value. This means that it is
impossible to directly alter the value of function parameter in the calling function. It can
only change the local copy within the function body. For example, the function
function f (x, n)
while (n-- > 0)
disp (x);
endwhile
endfunction
displays the value of the first argument n times. In this function, the variable n is used as a
temporary variable without having to worry that its value might also change in the calling
function. Call by value is also useful because it is always possible to pass constants for any
function parameter without first having to determine that the function will not attempt to
modify the parameter.
The caller may use a variable as the expression for the argument, but the called function
does not know this: it only knows what value the argument had. For example, given a
function called as
foo = "bar";
fcn (foo)
Chapter 10: Expressions 67
you should not think of the argument as being “the variable foo.” Instead, think of the
argument as the string value, "bar".
Even though Octave uses pass-by-value semantics for function arguments, values are not
copied unnecessarily. For example,
x = rand (1000);
f (x);
does not actually force two 1000 by 1000 element matrices to exist unless the function f
modifies the value of its argument. Then Octave must create a copy to avoid changing the
value outside the scope of the function f, or attempting (and probably failing!) to modify
the value of a constant or the value of a temporary result.
10.2.2 Recursion
With some restrictions1
, recursive function calls are allowed. A recursive function is one
which calls itself, either directly or indirectly. For example, here is an inefficient2
way to
compute the factorial of a given integer:
function retval = fact (n)
if (n > 0)
retval = n * fact (n-1);
else
retval = 1;
endif
endfunction
This function is recursive because it calls itself directly. It eventually terminates because
each time it calls itself, it uses an argument that is one less than was used for the previous
call. Once the argument is no longer greater than zero, it does not call itself, and the
recursion ends.
The built-in variable max_recursion_depth specifies a limit to the recursion depth and
prevents Octave from recursing infinitely.
Built-in Variablemax recursion depth
Limit the number of times a function may be called recursively. If the limit is exceeded,
an error message is printed and control returns to the top level.
The default value is 256.
10.3 Arithmetic Operators
The following arithmetic operators are available, and work on scalars and matrices.
1
Some of Octave’s function are implemented in terms of functions that cannot be called recursively. For
example, the ODE solver lsode is ultimately implemented in a Fortran subroutine that cannot be called
recursively, so lsode should not be called either directly or indirectly from within the user-supplied
function that lsode requires. Doing so will result in undefined behavior.
2
It would be much better to use prod (1:n), or gamma (n+1) instead, after first checking to ensure that
the value n is actually a positive integer.
68 GNU Octave
x + y Addition. If both operands are matrices, the number of rows and columns must
both agree. If one operand is a scalar, its value is added to all the elements of
the other operand.
x .+ y Element by element addition. This operator is equivalent to +.
x - y Subtraction. If both operands are matrices, the number of rows and columns
of both must agree.
x .- y Element by element subtraction. This operator is equivalent to -.
x * y Matrix multiplication. The number of columns of x must agree with the number
of rows of y.
x .* y Element by element multiplication. If both operands are matrices, the number
of rows and columns must both agree.
x / y Right division. This is conceptually equivalent to the expression
(inverse (y’) * x’)’
but it is computed without forming the inverse of y’.
If the system is not square, or if the coefficient matrix is singular, a minimum
norm solution is computed.
x ./ y Element by element right division.
x \ y Left division. This is conceptually equivalent to the expression
inverse (x) * y
but it is computed without forming the inverse of x.
If the system is not square, or if the coefficient matrix is singular, a minimum
norm solution is computed.
x .\ y Element by element left division. Each element of y is divided by each corresponding
element of x.
x ^ y
x ** y Power operator. If x and y are both scalars, this operator returns x raised to
the power y. If x is a scalar and y is a square matrix, the result is computed
using an eigenvalue expansion. If x is a square matrix. the result is computed
by repeated multiplication if y is an integer, and by an eigenvalue expansion if
y is not an integer. An error results if both x and y are matrices.
The implementation of this operator needs to be improved.
x .^ y
x .** y Element by element power operator. If both operands are matrices, the number
of rows and columns must both agree.
-x Negation.
+x Unary plus. This operator has no effect on the operand.
x’ Complex conjugate transpose. For real arguments, this operator is the same as
the transpose operator. For complex arguments, this operator is equivalent to
the expression
Chapter 10: Expressions 69
conj (x.’)
x.’ Transpose.
Note that because Octave’s element by element operators begin with a ‘.’, there is a
possible ambiguity for statements like
1./m
because the period could be interpreted either as part of the constant or as part of the
operator. To resolve this conflict, Octave treats the expression as if you had typed
(1) ./ m
and not
(1.) / m
Although this is inconsistent with the normal behavior of Octave’s lexer, which usually
prefers to break the input into tokens by preferring the longest possible match at any given
point, it is more useful in this case.
Built-in Variablewarn divide by zero
If the value of warn_divide_by_zero is nonzero, a warning is issued when Octave
encounters a division by zero. If the value is 0, the warning is omitted. The default
value is 1.
10.4 Comparison Operators
Comparison operators compare numeric values for relationships such as equality. They
are written using relational operators.
All of Octave’s comparison operators return a value of 1 if the comparison is true, or 0
if it is false. For matrix values, they all work on an element-by-element basis. For example,
[1, 2; 3, 4] == [1, 3; 2, 4]
⇒ 1 0
0 1
If one operand is a scalar and the other is a matrix, the scalar is compared to each
element of the matrix in turn, and the result is the same size as the matrix.
x < y True if x is less than y.
x <= y True if x is less than or equal to y.
x == y True if x is equal to y.
x >= y True if x is greater than or equal to y.
x > y True if x is greater than y.
x != y
x ~= y
x <> y True if x is not equal to y.
String comparisons may also be performed with the strcmp function, not with the comparison
operators listed above. See Chapter 5 [Strings], page 37.
70 GNU Octave
10.5 Boolean Expressions
10.5.1 Element-by-element Boolean Operators
An element-by-element boolean expression is a combination of comparison expressions
using the boolean operators “or” (‘|’), “and” (‘&’), and “not” (‘!’), along with parentheses
to control nesting. The truth of the boolean expression is computed by combining the truth
values of the corresponding elements of the component expressions. A value is considered
to be false if it is zero, and true otherwise.
Element-by-element boolean expressions can be used wherever comparison expressions
can be used. They can be used in if and while statements. However, if a matrix value
used as the condition in an if or while statement is only true if all of its elements are
nonzero.
Like comparison operations, each element of an element-by-element boolean expression
also has a numeric value (1 if true, 0 if false) that comes into play if the result of the boolean
expression is stored in a variable, or used in arithmetic.
Here are descriptions of the three element-by-element boolean operators.
boolean1 & boolean2
Elements of the result are true if both corresponding elements of boolean1 and
boolean2 are true.
boolean1 | boolean2
Elements of the result are true if either of the corresponding elements of
boolean1 or boolean2 is true.
! boolean
~ boolean Each element of the result is true if the corresponding element of boolean is
false.
For matrix operands, these operators work on an element-by-element basis. For example,
the expression
[1, 0; 0, 1] & [1, 0; 2, 3]
returns a two by two identity matrix.
For the binary operators, the dimensions of the operands must conform if both are
matrices. If one of the operands is a scalar and the other a matrix, the operator is applied
to the scalar and each element of the matrix.
For the binary element-by-element boolean operators, both subexpressions boolean1 and
boolean2 are evaluated before computing the result. This can make a difference when the
expressions have side effects. For example, in the expression
a & b++
the value of the variable b is incremented even if the variable a is zero.
This behavior is necessary for the boolean operators to work as described for matrixvalued
operands.
Chapter 10: Expressions 71
10.5.2 Short-circuit Boolean Operators
Combined with the implicit conversion to scalar values in if and while conditions, Octave’s
element-by-element boolean operators are often sufficient for performing most logical
operations. However, it is sometimes desirable to stop evaluating a boolean expression as
soon as the overall truth value can be determined. Octave’s short-circuit boolean operators
work this way.
boolean1 && boolean2
The expression boolean1 is evaluated and converted to a scalar using the equivalent
of the operation all (all (boolean1)). If it is false, the result of the overall
expression is 0. If it is true, the expression boolean2 is evaluated and converted
to a scalar using the equivalent of the operation all (all (boolean1)).
If it is true, the result of the overall expression is 1. Otherwise, the result of
the overall expression is 0.
boolean1 || boolean2
The expression boolean1 is evaluated and converted to a scalar using the equivalent
of the operation all (all (boolean1)). If it is true, the result of the overall
expression is 1. If it is false, the expression boolean2 is evaluated and converted
to a scalar using the equivalent of the operation all (all (boolean1)). If it
is true, the result of the overall expression is 1. Otherwise, the result of the
overall expression is 0.
The fact that both operands may not be evaluated before determining the overall truth
value of the expression can be important. For example, in the expression
a && b++
the value of the variable b is only incremented if the variable a is nonzero.
This can be used to write somewhat more concise code. For example, it is possible write
function f (a, b, c)
if (nargin > 2 && isstr (c))
...
instead of having to use two if statements to avoid attempting to evaluate an argument
that doesn’t exist. For example, without the short-circuit feature, it would be necessary to
write
function f (a, b, c)
if (nargin > 2)
if (isstr (c))
...
Writing
function f (a, b, c)
if (nargin > 2 & isstr (c))
...
would result in an error if f were called with one or two arguments because Octave would
be forced to try to evaluate both of the operands for the operator ‘&’.
72 GNU Octave
10.6 Assignment Expressions
An assignment is an expression that stores a new value into a variable. For example,
the following expression assigns the value 1 to the variable z:
z = 1
After this expression is executed, the variable z has the value 1. Whatever old value z
had before the assignment is forgotten. The ‘=’ sign is called an assignment operator.
Assignments can store string values also. For example, the following expression would
store the value "this food is good" in the variable message:
thing = "food"
predicate = "good"
message = [ "this " , thing , " is " , predicate ]
(This also illustrates concatenation of strings.)
Most operators (addition, concatenation, and so on) have no effect except to compute
a value. If you ignore the value, you might as well not use the operator. An assignment
operator is different. It does produce a value, but even if you ignore the value, the assignment
still makes itself felt through the alteration of the variable. We call this a side effect.
The left-hand operand of an assignment need not be a variable (see Chapter 9 [Variables],
page 53). It can also be an element of a matrix (see Section 10.1 [Index Expressions],
page 63) or a list of return values (see Section 10.2 [Calling Functions], page 65). These
are all called lvalues, which means they can appear on the left-hand side of an assignment
operator. The right-hand operand may be any expression. It produces the new value which
the assignment stores in the specified variable, matrix element, or list of return values.
It is important to note that variables do not have permanent types. The type of a
variable is simply the type of whatever value it happens to hold at the moment. In the
following program fragment, the variable foo has a numeric value at first, and a string value
later on:
octave:13> foo = 1
foo = 1
octave:13> foo = "bar"
foo = bar
When the second assignment gives foo a string value, the fact that it previously had a
numeric value is forgotten.
Assignment of a scalar to an indexed matrix sets all of the elements that are referenced
by the indices to the scalar value. For example, if a is a matrix with at least two columns,
a(:, 2) = 5
sets all the elements in the second column of a to 5.
Assigning an empty matrix ‘[]’ works in most cases to allow you to delete rows or
columns of matrices and vectors. See Section 4.1.1 [Empty Matrices], page 34. For example,
given a 4 by 5 matrix A, the assignment
A (3, :) = []
deletes the third row of A, and the assignment
A (:, 1:2:5) = []
deletes the first, third, and fifth columns.
Chapter 10: Expressions 73
An assignment is an expression, so it has a value. Thus, z = 1 as an expression has the
value 1. One consequence of this is that you can write multiple assignments together:
x = y = z = 0
stores the value 0 in all three variables. It does this because the value of z = 0, which is 0,
is stored into y, and then the value of y = z = 0, which is 0, is stored into x.
This is also true of assignments to lists of values, so the following is a valid expression
[a, b, c] = [u, s, v] = svd (a)
that is exactly equivalent to
[u, s, v] = svd (a)
a = u
b = s
c = v
In expressions like this, the number of values in each part of the expression need not
match. For example, the expression
[a, b, c, d] = [u, s, v] = svd (a)
is equivalent to the expression above, except that the value of the variable ‘d’ is left unchanged,
and the expression
[a, b] = [u, s, v] = svd (a)
is equivalent to
[u, s, v] = svd (a)
a = u
b = s
You can use an assignment anywhere an expression is called for. For example, it is valid
to write x != (y = 1) to set y to 1 and then test whether x equals 1. But this style tends
to make programs hard to read. Except in a one-shot program, you should rewrite it to get
rid of such nesting of assignments. This is never very hard.
print rhs assign valIf the value of this variable is non-zero, Octave will print the
value
of the right hand side of assignment expressions instead of the value of the left hand
side (after the assignment).
10.7 Increment Operators
Increment operators increase or decrease the value of a variable by 1. The operator to
increment a variable is written as ‘++’. It may be used to increment a variable either before
or after taking its value.
For example, to pre-increment the variable x, you would write ++x. This would add one
to x and then return the new value of x as the result of the expression. It is exactly the
same as the expression x = x + 1.
To post-increment a variable x, you would write x++. This adds one to the variable x,
but returns the value that x had prior to incrementing it. For example, if x is equal to 2,
the result of the expression x++ is 2, and the new value of x is 3.
74 GNU Octave
For matrix and vector arguments, the increment and decrement operators work on each
element of the operand.
Here is a list of all the increment and decrement expressions.
++x This expression increments the variable x. The value of the expression is the
new value of x. It is equivalent to the expression x = x + 1.
--x This expression decrements the variable x. The value of the expression is the
new value of x. It is equivalent to the expression x = x - 1.
x++ This expression causes the variable x to be incremented. The value of the
expression is the old value of x.
x-- This expression causes the variable x to be decremented. The value of the
expression is the old value of x.
It is not currently possible to increment index expressions. For example, you might
expect that the expression v(4)++ would increment the fourth element of the vector v, but
instead it results in a parse error. This problem may be fixed in a future release of Octave.
10.8 Operator Precedence
Operator precedence determines how operators are grouped, when different operators
appear close by in one expression. For example, ‘*’ has higher precedence than ‘+’. Thus,
the expression a + b * c means to multiply b and c, and then add a to the product (i.e., a
+ (b * c)).
You can overrule the precedence of the operators by using parentheses. You can think
of the precedence rules as saying where the parentheses are assumed if you do not write
parentheses yourself. In fact, it is wise to use parentheses whenever you have an unusual
combination of operators, because other people who read the program may not remember
what the precedence is in this case. You might forget as well, and then you too could make
a mistake. Explicit parentheses will help prevent any such mistake.
When operators of equal precedence are used together, the leftmost operator groups
first, except for the assignment and exponentiation operators, which group in the opposite
order. Thus, the expression a - b + c groups as (a - b) + c, but the expression a = b = c
groups as a = (b = c).
The precedence of prefix unary operators is important when another operator follows
the operand. For example, -x^2 means -(x^2), because ‘-’ has lower precedence than ‘^’.
Here is a table of the operators in Octave, in order of increasing precedence.
statement separators
‘;’, ‘,’.
assignment
‘=’. This operator groups right to left.
logical "or" and "and"
‘||’, ‘&&’.
element-wise "or" and "and"
‘|’, ‘&’.
Chapter 10: Expressions 75
relational
‘<’, ‘<=’, ‘==’, ‘>=’, ‘>’, ‘!=’, ‘~=’, ‘<>’.
colon ‘:’.
add, subtract
‘+’, ‘-’.
multiply, divide
‘*’, ‘/’, ‘\’, ‘.\’, ‘.*’, ‘./’.
transpose
‘’’, ‘.’’
unary plus, minus, increment, decrement, and ‘‘not’’
‘+’, ‘-’, ‘++’, ‘--’, ‘!’, ‘~’.
exponentiation
‘^’, ‘**’, ‘.^’, ‘.**’.
76 GNU Octave
Chapter 11: Evaluation 77
11 Evaluation
Normally, you evaluate expressions simply by typing them at the Octave prompt, or by
asking Octave to interpret commands that you have saved in a file.
Sometimes, you may find it necessary to evaluate an expression that has been computed
and stored in a string, or use a string as the name of a function to call. The eval and
feval functions allow you to do just that, and are necessary in order to evaluate commands
that are not known until run time, or to write functions that will need to call user-supplied
functions.
Built-in Functioneval (try, catch)
Parse the string try and evaluate it as if it were an Octave program, returning the last
value computed. If that fails, evaluate the string catch. The string try is evaluated in
the current context, so any results remain available after eval returns. For example,
eval ("a = 13")
a = 13
⇒ 13
In this case, the value of the evaluated expression is printed and it is also returned
returned from eval. Just as with any other expression, you can turn printing off by
ending the expression in a semicolon. For example,
eval ("a = 13;")
⇒ 13
In this example, the variable a has been given the value 13, but the value of the
expression is not printed. You can also turn off automatic printing for all expressions
executed by eval using the variable default_eval_print_flag.
Built-in Variabledefault eval print flag
If the value of this variable is nonzero, Octave prints the results of commands executed
by eval that do not end with semicolons. If it is zero, automatic printing is
suppressed. The default value is 1.
Built-in Functionfeval (name, ...)
Evaluate the function named name. Any arguments after the first are passed on to
the named function. For example,
feval ("acos", -1)
⇒ 3.1416
calls the function acos with the argument ‘-1’.
The function feval is necessary in order to be able to write functions that call usersupplied
functions, because Octave does not have a way to declare a pointer to a
function (like C) or to declare a special kind of variable that can be used to hold the
name of a function (like EXTERNAL in Fortran). Instead, you must refer to functions
by name, and use feval to call them.
78 GNU Octave
Here is a simple-minded function using feval that finds the root of a user-supplied
function of one variable using Newton’s method.
function result = newtroot (fname, x)
# usage: newtroot (fname, x)
#
# fname : a string naming a function f(x).
# x : initial guess
delta = tol = sqrt (eps);
maxit = 200;
fx = feval (fname, x);
for i = 1:maxit
if (abs (fx) < tol)
result = x;
return;
else
fx_new = feval (fname, x + delta);
deriv = (fx_new - fx) / delta;
x = x - fx / deriv;
fx = fx_new;
endif
endfor
result = x;
endfunction
Note that this is only meant to be an example of calling user-supplied functions and
should not be taken too seriously. In addition to using a more robust algorithm, any serious
code would check the number and type of all the arguments, ensure that the supplied
function really was a function, etc. See See Section 4.4 [Predicates for Numeric Objects],
page 36, for example, for a list of predicates for numeric objects, and See Section 9.2 [Status
of Variables], page 55, for a description of the exist function.
Chapter 12: Statements 79
12 Statements
Statements may be a simple constant expression or a complicated list of nested loops
and conditional statements.
Control statements such as if, while, and so on control the flow of execution in Octave
programs. All the control statements start with special keywords such as if and while,
to distinguish them from simple expressions. Many control statements contain other statements;
for example, the if statement contains another statement which may or may not be
executed.
Each control statement has a corresponding end statement that marks the end of the end
of the control statement. For example, the keyword endif marks the end of an if statement,
and endwhile marks the end of a while statement. You can use the keyword end anywhere
a more specific end keyword is expected, but using the more specific keywords is preferred
because if you use them, Octave is able to provide better diagnostics for mismatched or
missing end tokens.
The list of statements contained between keywords like if or while and the corresponding
end statement is called the body of a control statement.
12.1 The if Statement
The if statement is Octave’s decision-making statement. There are three basic forms
of an if statement. In its simplest form, it looks like this:
if (condition)
then-body
endif
condition is an expression that controls what the rest of the statement will do. The thenbody
is executed only if condition is true.
The condition in an if statement is considered true if its value is non-zero, and false if
its value is zero. If the value of the conditional expression in an if statement is a vector or
a matrix, it is considered true only if all of the elements are non-zero.
The second form of an if statement looks like this:
if (condition)
then-body
else
else-body
endif
If condition is true, then-body is executed; otherwise, else-body is executed.
Here is an example:
if (rem (x, 2) == 0)
printf ("x is even\n");
else
printf ("x is odd\n");
endif
In this example, if the expression rem (x, 2) == 0 is true (that is, the value of x is
divisible by 2), then the first printf statement is evaluated, otherwise the second printf
statement is evaluated.
80 GNU Octave
The third and most general form of the if statement allows multiple decisions to be
combined in a single statement. It looks like this:
if (condition)
then-body
elseif (condition)
elseif-body
else
else-body
endif
Any number of elseif clauses may appear. Each condition is tested in turn, and if one is
found to be true, its corresponding body is executed. If none of the conditions are true and
the else clause is present, its body is executed. Only one else clause may appear, and it
must be the last part of the statement.
In the following example, if the first condition is true (that is, the value of x is divisible
by 2), then the first printf statement is executed. If it is false, then the second condition
is tested, and if it is true (that is, the value of x is divisible by 3), then the second printf
statement is executed. Otherwise, the third printf statement is performed.
if (rem (x, 2) == 0)
printf ("x is even\n");
elseif (rem (x, 3) == 0)
printf ("x is odd and divisible by 3\n");
else
printf ("x is odd\n");
endif
Note that the elseif keyword must not be spelled else if, as is allowed in Fortran. If
it is, the space between the else and if will tell Octave to treat this as a new if statement
within another if statement’s else clause. For example, if you write
if (c1)
body-1
else if (c2)
body-2
endif
Octave will expect additional input to complete the first if statement. If you are using
Octave interactively, it will continue to prompt you for additional input. If Octave is reading
this input from a file, it may complain about missing or mismatched end statements, or, if
you have not used the more specific end statements (endif, endfor, etc.), it may simply
produce incorrect results, without producing any warning messages.
It is much easier to see the error if we rewrite the statements above like this,
if (c1)
body-1
else
if (c2)
body-2
endif
using the indentation to show how Octave groups the statements. See Chapter 13 [Functions
and Scripts], page 91.
Chapter 12: Statements 81
Built-in Variablewarn assign as truth value
If the value of warn_assign_as_truth_value is nonzero, a warning is issued for
statements like
if (s = t)
...
since such statements are not common, and it is likely that the intent was to write
if (s == t)
...
instead.
There are times when it is useful to write code that contains assignments within the
condition of a while or if statement. For example, statements like
while (c = getc())
...
are common in C programming.
It is possible to avoid all warnings about such statements by setting warn_assign_
as_truth_value to 0, but that may also let real errors like
if (x = 1) # intended to test (x == 1)!
...
slip by.
In such cases, it is possible suppress errors for specific statements by writing them
with an extra set of parentheses. For example, writing the previous example as
while ((c = getc()))
...
will prevent the warning from being printed for this statement, while allowing Octave
to warn about other assignments used in conditional contexts.
The default value of warn_assign_as_truth_value is 1.
12.2 The switch Statement
The switch statement was introduced in Octave 2.0.5. It should be considered experimental,
and details of the implementation may change slightly in future versions of Octave.
If you have comments or would like to share your experiences in trying to use this new command
in real programs, please send them to octave-maintainers@bevo.che.wisc.edu.
(But if you think you’ve found a bug, please report it to bug-octave@bevo.che.wisc.edu.
The general form of the switch statement is
switch expression
case label
command list
case label
command list
...
otherwise
command list
endswitch
82 GNU Octave
• The identifiers switch, case, otherwise, and endswitch are now keywords.
• The label may be any expression.
• Duplicate label values are not detected. The command list corresponding to the first
match will be executed.
• You must have at least one case label command list clause.
• The otherwise command list clause is optional.
• As with all other specific end keywords, endswitch may be replaced by end, but you
can get better diagnostics if you use the specific forms.
• Cases are exclusive, so they don’t ‘fall through’ as do the cases in the switch statement
of the C language.
• The command list elements are not optional. Making the list optional would have
meant requiring a separator between the label and the command list. Otherwise,
things like
switch (foo)
case (1) -2
...
would produce surprising results, as would
switch (foo)
case (1)
case (2)
doit ();
...
particularly for C programmers.
• The implementation is simple-minded and currently offers no real performance improvement
over an equivalent if block, even if all the labels are integer constants.
Perhaps a future variation on this could detect all constant integer labels and improve
performance by using a jump table.
Built-in Variablewarn variable switch label
If the value of this variable is nonzero, Octave will print a warning if a switch label
is not a constant or constant expression
12.3 The while Statement
In programming, a loop means a part of a program that is (or at least can be) executed
two or more times in succession.
The while statement is the simplest looping statement in Octave. It repeatedly executes
a statement as long as a condition is true. As with the condition in an if statement, the
condition in a while statement is considered true if its value is non-zero, and false if its
value is zero. If the value of the conditional expression in a while statement is a vector or
a matrix, it is considered true only if all of the elements are non-zero.
Octave’s while statement looks like this:
Chapter 12: Statements 83
while (condition)
body
endwhile
Here body is a statement or list of statements that we call the body of the loop, and
condition is an expression that controls how long the loop keeps running.
The first thing the while statement does is test condition. If condition is true, it executes
the statement body. After body has been executed, condition is tested again, and if it is
still true, body is executed again. This process repeats until condition is no longer true. If
condition is initially false, the body of the loop is never executed.
This example creates a variable fib that contains the first ten elements of the Fibonacci
sequence.
fib = ones (1, 10);
i = 3;
while (i <= 10)
fib (i) = fib (i-1) + fib (i-2);
i++;
endwhile
Here the body of the loop contains two statements.
The loop works like this: first, the value of i is set to 3. Then, the while tests whether
i is less than or equal to 10. This is the case when i equals 3, so the value of the i-th
element of fib is set to the sum of the previous two values in the sequence. Then the i++
increments the value of i and the loop repeats. The loop terminates when i reaches 11.
A newline is not required between the condition and the body; but using one makes the
program clearer unless the body is very simple.
See Section 12.1 [The if Statement], page 79, for a description of the variable warn_
assign_as_truth_value.
12.4 The do-until Statement
The do-until statement is similar to the while statement, except that it repeatedly
executes a statement until a condition becomes true, and the test of the condition is at
the end of the loop, so the body of the loop is always executed at least once. As with the
condition in an if statement, the condition in a do-until statement is considered true if its
value is non-zero, and false if its value is zero. If the value of the conditional expression in a
do-until statement is a vector or a matrix, it is considered true only if all of the elements
are non-zero.
Octave’s do-until statement looks like this:
do
body
until (condition)
Here body is a statement or list of statements that we call the body of the loop, and
condition is an expression that controls how long the loop keeps running.
This example creates a variable fib that contains the first ten elements of the Fibonacci
sequence.
84 GNU Octave
fib = ones (1, 10);
i = 2;
do
i++;
fib (i) = fib (i-1) + fib (i-2);
until (i == 10)
A newline is not required between the do keyword and the body; but using one makes
the program clearer unless the body is very simple.
See Section 12.1 [The if Statement], page 79, for a description of the variable warn_
assign_as_truth_value.
12.5 The for Statement
The for statement makes it more convenient to count iterations of a loop. The general
form of the for statement looks like this:
for var = expression
body
endfor
where body stands for any statement or list of statements, expression is any valid expression,
and var may take several forms. Usually it is a simple variable name or an indexed variable.
If the value of expression is a structure, var may also be a list. See Section 12.5.1 [Looping
Over Structure Elements], page 84, below.
The assignment expression in the for statement works a bit differently than Octave’s
normal assignment statement. Instead of assigning the complete result of the expression, it
assigns each column of the expression to var in turn. If expression is a range, a row vector,
or a scalar, the value of var will be a scalar each time the loop body is executed. If var is a
column vector or a matrix, var will be a column vector each time the loop body is executed.
The following example shows another way to create a vector containing the first ten
elements of the Fibonacci sequence, this time using the for statement:
fib = ones (1, 10);
for i = 3:10
fib (i) = fib (i-1) + fib (i-2);
endfor
This code works by first evaluating the expression 3:10, to produce a range of values from 3
to 10 inclusive. Then the variable i is assigned the first element of the range and the body
of the loop is executed once. When the end of the loop body is reached, the next value in
the range is assigned to the variable i, and the loop body is executed again. This process
continues until there are no more elements to assign.
Although it is possible to rewrite all for loops as while loops, the Octave language has
both statements because often a for loop is both less work to type and more natural to
think of. Counting the number of iterations is very common in loops and it can be easier
to think of this counting as part of looping rather than as something to do inside the loop.
12.5.1 Looping Over Structure Elements
A special form of the for statement allows you to loop over all the elements of a structure:
Chapter 12: Statements 85
for [ val, key ] = expression
body
endfor
In this form of the for statement, the value of expression must be a structure. If it is, key
and val are set to the name of the element and the corresponding value in turn, until there
are no more elements. For example,
x.a = 1
x.b = [1, 2; 3, 4]
x.c = "string"
for [val, key] = x
key
val
endfor
key = a
val = 1
key = b
val =
1 2
3 4
key = c
val = string
The elements are not accessed in any particular order. If you need to cycle through the
list in a particular way, you will have to use the function struct_elements and sort the
list yourself.
The key variable may also be omitted. If it is, the brackets are also optional. This is
useful for cycling through the values of all the structure elements when the names of the
elements do not need to be known.
12.6 The break Statement
The break statement jumps out of the innermost for or while loop that encloses it.
The break statement may only be used within the body of a loop. The following example
finds the smallest divisor of a given integer, and also identifies prime numbers:
86 GNU Octave
num = 103;
div = 2;
while (div*div <= num)
if (rem (num, div) == 0)
break;
endif
div++;
endwhile
if (rem (num, div) == 0)
printf ("Smallest divisor of %d is %d\n", num, div)
else
printf ("%d is prime\n", num);
endif
When the remainder is zero in the first while statement, Octave immediately breaks
out of the loop. This means that Octave proceeds immediately to the statement following
the loop and continues processing. (This is very different from the exit statement which
stops the entire Octave program.)
Here is another program equivalent to the previous one. It illustrates how the condition
of a while statement could just as well be replaced with a break inside an if:
num = 103;
div = 2;
while (1)
if (rem (num, div) == 0)
printf ("Smallest divisor of %d is %d\n", num, div);
break;
endif
div++;
if (div*div > num)
printf ("%d is prime\n", num);
break;
endif
endwhile
12.7 The continue Statement
The continue statement, like break, is used only inside for or while loops. It skips
over the rest of the loop body, causing the next cycle around the loop to begin immediately.
Contrast this with break, which jumps out of the loop altogether. Here is an example:
Chapter 12: Statements 87
# print elements of a vector of random
# integers that are even.
# first, create a row vector of 10 random
# integers with values between 0 and 100:
vec = round (rand (1, 10) * 100);
# print what we’re interested in:
for x = vec
if (rem (x, 2) != 0)
continue;
endif
printf ("%d\n", x);
endfor
If one of the elements of vec is an odd number, this example skips the print statement
for that element, and continues back to the first statement in the loop.
This is not a practical example of the continue statement, but it should give you a clear
understanding of how it works. Normally, one would probably write the loop like this:
for x = vec
if (rem (x, 2) == 0)
printf ("%d\n", x);
endif
endfor
12.8 The unwind_protect Statement
Octave supports a limited form of exception handling modelled after the unwind-protect
form of Lisp.
The general form of an unwind_protect block looks like this:
unwind_protect
body
unwind_protect_cleanup
cleanup
end_unwind_protect
Where body and cleanup are both optional and may contain any Octave expressions or
commands. The statements in cleanup are guaranteed to be executed regardless of how
control exits body.
This is useful to protect temporary changes to global variables from possible errors. For
example, the following code will always restore the original value of the built-in variable
do_fortran_indexing even if an error occurs while performing the indexing operation.
88 GNU Octave
save_do_fortran_indexing = do_fortran_indexing;
unwind_protect
do_fortran_indexing = 1;
elt = a (idx)
unwind_protect_cleanup
do_fortran_indexing = save_do_fortran_indexing;
end_unwind_protect
Without unwind_protect, the value of do fortran indexing would not be restored if an
error occurs while performing the indexing operation because evaluation would stop at the
point of the error and the statement to restore the value would not be executed.
12.9 The try Statement
In addition to unwind protect, Octave supports another limited form of exception han-
dling.
The general form of a try block looks like this:
try
body
catch
cleanup
end_try_catch
Where body and cleanup are both optional and may contain any Octave expressions or
commands. The statements in cleanup are only executed if an error occurs in body.
No warnings or error messages are printed while body is executing. If an error does occur
during the execution of body, cleanup can access the text of the message that would have
been printed in the builtin constant __error_text__. This is the same as eval (try, catch)
(which may now also use __error_text__) but it is more efficient since the commands do
not need to be parsed each time the try and catch statements are evaluated. See Chapter 14
[Error Handling], page 107, for more information about the __error_text__ variable.
Octave’s try block is a very limited variation on the Lisp condition-case form (limited
because it cannot handle different classes of errors separately). Perhaps at some point
Octave can have some sort of classification of errors and try-catch can be improved to be
as powerful as condition-case in Lisp.
12.10 Continuation Lines
In the Octave language, most statements end with a newline character and you must
tell Octave to ignore the newline character in order to continue a statement from one line
to the next. Lines that end with the characters ... or \ are joined with the following line
before they are divided into tokens by Octave’s parser. For example, the lines
x = long_variable_name ...
+ longer_variable_name \
- 42
form a single statement. The backslash character on the second line above is interpreted a
continuation character, not as a division operator.
Chapter 12: Statements 89
For continuation lines that do not occur inside string constants, whitespace and comments
may appear between the continuation marker and the newline character. For example,
the statement
x = long_variable_name ... # comment one
+ longer_variable_name \ # comment two
- 42 # last comment
is equivalent to the one shown above. Inside string constants, the continuation marker must
appear at the end of the line just before the newline character.
Input that occurs inside parentheses can be continued to the next line without having
to use a continuation marker. For example, it is possible to write statements like
if (fine_dining_destination == on_a_boat
|| fine_dining_destination == on_a_train)
suess (i, will, not, eat, them, sam, i, am, i,
will, not, eat, green, eggs, and, ham);
endif
without having to add to the clutter with continuation markers.
90 GNU Octave
Chapter 13: Functions and Script Files 91
13 Functions and Script Files
Complicated Octave programs can often be simplified by defining functions. Functions
can be defined directly on the command line during interactive Octave sessions, or in external
files, and can be called just like built-in functions.
13.1 Defining Functions
In its simplest form, the definition of a function named name looks like this:
function name
body
endfunction
A valid function name is like a valid variable name: a sequence of letters, digits and underscores,
not starting with a digit. Functions share the same pool of names as variables.
The function body consists of Octave statements. It is the most important part of the
definition, because it says what the function should actually do.
For example, here is a function that, when executed, will ring the bell on your terminal
(assuming that it is possible to do so):
function wakeup
printf ("\a");
endfunction
The printf statement (see Chapter 15 [Input and Output], page 109) simply tells Octave
to print the string "\a". The special character ‘\a’ stands for the alert character (ASCII
7). See Chapter 5 [Strings], page 37.
Once this function is defined, you can ask Octave to evaluate it by typing the name of
the function.
Normally, you will want to pass some information to the functions you define. The
syntax for passing parameters to a function in Octave is
function name (arg-list)
body
endfunction
where arg-list is a comma-separated list of the function’s arguments. When the function is
called, the argument names are used to hold the argument values given in the call. The list
of arguments may be empty, in which case this form is equivalent to the one shown above.
To print a message along with ringing the bell, you might modify the beep to look like
this:
function wakeup (message)
printf ("\a%s\n", message);
endfunction
Calling this function using a statement like this
wakeup ("Rise and shine!");
will cause Octave to ring your terminal’s bell and print the message ‘Rise and shine!’,
followed by a newline character (the ‘\n’ in the first argument to the printf statement).
In most cases, you will also want to get some information back from the functions you
define. Here is the syntax for writing a function that returns a single value:
92 GNU Octave
function ret-var = name (arg-list)
body
endfunction
The symbol ret-var is the name of the variable that will hold the value to be returned by
the function. This variable must be defined before the end of the function body in order
for the function to return a value.
Variables used in the body of a function are local to the function. Variables named
in arg-list and ret-var are also local to the function. See Section 9.1 [Global Variables],
page 53, for information about how to access global variables inside a function.
For example, here is a function that computes the average of the elements of a vector:
function retval = avg (v)
retval = sum (v) / length (v);
endfunction
If we had written avg like this instead,
function retval = avg (v)
if (is_vector (v))
retval = sum (v) / length (v);
endif
endfunction
and then called the function with a matrix instead of a vector as the argument, Octave
would have printed an error message like this:
error: ‘retval’ undefined near line 1 column 10
error: evaluating index expression near line 7, column 1
because the body of the if statement was never executed, and retval was never defined.
To prevent obscure errors like this, it is a good idea to always make sure that the return
variables will always have values, and to produce meaningful error messages when problems
are encountered. For example, avg could have been written like this:
function retval = avg (v)
retval = 0;
if (is_vector (v))
retval = sum (v) / length (v);
else
error ("avg: expecting vector argument");
endif
endfunction
There is still one additional problem with this function. What if it is called without an
argument? Without additional error checking, Octave will probably print an error message
that won’t really help you track down the source of the error. To allow you to catch errors
like this, Octave provides each function with an automatic variable called nargin. Each
time a function is called, nargin is automatically initialized to the number of arguments
that have actually been passed to the function. For example, we might rewrite the avg
function like this:
Chapter 13: Functions and Script Files 93
function retval = avg (v)
retval = 0;
if (nargin != 1)
usage ("avg (vector)");
endif
if (is_vector (v))
retval = sum (v) / length (v);
else
error ("avg: expecting vector argument");
endif
endfunction
Although Octave does not automatically report an error if you call a function with more
arguments than expected, doing so probably indicates that something is wrong. Octave
also does not automatically report an error if a function is called with too few arguments,
but any attempt to use a variable that has not been given a value will result in an error.
To avoid such problems and to provide useful messages, we check for both possibilities and
issue our own error message.
Automatic Variablenargin
When a function is called, this local variable is automatically initialized to the number
of arguments passed to the function. At the top level, nargin holds the number of
command line arguments that were passed to Octave.
Built-in Variablesilent functions
If the value of silent_functions is nonzero, internal output from a function is
suppressed. Otherwise, the results of expressions within a function body that are not
terminated with a semicolon will have their values printed. The default value is 0.
For example, if the function
function f ()
2 + 2
endfunction
is executed, Octave will either print ‘ans = 4’ or nothing depending on the value of
silent_functions.
Built-in Variablewarn missing semicolon
If the value of this variable is nonzero, Octave will warn when statements in function
definitions don’t end in semicolons. The default value is 0.
13.2 Multiple Return Values
Unlike many other computer languages, Octave allows you to define functions that return
more than one value. The syntax for defining functions that return multiple values is
function [ret-list] = name (arg-list)
body
endfunction
94 GNU Octave
where name, arg-list, and body have the same meaning as before, and ret-list is a commaseparated
list of variable names that will hold the values returned from the function. The
list of return values must have at least one element. If ret-list has only one element, this
form of the function statement is equivalent to the form described in the previous section.
Here is an example of a function that returns two values, the maximum element of a
vector and the index of its first occurrence in the vector.
function [max, idx] = vmax (v)
idx = 1;
max = v (idx);
for i = 2:length (v)
if (v (i) > max)
max = v (i);
idx = i;
endif
endfor
endfunction
In this particular case, the two values could have been returned as elements of a single
array, but that is not always possible or convenient. The values to be returned may not
have compatible dimensions, and it is often desirable to give the individual return values
distinct names.
In addition to setting nargin each time a function is called, Octave also automatically
initializes nargout to the number of values that are expected to be returned. This allows
you to write functions that behave differently depending on the number of values that the
user of the function has requested. The implicit assignment to the built-in variable ans
does not figure in the count of output arguments, so the value of nargout may be zero.
The svd and lu functions are examples of built-in functions that behave differently
depending on the value of nargout.
It is possible to write functions that only set some return values. For example, calling
the function
function [x, y, z] = f ()
x = 1;
z = 2;
endfunction
as
[a, b, c] = f ()
produces:
a = 1
b = [](0x0)
c = 2
provided that the built-in variable define_all_return_values is nonzero and the value of
default_return_value is ‘[]’. See Section 9.3 [Summary of Built-in Variables], page 56.
Chapter 13: Functions and Script Files 95
Automatic Variablenargout
When a function is called, this local variable is automatically initialized to the number
of arguments expected to be returned. For example,
f ()
will result in nargout being set to 0 inside the function f and
[s, t] = f ()
will result in nargout being set to 2 inside the function f.
At the top level, nargout is undefined.
Built-in Variabledefault return value
The value given to otherwise uninitialized return values if define_all_return_
values is nonzero. The default value is [].
Built-in Variabledefine all return values
If the value of define_all_return_values is nonzero, Octave will substitute the
value specified by default_return_value for any return values that remain undefined
when a function returns. The default value is 0.
Function Filenargchk (nargin min, nargin max, n)
If n is in the range nargin min through nargin max inclusive, return the empty matrix.
Otherwise, return a message indicating whether n is too large or too small.
This is useful for checking to see that the number of arguments supplied to a function
is within an acceptable range.
13.3 Variable-length Argument Lists
Octave has a real mechanism for handling functions that take an unspecified number
of arguments, so it is not necessary to place an upper bound on the number of optional
arguments that a function can accept.
Here is an example of a function that uses the new syntax to print a header followed by
an unspecified number of values:
function foo (heading, ...)
disp (heading);
va_start ();
## Pre-decrement to skip ‘heading’ arg.
while (--nargin)
disp (va_arg ());
endwhile
endfunction
The ellipsis that marks the variable argument list may only appear once and must be
the last element in the list of arguments.
96 GNU Octave
Built-in Functionva arg ()
Return the value of hte next available argument and move the internal pointer to
the next argument. It is an error to call va_arg when ther eare no more arguments
available, or in a function that has not been declared to take a variable number of
parameters.
Built-in Functionva start ()
Position an internal pointer to the first unnamed argument in functions that have been
declared to accept a variable number of arguments. It is an error to call va_start in
a function that has not been declared to take a variable number of parameters.
Sometimes it is useful to be able to pass all unnamed arguments to another function.
The keyword all va args makes this very easy to do. For example,
function f (...)
while (nargin--)
disp (va_arg ())
endwhile
endfunction
function g (...)
f ("begin", all_va_args, "end")
endfunction
g (1, 2, 3)
begin
1
2
3
end
Keywordall va args
This keyword stands for the entire list of optional argument, so it is possible to use
it more than once within the same function without having to call va_start. It can
only be used within functions that take a variable number of arguments. It is an error
to use it in other contexts.
13.4 Variable-length Return Lists
Octave also has a real mechanism for handling functions that return an unspecified
number of values, so it is no longer necessary to place an upper bound on the number of
outputs that a function can produce.
Here is an example of a function that uses a variable-length return list to produce n
values:
Chapter 13: Functions and Script Files 97
function [...] = f (n, x)
for i = 1:n
vr_val (i * x);
endfor
endfunction
[dos, quatro] = f (2, 2)
⇒ dos = 2
⇒ quatro = 4
As with variable argument lists, the ellipsis that marks the variable return list may only
appear once and must be the last element in the list of returned values.
Built-in Functionvr val (x)
Each time this function is called, it places the value of its argument at the end of the
list of values to return from the current function. Once vr_val has been called, there
is no way to go back to the beginning of the list and rewrite any of the return values.
This function may only be called within functions that have been declared to return
an unspecified number of output arguments.
13.5 Returning From a Function
The body of a user-defined function can contain a return statement. This statement
returns control to the rest of the Octave program. It looks like this:
return
Unlike the return statement in C, Octave’s return statement cannot be used to return
a value from a function. Instead, you must assign values to the list of return variables that
are part of the function statement. The return statement simply makes it easier to exit
a function from a deeply nested loop or conditional statement.
Here is an example of a function that checks to see if any elements of a vector are nonzero.
function retval = any_nonzero (v)
retval = 0;
for i = 1:length (v)
if (v (i) != 0)
retval = 1;
return;
endif
endfor
printf ("no nonzero elements found\n");
endfunction
Note that this function could not have been written using the break statement to exit
the loop once a nonzero value is found without adding extra logic to avoid printing the
message if the vector does contain a nonzero element.
Keywordreturn
When Octave encounters the keyword return inside a function or script, it returns
control to be caller immediately. At the top level, the return statement is ignored. A
return statement is assumed at the end of every function definition.
98 GNU Octave
Built-in Variablereturn last computed value
If the value of return_last_computed_value is true, and a function is defined without
explicitly specifying a return value, the function will return the value of the last
expression. Otherwise, no value will be returned. The default value is 0.
For example, the function
function f ()
2 + 2;
endfunction
will either return nothing, if the value of return_last_computed_value is 0, or 4, if
the value of return_last_computed_value is nonzero.
13.6 Function Files
Except for simple one-shot programs, it is not practical to have to define all the functions
you need each time you need them. Instead, you will normally want to save them in a file
so that you can easily edit them, and save them for use at a later time.
Octave does not require you to load function definitions from files before using them.
You simply need to put the function definitions in a place where Octave can find them.
When Octave encounters an identifier that is undefined, it first looks for variables or
functions that are already compiled and currently listed in its symbol table. If it fails to
find a definition there, it searches the list of directories specified by the built-in variable
LOADPATH for files ending in ‘.m’ that have the same base name as the undefined identifier.1
Once Octave finds a file with a name that matches, the contents of the file are read. If
it defines a single function, it is compiled and executed. See Section 13.7 [Script Files],
page 100, for more information about how you can define more than one function in a
single file.
When Octave defines a function from a function file, it saves the full name of the file it
read and the time stamp on the file. After that, it checks the time stamp on the file every
time it needs the function. If the time stamp indicates that the file has changed since the
last time it was read, Octave reads it again.
Checking the time stamp allows you to edit the definition of a function while Octave is
running, and automatically use the new function definition without having to restart your
Octave session. Checking the time stamp every time a function is used is rather inefficient,
but it has to be done to ensure that the correct function definition is used.
To avoid degrading performance unnecessarily by checking the time stamps on functions
that are not likely to change, Octave assumes that function files in the directory tree ‘octavehome/share/octave/version/m’
will not change, so it doesn’t have to check their time
stamps every time the functions defined in those files are used. This is normally a very
good assumption and provides a significant improvement in performance for the function
files that are distributed with Octave.
If you know that your own function files will not change while you are running Octave,
you can improve performance by setting the variable ignore_function_time_stamp to
"all", so that Octave will ignore the time stamps for all function files. Setting it to
1
The ‘.m’ suffix was chosen for compatibility with Matlab.
Chapter 13: Functions and Script Files 99
"system" gives the default behavior. If you set it to anything else, Octave will check the
time stamps on all function files.
Built-in VariableDEFAULT LOADPATH
A colon separated list of directories in which to search for function files by default.
The value of this variable is also automatically substituted for leading, trailing, or
doubled colons that appear in the built-in variable LOADPATH.
Built-in VariableLOADPATH
A colon separated list of directories in which to search for function files. See Chapter
13 [Functions and Scripts], page 91. The value of LOADPATH overrides the environment
variable OCTAVE_PATH. See Appendix C [Installation], page 305.
LOADPATH is now handled in the same way as TEX handles TEXINPUTS. Leading,
trailing, or doubled colons that appear in LOADPATH are replaced by the value of
DEFAULT_LOADPATH. The default value of LOADPATH is ":", which tells Octave to
search in the directories specified by DEFAULT_LOADPATH.
In addition, if any path element ends in ‘//’, that directory and all subdirectories it
contains are searched recursively for function files. This can result in a slight delay as
Octave caches the lists of files found in the LOADPATH the first time Octave searches
for a function. After that, searching is usually much faster because Octave normally
only needs to search its internal cache for files.
To improve performance of recursive directory searching, it is best for each directory
that is to be searched recursively to contain either additional subdirectories or
function files, but not a mixture of both.
See Section 13.9 [Organization of Functions], page 104, for a description of the function
file directories that are distributed with Octave.
Built-in Functionrehash ()
Reinitialize Octave’s LOADPATH directory cache.
Built-in Functionfile in loadpath (name)
Look up name in Octave’s LOADPATH.
Built-in Variableignore function time stamp
This variable can be used to prevent Octave from making the system call stat each
time it looks up functions defined in function files. If ignore_function_time_stamp
to "system", Octave will not automatically recompile function files in subdirectories
of ‘octave-home/lib/version’ if they have changed since they were last compiled, but
will recompile other function files in the LOADPATH if they change. If set to "all",
Octave will not recompile any function files unless their definitions are removed with
clear. For any other value of ignore_function_time_stamp, Octave will always
check to see if functions defined in function files need to recompiled. The default
value of ignore_function_time_stamp is "system".
100 GNU Octave
Built-in Variablewarn function name clash
If the value of warn_function_name_clash is nonzero, a warning is issued when
Octave finds that the name of a function defined in a function file differs from the
name of the file. (If the names disagree, the name declared inside the file is ignored.)
If the value is 0, the warning is omitted. The default value is 1.
Built-in Variablewarn future time stamp
If the value of this variable is nonzero, Octave will print a warning if it finds a function
file with a time stamp that is in the future.
13.7 Script Files
A script file is a file containing (almost) any sequence of Octave commands. It is read
and evaluated just as if you had typed each command at the Octave prompt, and provides
a convenient way to perform a sequence of commands that do not logically belong inside a
function.
Unlike a function file, a script file must not begin with the keyword function. If it does,
Octave will assume that it is a function file, and that it defines a single function that should
be evaluated as soon as it is defined.
A script file also differs from a function file in that the variables named in a script file
are not local variables, but are in the same scope as the other variables that are visible on
the command line.
Even though a script file may not begin with the function keyword, it is possible to
define more than one function in a single script file and load (but not execute) all of them
at once. To do this, the first token in the file (ignoring comments and other white space)
must be something other than function. If you have no other statements to evaluate, you
can use a statement that has no effect, like this:
# Prevent Octave from thinking that this
# is a function file:
1;
# Define function one:
function one ()
...
To have Octave read and compile these functions into an internal form, you need to make
sure that the file is in Octave’s LOADPATH, then simply type the base name of the file that
contains the commands. (Octave uses the same rules to search for script files as it does to
search for function files.)
If the first token in a file (ignoring comments) is function, Octave will compile the function
and try to execute it, printing a message warning about any non-whitespace characters
that appear after the function definition.
Note that Octave does not try to look up the definition of any identifier until it needs
to evaluate it. This means that Octave will compile the following statements if they appear
in a script file, or are typed at the command line,
Chapter 13: Functions and Script Files 101
# not a function file:
1;
function foo ()
do_something ();
endfunction
function do_something ()
do_something_else ();
endfunction
even though the function do_something is not defined before it is referenced in the function
foo. This is not an error because Octave does not need to resolve all symbols that are
referenced by a function until the function is actually evaluated.
Since Octave doesn’t look for definitions until they are needed, the following code will
always print ‘bar = 3’ whether it is typed directly on the command line, read from a script
file, or is part of a function body, even if there is a function or script file called ‘bar.m’ in
Octave’s LOADPATH.
eval ("bar = 3");
bar
Code like this appearing within a function body could fool Octave if definitions were
resolved as the function was being compiled. It would be virtually impossible to make
Octave clever enough to evaluate this code in a consistent fashion. The parser would have
to be able to perform the call to eval at compile time, and that would be impossible unless
all the references in the string to be evaluated could also be resolved, and requiring that
would be too restrictive (the string might come from user input, or depend on things that
are not known until the function is evaluated).
Although Octave normally executes commands from script files that have the name
‘file.m’, you can use the function source to execute commands from any file.
Built-in Functionsource (file)
Parse and execute the contents of file. This is equivalent to executing commands from
a script file, but without requiring the file to be named ‘file.m’.
13.8 Dynamically Linked Functions
On some systems, Octave can dynamically load and execute functions written in C++.
Octave can only directly call functions written in C++, but you can also load functions
written in other languages by calling them from a simple wrapper function written in C++.
Here is an example of how to write a C++ function that Octave can load, with commentary.
The source for this function is included in the source distributions of Octave, in the
file ‘examples/oregonator.cc’. It defines the same set of differential equations that are
used in the example problem of Section 22.1 [Ordinary Differential Equations], page 177.
By running that example and this one, we can compare the execution times to see what
sort of increase in speed you can expect by using dynamically linked functions.
The function defined in ‘oregonator.cc’ contains just 8 statements, and is not much
different than the code defined in the corresponding M-file (also distributed with Octave in
the file ‘examples/oregonator.m’).
Here is the complete text of ‘oregonator.cc’:
102 GNU Octave
just
#include <octave/oct.h>
DEFUN_DLD (oregonator, args, ,
"The ‘oregonator’.")
{
ColumnVector dx (3);
ColumnVector x (args(0).vector_value ());
dx(0) = 77.27 * (x(1) - x(0)*x(1) + x(0)
- 8.375e-06*pow (x(0), 2));
dx(1) = (x(2) - x(0)*x(1) - x(1)) / 77.27;
dx(2) = 0.161*(x(0) - x(2));
return octave_value (dx);
}
The first line of the file,
#include <octave/oct.h>
includes declarations for all of Octave’s internal functions that you will need. If you need
other functions from the standard C++ or C libraries, you can include the necessary headers
here.
The next two lines
DEFUN_DLD (oregonator, args, ,
"The ‘oregonator’.")
declares the function. The macro DEFUN_DLD and the macros that it depends on are defined
in the files ‘defun-dld.h’, ‘defun.h’, and ‘defun-int.h’ (these files are included in the
header file ‘octave/oct.h’).
Note that the third parameter to DEFUN_DLD (nargout) is not used, so it is omitted
from the list of arguments in order to avoid the warning from gcc about an unused function
parameter.
The next line,
ColumnVector dx (3);
simply declares an object to store the right hand sides of the differential equation, and the
statement
ColumnVector x (args(0).vector_value ());
extracts a vector from the first input argument. The vector_value method is used so
that the user of the function can pass either a row or column vector. The ColumnVector
constructor is needed because the ODE class requires a column vector. The variable args
is passed to functions defined with DEFUN_DLD as an octave_value_list object, which
includes methods for getting the length of the list and extracting individual elements.
In this example, we don’t check for errors, but that is not difficult. All of the Octave’s
built-in functions do some form of checking on their arguments, so you can check the source
Chapter 13: Functions and Script Files 103
code for those functions for examples of various strategies for verifying that the correct
number and types of arguments have been supplied.
The next statements
ColumnVector dx (3);
dx(0) = 77.27 * (x(1) - x(0)*x(1) + x(0)
- 8.375e-06*pow (x(0), 2));
dx(1) = (x(2) - x(0)*x(1) - x(1)) / 77.27;
dx(2) = 0.161*(x(0) - x(2));
define the right hand side of the differential equation. Finally, we can return dx:
return octave_value (dx);
The actual return type is octave_value_list, but it is only necessary to convert the return
type to an octave_value because there is a default constructor that can automatically
create an object of that type from an octave_value object, so we can just use that instead.
To use this file, your version of Octave must support dynamic linking. To find out if
it does, type the command octave_config_info ("dld") at the Octave prompt. Support
for dynamic linking is included if this command returns 1.
To compile the example file, type the command ‘mkoctfile oregonator.cc’ at the shell
prompt. The script mkoctfile should have been installed along with Octave. Running
it will create a file called ‘oregonator.oct’ that can be loaded by Octave. To test the
‘oregonator.oct’ file, start Octave and type the command
oregonator ([1, 2, 3], 0)
at the Octave prompt. Octave should respond by printing
ans =
77.269353
-0.012942
-0.322000
You can now use the ‘oregonator.oct’ file just as you would the oregonator.m file to
solve the set of differential equations.
On a 133 MHz Pentium running Linux, Octave can solve the problem shown in Section
22.1 [Ordinary Differential Equations], page 177, in about 1.4 seconds using the dynamically
linked function, compared to about 19 seconds using the M-file. Similar decreases
in execution time can be expected for other functions, particularly those that rely on functions
like lsode that require user-supplied functions.
Just as for M-files, Octave will automatically reload a dynamically linked function when
the file that defines it is more recent than the last time that the function was loaded. If
more than one function is defined in a single ‘.oct’ file, reloading the file may force other
functions to be cleared and reloaded. If all the functions loaded from a given ‘.oct’ file are
cleared, Octave will automatically unload the ‘.oct’ file.
104 GNU Octave
Built-in Variablewarn reload forces clear
If several functions have been loaded from the same file, Octave must clear all the
functions before any one of them can be reloaded. If warn_reload_forces_clear,
Octave will warn you when this happens, and print a list of the additional functions
that it is forced to clear.
variables can hide functionsIf the value of this variable is nonzero, assignments to
variables may
hide previously defined functions of the same name. A negative value will cause
Octave to print a warning, but allow the operation.
Additional examples for writing dynamically linked functions are available in the files in
the ‘src’ directory of the Octave distribution. Currently, this includes the files
balance.cc fft2.cc inv.cc qzval.cc
chol.cc filter.cc log.cc schur.cc
colloc.cc find.cc lsode.cc sort.cc
dassl.cc fsolve.cc lu.cc svd.cc
det.cc givens.cc minmax.cc syl.cc
eig.cc hess.cc pinv.cc
expm.cc ifft.cc qr.cc
fft.cc ifft2.cc quad.cc
These files use the macro DEFUN_DLD_BUILTIN instead of DEFUN_DLD. The difference between
these two macros is just that DEFUN_DLD_BUILTIN can define a built-in function that is not
dynamically loaded if the operating system does not support dynamic linking. To define
your own dynamically linked functions you should use DEFUN_DLD.
There is currently no detailed description of all the functions that you can call in a
built-in function. For the time being, you will have to read the source code for Octave.
13.9 Organization of Functions Distributed with Octave
Many of Octave’s standard functions are distributed as function files. They are loosely
organized by topic, in subdirectories of ‘octave-home/lib/octave/version/m’, to make it
easier to find them.
The following is a list of all the function file subdirectories, and the types of functions
you will find there.
‘audio’ Functions for playing and recording sounds.
‘control’ Functions for design and simulation of automatic control systems.
‘elfun’ Elementary functions.
‘general’ Miscellaneous matrix manipulations, like flipud, rot90, and triu, as well as
other basic functions, like is_matrix, nargchk, etc.
‘image’ Image processing tools. These functions require the X Window System.
‘io’ Input-ouput functions.
‘linear-algebra’
Functions for linear algebra.
Chapter 13: Functions and Script Files 105
‘miscellaneous’
Functions that don’t really belong anywhere else.
‘plot’ A set of functions that implement the Matlab-like plotting functions.
‘polynomial’
Functions for manipulating polynomials.
‘set’ Functions for creating and manipulating sets of unique values.
‘signal’ Functions for signal processing applications.
‘specfun’ Special functions.
‘special-matrix’
Functions that create special matrix forms.
‘startup’ Octave’s system-wide startup file.
‘statistics’
Statistical functions.
‘strings’ Miscellaneous string-handling functions.
‘time’ Functions related to time keeping.
106 GNU Octave
Chapter 14: Error Handling 107
14 Error Handling
Octave includes several functions for printing error and warning messages. When you
write functions that need to take special action when they encounter abnormal conditions,
you should print the error messages using the functions described in this chapter.
Built-in Functionerror (template, ...)
The error function formats the optional arguments under the control of the template
string template using the same rules as the printf family of functions (see
Section 15.2.4 [Formatted Output], page 118). The resulting message is prefixed by
the string ‘error: ’ and printed on the stderr stream.
Calling error also sets Octave’s internal error state such that control will return to
the top level without evaluating any more commands. This is useful for aborting from
functions or scripts.
If the error message does not end with a new line character, Octave will print a
traceback of all the function calls leading to the error. For example, given the following
function definitions:
function f () g () end
function g () h () end
function h () nargin == 1 || error ("nargin != 1"); end
calling the function f will result in a list of messages that can help you to quickly
locate the exact location of the error:
f ()
error: nargin != 1
error: evaluating index expression near line 1, column 30
error: evaluating binary operator ‘||’ near line 1, column 27
error: called from ‘h’
error: called from ‘g’
error: called from ‘f’
If the error message ends in a new line character, Octave will print the message but
will not display any traceback messages as it returns control to the top level. For
example, modifying the error message in the previous example to end in a new line
causes Octave to only print a single message:
function h () nargin == 1 || error ("nargin != 1\n"); end
f ()
error: nargin != 1
Built-in Variableerror text
This variable contains the text of error messages that would have been printed in
the body of the most recent unwind_protect or try statement or the try part of
the most recent call to the eval function. Outside of the unwind_protect and try
statements or the eval function, or if no error has occurred within them, the value
of error_text is guaranteed to be the empty string.
Note that the message does not include the first ‘error: ’ prefix, so that it may easily
be passed to the error function without additional processing1
.
1
Yes, it’s a kluge, but it seems to be a reasonably useful one.
108 GNU Octave
See Section 12.9 [The try Statement], page 88, and Section 12.8 [The unwind protect
Statement], page 87.
Built-in Variablebeep on error
If the value of beep_on_error is nonzero, Octave will try to ring your terminal’s bell
before printing an error message. The default value is 0.
Built-in Functionwarning (msg)
Print a warning message msg prefixed by the string ‘warning: ’. After printing the
warning message, Octave will continue to execute commands. You should use this
function when you want to notify the user of an unusual condition, but only when it
makes sense for your program to go on.
Built-in Functionusage (msg)
Print the message msg, prefixed by the string ‘usage: ’, and set Octave’s internal
error state such that control will return to the top level without evaluating any more
commands. This is useful for aborting from functions.
After usage is evaluated, Octave will print a traceback of all the function calls leading
to the usage message.
You should use this function for reporting problems errors that result from an improper
call to a function, such as calling a function with an incorrect number of
arguments, or with arguments of the wrong type. For example, most functions distributed
with Octave begin with code like this
if (nargin != 2)
usage ("foo (a, b)");
endif
to check for the proper number of arguments.
The following pair of functions are of limited usefulness, and may be removed from future
versions of Octave.
Function Fileperror (name, num)
Print the error message for function name corresponding to the error number num.
This function is intended to be used to print useful error messages for those functions
that return numeric error codes.
Function Filestrerror (name, num)
Return the text of an error message for function name corresponding to the error
number num. This function is intended to be used to print useful error messages for
those functions that return numeric error codes.
Chapter 15: Input and Output 109
15 Input and Output
There are two distinct classes of input and output functions. The first set are modeled
after the functions available in Matlab. The second set are modeled after the standard
I/O library used by the C programming language and offer more flexibility and control over
the output.
When running interactively, Octave normally sends any output intended for your terminal
that is more than one screen long to a paging program, such as less or more. This
avoids the problem of having a large volume of output stream by before you can read it.
With less (and some versions of more) you can also scan forward and backward, and search
for specific items.
Normally, no output is displayed by the pager until just before Octave is ready to print
the top level prompt, or read from the standard input (for example, by using the fscanf or
scanf functions). This means that there may be some delay before any output appears on
your screen if you have asked Octave to perform a significant amount of work with a single
command statement. The function fflush may be used to force output to be sent to the
pager (or any other stream) immediately.
You can select the program to run as the pager by setting the variable PAGER, and you
can turn paging off by setting the value of the variable page_screen_output to 0.
Commandmore
Commandmore on
Commandmore off
Turn output pagination on or off. Without an argument, more toggles the current
state.
Built-in VariablePAGER
The default value is normally "less", "more", or "pg", depending on what programs
are installed on your system. See Appendix C [Installation], page 305.
When running interactively, Octave sends any output intended for your terminal that
is more than one screen long to the program named by the value of the variable PAGER.
Built-in Variablepage screen output
If the value of page_screen_output is nonzero, all output intended for the screen that
is longer than one page is sent through a pager. This allows you to view one screenful
at a time. Some pagers (such as less—see Appendix C [Installation], page 305) are
also capable of moving backward on the output. The default value is 1.
Built-in Variablepage output immediately
If the value of page_output_immediately is nonzero, Octave sends output to the
pager as soon as it is available. Otherwise, Octave buffers its output and waits until
just before the prompt is printed to flush it to the pager. The default value is 0.
110 GNU Octave
Built-in Functionfflush (fid)
Flush output to fid. This is useful for ensuring that all pending output makes it to
the screen before some other event occurs. For example, it is always a good idea to
flush the standard output stream before calling input.
15.1 Basic Input and Output
15.1.1 Terminal Output
Since Octave normally prints the value of an expression as soon as it has been evaluated,
the simplest of all I/O functions is a simple expression. For example, the following expression
will display the value of pi
pi
pi = 3.1416
This works well as long as it is acceptable to have the name of the variable (or ‘ans’)
printed along with the value. To print the value of a variable without printing its name,
use the function disp.
The format command offers some control over the way Octave prints values with disp
and through the normal echoing mechanism.
Built-in Variableans
This variable holds the most recently computed result that was not explicitly assigned
to a variable. For example, after the expression
3^2 + 4^2
is evaluated, the value of ans is 25.
Built-in Functionfdisp (fid, x)
Display the value of x on the stream fid. For example,
disp (stdout, "The value of pi is:"), disp (stdout, pi)
the value of pi is:
3.1416
Note that the output from disp always ends with a newline.
If an output value is requested, disp prints nothing and returns the formatted output
in a string.
Built-in Functiondisp (x)
Display the value of x. For example,
disp ("The value of pi is:"), disp (pi)
the value of pi is:
3.1416
Note that the output from disp always ends with a newline.
If an output value is requested, disp prints nothing and returns the formatted output
in a string.
Chapter 15: Input and Output 111
Commandformat options
Control the format of the output produced by disp and Octave’s normal echoing
mechanism. Valid options are listed in the following table.
short Octave will try to print numbers with at least 3 significant figures within
a field that is a maximum of 8 characters wide.
If Octave is unable to format a matrix so that columns line up on the
decimal point and all the numbers fit within the maximum field width, it
switches to an ‘e’ format.
long Octave will try to print numbers with at least 15 significant figures within
a field that is a maximum of 24 characters wide.
As will the ‘short’ format, Octave will switch to an ‘e’ format if it is
unable to format a matrix so that columns line up on the decimal point
and all the numbers fit within the maximum field width.
long e
short e The same as ‘format long’ or ‘format short’ but always display output
with an ‘e’ format. For example, with the ‘short e’ format, pi is displayed
as 3.14e+00.
long E
short E The same as ‘format long e’ or ‘format short e’ but always display output
with an uppercase ‘E’ format. For example, with the ‘long E’ format,
pi is displayed as 3.14159265358979E+00.
free
none Print output in free format, without trying to line up columns of matrices
on the decimal point. This also causes complex numbers to be
formatted like this ‘(0.604194, 0.607088)’ instead of like this ‘0.60419
+ 0.60709i’.
bank Print in a fixed format with two places to the right of the decimal point.
+ Print a ‘+’ symbol for nonzero matrix elements and a space for zero matrix
elements. This format can be very useful for examining the structure of
a large matrix.
hex Print the hexadecimal representation numbers as they are stored in memory.
For example, on a workstation which stores 8 byte real values in IEEE
format with the least significant byte first, the value of pi when printed
in hex format is 400921fb54442d18. This format only works for numeric
values.
bit Print the bit representation of numbers as stored in memory. For example,
the value of pi is
01000000000010010010000111111011
01010100010001000010110100011000
(shown here in two 32 bit sections for typesetting purposes) when printed
in bit format on a workstation which stores 8 byte real values in IEEE
format with the least significant byte first. This format only works for
numeric types.
112 GNU Octave
By default, Octave will try to print numbers with at least 5 significant figures within
a field that is a maximum of 10 characters wide.
If Octave is unable to format a matrix so that columns line up on the decimal point
and all the numbers fit within the maximum field width, it switches to an ‘e’ format.
If format is invoked without any options, the default format state is restored.
Built-in Variableprint answer id name
If the value of print_answer_id_name is nonzero, variable names are printed along
with the result. Otherwise, only the result values are printed. The default value is 1.
15.1.2 Terminal Input
Octave has three functions that make it easy to prompt users for input. The input and
menu functions are normally used for managing an interactive dialog with a user, and the
keyboard function is normally used for doing simple debugging.
Built-in Functioninput (prompt)
Built-in Functioninput (prompt, "s")
Print a prompt and wait for user input. For example,
input ("Pick a number, any number! ")
prints the prompt
Pick a number, any number!
and waits for the user to enter a value. The string entered by the user is evaluated
as an expression, so it may be a literal constant, a variable name, or any other valid
expression.
Currently, input only returns one value, regardless of the number of values produced
by the evaluation of the expression.
If you are only interested in getting a literal string value, you can call input with the
character string "s" as the second argument. This tells Octave to return the string
entered by the user directly, without evaluating it first.
Because there may be output waiting to be displayed by the pager, it is a good
idea to always call fflush (stdout) before calling input. This will ensure that all
pending output is written to the screen before your prompt. See Chapter 15 [Input
and Output], page 109.
Function Filemenu (title, opt1, ...)
Print a title string followed by a series of options. Each option will be printed along
with a number. The return value is the number of the option selected by the user.
This function is useful for interactive programs. There is no limit to the number of
options that may be passed in, but it may be confusing to present more than will fit
easily on one screen.
Chapter 15: Input and Output 113
Built-in Functionkeyboard (prompt)
This function is normally used for simple debugging. When the keyboard function
is executed, Octave prints a prompt and waits for user input. The input strings are
then evaluated and the results are printed. This makes it possible to examine the
values of variables within a function, and to assign new values to variables. No value
is returned from the keyboard function, and it continues to prompt for input until
the user types ‘quit’, or ‘exit’.
If keyboard is invoked without any arguments, a default prompt of ‘debug> ’ is used.
For both input and keyboard, the normal command line history and editing functions
are available at the prompt.
Octave also has a function that makes it possible to get a single character from the
keyboard without requiring the user to type a carriage return.
Built-in Functionkbhit ()
Read a single keystroke from the keyboard. If called with one argument, don’t wait
for a keypress. For example,
x = kbhit ();
will set x to the next character typed at the keyboard as soon as it is typed.
x = kbhit (1);
identical to the above example, but don’t wait for a keypress, returning the empty
string if no key is available.
15.1.3 Simple File I/O
The save and load commands allow data to be written to and read from disk files in
various formats. The default format of files written by the save command can be controlled
using the built-in variables default_save_format and save_precision.
Note that Octave can not yet save or load structure variables or any user-defined types.
Commandsave options file v1 v2 . . .
Save the named variables v1, v2, . . . in the file file. The special filename ‘-’ can be
used to write the output to your terminal. If no variable names are listed, Octave
saves all the variables in the current scope. Valid options for the save command are
listed in the following table. Options that modify the output format override the
format specified by the built-in variable default_save_format.
-ascii Save the data in Octave’s text data format.
-binary Save the data in Octave’s binary data format.
-float-binary
Save the data in Octave’s binary data format but only using single precision.
You should use this format only if you know that all the values to
be saved can be represented in single precision.
-mat-binary
Save the data in Matlab’s binary data format.
114 GNU Octave
-mat4-binary
Save the data in the binary format written by Matlab version 4.
-hdf5 Save the data in HDF5 format. (HDF5 is a free, portable binary format
developed by the National Center for Supercomputing Applications at
the University of Illinois.)
HDF5 load and save are not available, as this Octave executable was not
linked with the HDF5 library.
-float-hdf5
Save the data in HDF5 format but only using single precision. You should
use this format only if you know that all the values to be saved can be
represented in single precision.
-save-builtins
Force Octave to save the values of built-in variables too. By default,
Octave does not save built-in variables.
The list of variables to save may include wildcard patterns containing the following
special characters:
? Match any single character.
* Match zero or more characters.
[ list ] Match the list of characters specified by list. If the first character is !
or ^, match all characters except those specified by list. For example,
the pattern ‘[a-zA-Z]’ will match all lower and upper case alphabetic
characters.
Except when using the Matlab binary data file format, saving global variables also
saves the global status of the variable, so that if it is restored at a later time using
‘load’, it will be restored as a global variable.
The command
save -binary data a b*
saves the variable ‘a’ and all variables beginning with ‘b’ to the file ‘data’ in Octave’s
binary format.
There are three variables that modify the behavior of save and one that controls whether
variables are saved when Octave exits unexpectedly.
Built-in Variablecrash dumps octave core
If this variable is set to a nonzero value, Octave tries to save all current variables the
the file "octave-core" if it crashes or receives a hangup, terminate or similar signal.
The default value is 1.
Built-in Variabledefault save format
This variable specifies the default format for the save command. It should have one
of the following values: "ascii", "binary", float-binary, or "mat-binary". The
initial default save format is Octave’s text format.
Chapter 15: Input and Output 115
Built-in Variablesave precision
This variable specifies the number of digits to keep when saving data in text format.
The default value is 17.
Commandload options file v1 v2 . . .
Load the named variables from the file file. As with save, you may specify a list
of variables and load will only extract those variables with names that match. For
example, to restore the variables saved in the file ‘data’, use the command
load data
Octave will refuse to overwrite existing variables unless you use the option ‘-force’.
If a variable that is not marked as global is loaded from a file when a global symbol
with the same name already exists, it is loaded in the global symbol table. Also, if
a variable is marked as global in a file and a local symbol exists, the local symbol is
moved to the global symbol table and given the value from the file. Since it seems
that both of these cases are likely to be the result of some sort of error, they will
generate warnings.
The load command can read data stored in Octave’s text and binary formats, and
Matlab’s binary format. It will automatically detect the type of file and do conversion
from different floating point formats (currently only IEEE big and little endian,
though other formats may added in the future).
Valid options for load are listed in the following table.
-force Force variables currently in memory to be overwritten by variables with
the same name found in the file.
-ascii Force Octave to assume the file is in Octave’s text format.
-binary Force Octave to assume the file is in Octave’s binary format.
-mat-binary
Force Octave to assume the file is in Matlab’s binary format.
-mat4-binary
Force Octave to assume the file is in the binary format written by Matlab
version 4.
-hdf5 Force Octave to assume the file is in HDF5 format. (HDF5 is a free,
portable binary format developed by the National Center for Supercomputing
Applications at the University of Illinois.) Note that Octave can
read HDF5 files not created by itself, but may skip some datasets in formats
that it cannot support. In particular, it will skip datasets of data
types that it does not recognize, with dimensionality > 2, or with names
that aren’t valid Octave identifiers See, however, the ‘-import’ option to
ameliorate this somewhat.
HDF5 load and save are not available, as this Octave executable was not
linked with the HDF5 library.
-import Make a stronger attempt to import foreign datasets. Currently, this
means that for HDF5 files, invalid characters in names are converted to
116 GNU Octave
‘_’, and datasets with dimensionality > 2 are imported as lists of matrices
(or lists of lists of matrices, or ...).
15.2 C-Style I/O Functions
Octave’s C-style input and output functions provide most of the functionality of the C
programming language’s standard I/O library. The argument lists for some of the input
functions are slightly different, however, because Octave has no way of passing arguments
by reference.
In the following, file refers to a file name and fid refers to an integer file number, as
returned by fopen.
There are three files that are always available. Although these files can be accessed using
their corresponding numeric file ids, you should always use the symbolic names given in the
table below, since it will make your programs easier to understand.
Built-in Variablestdin
The standard input stream (file id 0). When Octave is used interactively, this is
filtered through the command line editing functions.
Built-in Variablestdout
The standard output stream (file id 1). Data written to the standard output is
normally filtered through the pager.
Built-in Variablestderr
The standard error stream (file id 2). Even if paging is turned on, the standard error
is not sent to the pager. It is useful for error messages and prompts.
15.2.1 Opening and Closing Files
Built-in Function[fid, msg] = fopen (name, mode, arch)
Built-in Functionfid list = fopen ("all")
Built-in Functionfile = fopen (fid)
The first form of the fopen function opens the named file with the specified mode
(read-write, read-only, etc.) and architecture interpretation (IEEE big endian, IEEE
little endian, etc.), and returns an integer value that may be used to refer to the file
later. If an error occurs, fid is set to −1 and msg contains the corresponding system
error message. The mode is a one or two character string that specifies whether the
file is to be opened for reading, writing, or both.
The second form of the fopen function returns a vector of file ids corresponding to
all the currently open files, excluding the stdin, stdout, and stderr streams.
The third form of the fopen function returns the name of a currently open file given
its file id.
For example,
Chapter 15: Input and Output 117
myfile = fopen ("splat.dat", "r", "ieee-le");
opens the file ‘splat.dat’ for reading. If necessary, binary numeric values will be
read assuming they are stored in IEEE format with the least significant bit first, and
then converted to the native representation.
Opening a file that is already open simply opens it again and returns a separate file
id. It is not an error to open a file several times, though writing to the same file
through several different file ids may produce unexpected results.
The possible values ‘mode’ may have are
‘r’ Open a file for reading.
‘w’ Open a file for writing. The previous contents are discared.
‘a’ Open or create a file for writing at the end of the file.
‘r+’ Open an existing file for reading and writing.
‘w+’ Open a file for reading or writing. The previous contents are discarded.
‘a+’ Open or create a file for reading or writing at the end of the file.
The parameter arch is a string specifying the default data format for the file. Valid
values for arch are:
‘native’ The format of the current machine (this is the default).
‘ieee-le’ IEEE big endian format.
‘ieee-be’ IEEE little endian format.
‘vaxd’ VAX D floating format.
‘vaxg’ VAX G floating format.
‘cray’ Cray floating format.
however, conversions are currently only supported for ‘native’ ‘ieee-be’, and
‘ieee-le’ formats.
Built-in Functionfclose (fid)
Closes the specified file. If an error is encountered while trying to close the file, an
error message is printed and fclose returns 0. Otherwise, it returns 1.
15.2.2 Simple Output
Built-in Functionfputs (fid, string)
Write a string to a file with no formatting.
Function Fileputs (string)
Write a string to the standard output with no formatting.
118 GNU Octave
15.2.3 Line-Oriented Input
Built-in Functionfgetl (fid, len)
Read characters from a file, stopping after a newline, or EOF, or len characters have
been read. The characters read, excluding the possible trailing newline, are returned
as a string.
If len is omitted, fgetl reads until the next newline character.
If there are no more characters to read, fgetl returns −1.
Built-in Functionfgets (fid, len)
Read characters from a file, stopping after a newline, or EOF, or len characters have
been read. The characters read, including the possible trailing newline, are returned
as a string.
If len is omitted, fgets reads until the next newline character.
If there are no more characters to read, fgets returns −1.
15.2.4 Formatted Output
This section describes how to call printf and related functions.
The following functions are available for formatted output. They are modelled after the
C language functions of the same name, but they interpret the format template differently
in order to improve the performance of printing vector and matrix values.
Function Fileprintf (template, ...)
The printf function prints the optional arguments under the control of the template
string template to the stream stdout.
Built-in Functionfprintf (fid, template, ...)
This function is just like printf, except that the output is written to the stream fid
instead of stdout.
Built-in Functionsprintf (template, ...)
This is like printf, except that the output is returned as a string. Unlike the C
library function, which requires you to provide a suitably sized string as an argument,
Octave’s sprintf function returns the string, automatically sized to hold all of the
items converted.
The printf function can be used to print any number of arguments. The template
string argument you supply in a call provides information not only about the number of
additional arguments, but also about their types and what style should be used for printing
them.
Ordinary characters in the template string are simply written to the output stream
as-is, while conversion specifications introduced by a ‘%’ character in the template cause
subsequent arguments to be formatted and written to the output stream. For example,
Chapter 15: Input and Output 119
pct = 37;
filename = "foo.txt";
printf ("Processing of ‘%s’ is %d%% finished.\nPlease be patient.\n",
filename, pct);
produces output like
Processing of ‘foo.txt’ is 37% finished.
Please be patient.
This example shows the use of the ‘%d’ conversion to specify that a scalar argument
should be printed in decimal notation, the ‘%s’ conversion to specify printing of a string
argument, and the ‘%%’ conversion to print a literal ‘%’ character.
There are also conversions for printing an integer argument as an unsigned value in
octal, decimal, or hexadecimal radix (‘%o’, ‘%u’, or ‘%x’, respectively); or as a character
value (‘%c’).
Floating-point numbers can be printed in normal, fixed-point notation using the ‘%f’
conversion or in exponential notation using the ‘%e’ conversion. The ‘%g’ conversion uses
either ‘%e’ or ‘%f’ format, depending on what is more appropriate for the magnitude of the
particular number.
You can control formatting more precisely by writing modifiers between the ‘%’ and
the character that indicates which conversion to apply. These slightly alter the ordinary
behavior of the conversion. For example, most conversion specifications permit you to
specify a minimum field width and a flag indicating whether you want the result left- or
right-justified within the field.
The specific flags and modifiers that are permitted and their interpretation vary depending
on the particular conversion. They’re all described in more detail in the following
sections.
15.2.5 Output Conversion for Matrices
When given a matrix value, Octave’s formatted output functions cycle through the
format template until all the values in the matrix have been printed. For example,
printf ("%4.2f %10.2e %8.4g\n", hilb (3));
1.00 5.00e-01 0.3333
0.50 3.33e-01 0.25
0.33 2.50e-01 0.2
If more than one value is to be printed in a single call, the output functions do not
return to the beginning of the format template when moving on from one value to the next.
This can lead to confusing output if the number of elements in the matrices are not exact
multiples of the number of conversions in the format template. For example,
printf ("%4.2f %10.2e %8.4g\n", [1, 2], [3, 4]);
1.00 2.00e+00 3
4.00
If this is not what you want, use a series of calls instead of just one.
120 GNU Octave
15.2.6 Output Conversion Syntax
This section provides details about the precise syntax of conversion specifications that
can appear in a printf template string.
Characters in the template string that are not part of a conversion specification are
printed as-is to the output stream.
The conversion specifications in a printf template string have the general form:
% flags width [ . precision ] type conversion
For example, in the conversion specifier ‘%-10.8ld’, the ‘-’ is a flag, ‘10’ specifies the field
width, the precision is ‘8’, the letter ‘l’ is a type modifier, and ‘d’ specifies the conversion
style. (This particular type specifier says to print a numeric argument in decimal notation,
with a minimum of 8 digits left-justified in a field at least 10 characters wide.)
In more detail, output conversion specifications consist of an initial ‘%’ character followed
in sequence by:
• Zero or more flag characters that modify the normal behavior of the conversion speci-
fication.
• An optional decimal integer specifying the minimum field width. If the normal conversion
produces fewer characters than this, the field is padded with spaces to the specified
width. This is a minimum value; if the normal conversion produces more characters
than this, the field is not truncated. Normally, the output is right-justified within the
field.
You can also specify a field width of ‘*’. This means that the next argument in the
argument list (before the actual value to be printed) is used as the field width. The
value is rounded to the nearest integer. If the value is negative, this means to set the
‘-’ flag (see below) and to use the absolute value as the field width.
• An optional precision to specify the number of digits to be written for the numeric
conversions. If the precision is specified, it consists of a period (‘.’) followed optionally
by a decimal integer (which defaults to zero if omitted).
You can also specify a precision of ‘*’. This means that the next argument in the
argument list (before the actual value to be printed) is used as the precision. The value
must be an integer, and is ignored if it is negative.
• An optional type modifier character. This character is ignored by Octave’s printf
function, but is recognized to provide compatibility with the C language printf.
• A character that specifies the conversion to be applied.
The exact options that are permitted and how they are interpreted vary between the
different conversion specifiers. See the descriptions of the individual conversions for information
about the particular options that they use.
15.2.7 Table of Output Conversions
Here is a table summarizing what all the different conversions do:
‘%d’, ‘%i’ Print an integer as a signed decimal number. See Section 15.2.8 [Integer Conversions],
page 121, for details. ‘%d’ and ‘%i’ are synonymous for output, but are
different when used with scanf for input (see Section 15.2.13 [Table of Input
Conversions], page 125).
Chapter 15: Input and Output 121
‘%o’ Print an integer as an unsigned octal number. See Section 15.2.8 [Integer Conversions],
page 121, for details.
‘%u’ Print an integer as an unsigned decimal number. See Section 15.2.8 [Integer
Conversions], page 121, for details.
‘%x’, ‘%X’ Print an integer as an unsigned hexadecimal number. ‘%x’ uses lower-case letters
and ‘%X’ uses upper-case. See Section 15.2.8 [Integer Conversions], page 121,
for details.
‘%f’ Print a floating-point number in normal (fixed-point) notation. See
Section 15.2.9 [Floating-Point Conversions], page 122, for details.
‘%e’, ‘%E’ Print a floating-point number in exponential notation. ‘%e’ uses lower-case letters
and ‘%E’ uses upper-case. See Section 15.2.9 [Floating-Point Conversions],
page 122, for details.
‘%g’, ‘%G’ Print a floating-point number in either normal (fixed-point) or exponential notation,
whichever is more appropriate for its magnitude. ‘%g’ uses lower-case
letters and ‘%G’ uses upper-case. See Section 15.2.9 [Floating-Point Conversions],
page 122, for details.
‘%c’ Print a single character. See Section 15.2.10 [Other Output Conversions],
page 123.
‘%s’ Print a string. See Section 15.2.10 [Other Output Conversions], page 123.
‘%%’ Print a literal ‘%’ character. See Section 15.2.10 [Other Output Conversions],
page 123.
If the syntax of a conversion specification is invalid, unpredictable things will happen,
so don’t do this. If there aren’t enough function arguments provided to supply values for
all the conversion specifications in the template string, or if the arguments are not of the
correct types, the results are unpredictable. If you supply more arguments than conversion
specifications, the extra argument values are simply ignored; this is sometimes useful.
15.2.8 Integer Conversions
This section describes the options for the ‘%d’, ‘%i’, ‘%o’, ‘%u’, ‘%x’, and ‘%X’ conversion
specifications. These conversions print integers in various formats.
The ‘%d’ and ‘%i’ conversion specifications both print an numeric argument as a signed
decimal number; while ‘%o’, ‘%u’, and ‘%x’ print the argument as an unsigned octal, decimal,
or hexadecimal number (respectively). The ‘%X’ conversion specification is just like ‘%x’
except that it uses the characters ‘ABCDEF’ as digits instead of ‘abcdef’.
The following flags are meaningful:
‘-’ Left-justify the result in the field (instead of the normal right-justification).
‘+’ For the signed ‘%d’ and ‘%i’ conversions, print a plus sign if the value is positive.
‘ ’ For the signed ‘%d’ and ‘%i’ conversions, if the result doesn’t start with a plus
or minus sign, prefix it with a space character instead. Since the ‘+’ flag ensures
that the result includes a sign, this flag is ignored if you supply both of them.
122 GNU Octave
‘#’ For the ‘%o’ conversion, this forces the leading digit to be ‘0’, as if by increasing
the precision. For ‘%x’ or ‘%X’, this prefixes a leading ‘0x’ or ‘0X’ (respectively) to
the result. This doesn’t do anything useful for the ‘%d’, ‘%i’, or ‘%u’ conversions.
‘0’ Pad the field with zeros instead of spaces. The zeros are placed after any
indication of sign or base. This flag is ignored if the ‘-’ flag is also specified, or
if a precision is specified.
If a precision is supplied, it specifies the minimum number of digits to appear; leading
zeros are produced if necessary. If you don’t specify a precision, the number is printed with
as many digits as it needs. If you convert a value of zero with an explicit precision of zero,
then no characters at all are produced.
15.2.9 Floating-Point Conversions
This section discusses the conversion specifications for floating-point numbers: the ‘%f’,
‘%e’, ‘%E’, ‘%g’, and ‘%G’ conversions.
The ‘%f’ conversion prints its argument in fixed-point notation, producing output of the
form [-]ddd.ddd, where the number of digits following the decimal point is controlled by
the precision you specify.
The ‘%e’ conversion prints its argument in exponential notation, producing output of
the form [-]d.ddde[+|-]dd. Again, the number of digits following the decimal point is
controlled by the precision. The exponent always contains at least two digits. The ‘%E’
conversion is similar but the exponent is marked with the letter ‘E’ instead of ‘e’.
The ‘%g’ and ‘%G’ conversions print the argument in the style of ‘%e’ or ‘%E’ (respectively)
if the exponent would be less than -4 or greater than or equal to the precision; otherwise
they use the ‘%f’ style. Trailing zeros are removed from the fractional portion of the result
and a decimal-point character appears only if it is followed by a digit.
The following flags can be used to modify the behavior:
‘-’ Left-justify the result in the field. Normally the result is right-justified.
‘+’ Always include a plus or minus sign in the result.
‘ ’ If the result doesn’t start with a plus or minus sign, prefix it with a space
instead. Since the ‘+’ flag ensures that the result includes a sign, this flag is
ignored if you supply both of them.
‘#’ Specifies that the result should always include a decimal point, even if no digits
follow it. For the ‘%g’ and ‘%G’ conversions, this also forces trailing zeros after
the decimal point to be left in place where they would otherwise be removed.
‘0’ Pad the field with zeros instead of spaces; the zeros are placed after any sign.
This flag is ignored if the ‘-’ flag is also specified.
The precision specifies how many digits follow the decimal-point character for the ‘%f’,
‘%e’, and ‘%E’ conversions. For these conversions, the default precision is 6. If the precision
is explicitly 0, this suppresses the decimal point character entirely. For the ‘%g’ and ‘%G’
conversions, the precision specifies how many significant digits to print. Significant digits
are the first digit before the decimal point, and all the digits after it. If the precision is 0
or not specified for ‘%g’ or ‘%G’, it is treated like a value of 1. If the value being printed
Chapter 15: Input and Output 123
cannot be expressed precisely in the specified number of digits, the value is rounded to the
nearest number that fits.
15.2.10 Other Output Conversions
This section describes miscellaneous conversions for printf.
The ‘%c’ conversion prints a single character. The ‘-’ flag can be used to specify leftjustification
in the field, but no other flags are defined, and no precision or type modifier
can be given. For example:
printf ("%c%c%c%c%c", "h", "e", "l", "l", "o");
prints ‘hello’.
The ‘%s’ conversion prints a string. The corresponding argument must be a string. A
precision can be specified to indicate the maximum number of characters to write; otherwise
characters in the string up to but not including the terminating null character are written
to the output stream. The ‘-’ flag can be used to specify left-justification in the field, but
no other flags or type modifiers are defined for this conversion. For example:
printf ("%3s%-6s", "no", "where");
prints ‘ nowhere ’ (note the leading and trailing spaces).
15.2.11 Formatted Input
Octave provides the scanf, fscanf, and sscanf functions to read formatted input.
There are two forms of each of these functions. One can be used to extract vectors of data
from a file, and the other is more ‘C-like’.
Built-in Function[val, count] = fscanf (fid, template, size)
Built-in Function[v1, v2, ..., count] = fscanf (fid, template, "C")
In the first form, read from fid according to template, returning the result in the
matrix val.
The optional argument size specifies the amount of data to read and may be one of
Inf Read as much as possible, returning a column vector.
nr Read up to nr elements, returning a column vector.
[nr, Inf] Read as much as possible, returning a matrix with nr rows. If the number
of elements read is not an exact multiple of nr, the last column is padded
with zeros.
[nr, nc] Read up to nr * nc elements, returning a matrix with nr rows. If the
number of elements read is not an exact multiple of nr, the last column
is padded with zeros.
If size is omitted, a value of Inf is assumed.
A string is returned if template specifies only character conversions.
The number of items successfully read is returned in count.
In the second form, read from fid according to template, with each conversion specifier
in template corresponding to a single scalar return value. This form is more ‘C-like’,
and also compatible with previous versions of Octave. The number of successful
conversions is returned in count
124 GNU Octave
Built-in Function[val, count] = sscanf (string, template, size)
Built-in Function[v1, v2, ..., count] = sscanf (string, template, "C")
This is like fscanf, except that the characters are taken from the string string instead
of from a stream. Reaching the end of the string is treated as an end-of-file condition.
Calls to scanf are superficially similar to calls to printf in that arbitrary arguments are
read under the control of a template string. While the syntax of the conversion specifications
in the template is very similar to that for printf, the interpretation of the template is
oriented more towards free-format input and simple pattern matching, rather than fixedfield
formatting. For example, most scanf conversions skip over any amount of “white
space” (including spaces, tabs, and newlines) in the input file, and there is no concept
of precision for the numeric input conversions as there is for the corresponding output
conversions. Ordinarily, non-whitespace characters in the template are expected to match
characters in the input stream exactly.
When a matching failure occurs, scanf returns immediately, leaving the first nonmatching
character as the next character to be read from the stream, and scanf returns all
the items that were successfully converted.
The formatted input functions are not used as frequently as the formatted output functions.
Partly, this is because it takes some care to use them properly. Another reason is
that it is difficult to recover from a matching error.
15.2.12 Input Conversion Syntax
A scanf template string is a string that contains ordinary multibyte characters interspersed
with conversion specifications that start with ‘%’.
Any whitespace character in the template causes any number of whitespace characters
in the input stream to be read and discarded. The whitespace characters that are matched
need not be exactly the same whitespace characters that appear in the template string. For
example, write ‘ , ’ in the template to recognize a comma with optional whitespace before
and after.
Other characters in the template string that are not part of conversion specifications
must match characters in the input stream exactly; if this is not the case, a matching
failure occurs.
The conversion specifications in a scanf template string have the general form:
% flags width type conversion
In more detail, an input conversion specification consists of an initial ‘%’ character followed
in sequence by:
• An optional flag character ‘*’, which says to ignore the text read for this specification.
When scanf finds a conversion specification that uses this flag, it reads input as directed
by the rest of the conversion specification, but it discards this input, does not return
any value, and does not increment the count of successful assignments.
• An optional decimal integer that specifies the maximum field width. Reading of characters
from the input stream stops either when this maximum is reached or when a
non-matching character is found, whichever happens first. Most conversions discard
initial whitespace characters, and these discarded characters don’t count towards the
Chapter 15: Input and Output 125
maximum field width. Conversions that do not discard initial whitespace are explicitly
documented.
• An optional type modifier character. This character is ignored by Octave’s scanf
function, but is recognized to provide compatibility with the C language scanf.
• A character that specifies the conversion to be applied.
The exact options that are permitted and how they are interpreted vary between the
different conversion specifiers. See the descriptions of the individual conversions for information
about the particular options that they allow.
15.2.13 Table of Input Conversions
Here is a table that summarizes the various conversion specifications:
‘%d’ Matches an optionally signed integer written in decimal. See Section 15.2.14
[Numeric Input Conversions], page 126.
‘%i’ Matches an optionally signed integer in any of the formats that the C language
defines for specifying an integer constant. See Section 15.2.14 [Numeric Input
Conversions], page 126.
‘%o’ Matches an unsigned integer written in octal radix. See Section 15.2.14 [Numeric
Input Conversions], page 126.
‘%u’ Matches an unsigned integer written in decimal radix. See Section 15.2.14
[Numeric Input Conversions], page 126.
‘%x’, ‘%X’ Matches an unsigned integer written in hexadecimal radix. See Section 15.2.14
[Numeric Input Conversions], page 126.
‘%e’, ‘%f’, ‘%g’, ‘%E’, ‘%G’
Matches an optionally signed floating-point number. See Section 15.2.14 [Numeric
Input Conversions], page 126.
‘%s’ Matches a string containing only non-whitespace characters. See Section 15.2.15
[String Input Conversions], page 126.
‘%c’ Matches a string of one or more characters; the number of characters read
is controlled by the maximum field width given for the conversion. See Section
15.2.15 [String Input Conversions], page 126.
‘%%’ This matches a literal ‘%’ character in the input stream. No corresponding
argument is used.
If the syntax of a conversion specification is invalid, the behavior is undefined. If there
aren’t enough function arguments provided to supply addresses for all the conversion specifications
in the template strings that perform assignments, or if the arguments are not of
the correct types, the behavior is also undefined. On the other hand, extra arguments are
simply ignored.
126 GNU Octave
15.2.14 Numeric Input Conversions
This section describes the scanf conversions for reading numeric values.
The ‘%d’ conversion matches an optionally signed integer in decimal radix.
The ‘%i’ conversion matches an optionally signed integer in any of the formats that the
C language defines for specifying an integer constant.
For example, any of the strings ‘10’, ‘0xa’, or ‘012’ could be read in as integers under
the ‘%i’ conversion. Each of these specifies a number with decimal value 10.
The ‘%o’, ‘%u’, and ‘%x’ conversions match unsigned integers in octal, decimal, and hexadecimal
radices, respectively.
The ‘%X’ conversion is identical to the ‘%x’ conversion. They both permit either uppercase
or lowercase letters to be used as digits.
Unlike the C language scanf, Octave ignores the ‘h’, ‘l’, and ‘L’ modifiers.
15.2.15 String Input Conversions
This section describes the scanf input conversions for reading string and character
values: ‘%s’ and ‘%c’.
The ‘%c’ conversion is the simplest: it matches a fixed number of characters, always. The
maximum field with says how many characters to read; if you don’t specify the maximum,
the default is 1. This conversion does not skip over initial whitespace characters. It reads
precisely the next n characters, and fails if it cannot get that many.
The ‘%s’ conversion matches a string of non-whitespace characters. It skips and discards
initial whitespace, but stops when it encounters more whitespace after having read
something.
For example, reading the input:
hello, world
with the conversion ‘%10c’ produces " hello, wo", but reading the same input with the
conversion ‘%10s’ produces "hello,".
15.2.16 Binary I/O
Octave can read and write binary data using the functions fread and fwrite, which are
patterned after the standard C functions with the same names. The are able to automatically
swap the byte order of integer data and convert among ths supported floating point
formats as the data are read.
Built-in Function[val, count] = fread (fid, size, precision, skip, arch)
Read binary data of type precision from the specified file ID fid.
The optional argument size specifies the amount of data to read and may be one of
Inf Read as much as possible, returning a column vector.
nr Read up to nr elements, returning a column vector.
Chapter 15: Input and Output 127
[nr, Inf] Read as much as possible, returning a matrix with nr rows. If the number
of elements read is not an exact multiple of nr, the last column is padded
with zeros.
[nr, nc] Read up to nr * nc elements, returning a matrix with nr rows. If the
number of elements read is not an exact multiple of nr, the last column
is padded with zeros.
If size is omitted, a value of Inf is assumed.
The optional argument precision is a string specifying the type of data to read and
may be one of
"char"
"char*1"
"integer*1"
"int8" Single character.
"signed char"
"schar" Signed character.
"unsigned char"
"uchar" Unsigned character.
"short" Short integer.
"unsigned short"
"ushort" Unsigned short integer.
"int" Integer.
"unsigned int"
"uint" Unsigned integer.
"long" Long integer.
"unsigned long"
"ulong" Unsigned long integer.
"float"
"float32"
"real*4" Single precision float.
"double"
"float64"
"real*8" Double precision float.
"integer*2"
"int16" Two byte integer.
"integer*4"
"int32" Four byte integer.
The default precision is "uchar".
The optional argument skip specifies the number of bytes to skip before each element
is read. If it is not specified, a value of 0 is assumed.
The optional argument arch is a string specifying the data format for the file. Valid
values are
128 GNU Octave
"native" The format of the current machine.
"ieee-le"
IEEE big endian.
"ieee-be"
IEEE little endian.
"vaxd" VAX D floating format.
"vaxg" VAX G floating format.
"cray" Cray floating format.
Conversions are currently only supported for "ieee-be" and "ieee-le" formats.
The data read from the file is returned in val, and the number of values read is
returned in count
Built-in Functioncount = fwrite (fid, data, precision, skip, arch)
Write data in binary form of type precision to the specified file ID fid, returning the
number of values successfully written to the file.
The argument data is a matrix of values that are to be written to the file. The values
are extracted in column-major order.
The remaining arguments precision, skip, and arch are optional, and are interpreted
as described for fread.
The behavior of fwrite is undefined if the values in data are too large to fit in the
specified precision.
15.2.17 Temporary Files
Built-in Functiontmpnam ()
Return a unique temporary file name as a string.
Since the named file is not opened, by tmpnam, it is possible (though relatively unlikely)
that it will not be available by the time your program attempts to open it.
15.2.18 End of File and Errors
Built-in Functionfeof (fid)
Return 1 if an end-of-file condition has been encountered for a given file and 0 otherwise.
Note that it will only return 1 if the end of the file has already been encountered,
not if the next read operation will result in an end-of-file condition.
Built-in Functionferror (fid)
Return 1 if an error condition has been encountered for a given file and 0 otherwise.
Note that it will only return 1 if an error has already been encountered, not if the
next operation will result in an error condition.
Chapter 15: Input and Output 129
Built-in Functionfreport ()
Print a list of which files have been opened, and whether they are open for reading,
writing, or both. For example,
freport ()
number mode name
0 r stdin
1 w stdout
2 w stderr
3 r myfile
15.2.19 File Positioning
Three functions are available for setting and determining the position of the file pointer
for a given file.
Built-in Functionftell (fid)
Return the position of the file pointer as the number of characters from the beginning
of the file fid.
Built-in Functionfseek (fid, offset, origin)
Set the file pointer to any location within the file fid. The pointer is positioned
offset characters from the origin, which may be one of the predefined variables SEEK_
CUR (current position), SEEK_SET (beginning), or SEEK_END (end of file). If origin is
omitted, SEEK_SET is assumed. The offset must be zero, or a value returned by ftell
(in which case origin must be SEEK_SET.
Built-in VariableSEEK SET
Built-in VariableSEEK CUR
Built-in VariableSEEK END
These variables may be used as the optional third argument for the function fseek.
SEEK_SET Position file relative to the beginning.
SEEK_CUR Position file relative to the current position.
SEEK_END used with fseek to position file relative to the end.
Built-in Functionfrewind (fid)
Move the file pointer to the beginning of the file fid, returning 1 for success, and 0 if
an error was encountered. It is equivalent to fseek (fid, 0, SEEK_SET).
The following example stores the current file position in the variable marker, moves the
pointer to the beginning of the file, reads four characters, and then returns to the original
position.
marker = ftell (myfile);
frewind (myfile);
fourch = fgets (myfile, 4);
fseek (myfile, marker, SEEK_SET);
130 GNU Octave
Chapter 16: Plotting 131
16 Plotting
All of Octave’s plotting functions use gnuplot to handle the actual graphics. There
are two low-level functions, gplot and gsplot, that behave almost exactly like the corresponding
gnuplot functions plot and splot. A number of other higher level plotting
functions, patterned after the graphics functions found in Matlab version 3.5, are also
available. These higher level functions are all implemented in terms of the two low-level
plotting functions.
16.1 Two-Dimensional Plotting
Commandgplot ranges expression using title style
Generate a 2-dimensional plot.
The ranges, using, title, and style arguments are optional, and the using, title and
style qualifiers may appear in any order after the expression. You may plot multiple
expressions with a single command by separating them with commas. Each expression
may have its own set of qualifiers.
The optional item ranges has the syntax
[ x_lo : x_up ] [ y_lo : y_up ]
and may be used to specify the ranges for the axes of the plot, independent of the
actual range of the data. The range for the y axes and any of the individual limits
may be omitted. A range [:] indicates that the default limits should be used. This
normally means that a range just large enough to include all the data points will be
used.
The expression to be plotted must not contain any literal matrices (e.g. [ 1, 2; 3,
4 ]) since it is nearly impossible to distinguish a plot range from a matrix of data.
See the help for gnuplot for a description of the syntax for the optional items.
By default, the gplot command plots the second column of a matrix versus the first.
If the matrix only has one column, it is taken as a vector of y-coordinates and the
x-coordinate is taken as the element index, starting with zero. For example,
gplot rand (100,1) with linespoints
will plot 100 random values and connect them with lines. When gplot is used to plot
a column vector, the indices of the elements are taken as x values.
If there are more than two columns, you can choose which columns to plot with the
using qualifier. For example, given the data
x = (-10:0.1:10)’;
data = [x, sin(x), cos(x)];
the command
gplot [-11:11] [-1.1:1.1] \
data with lines, data using 1:3 with impulses
will plot two lines. The first line is generated by the command data with lines, and
is a graph of the sine function over the range −10 to 10. The data is taken from the
132 GNU Octave
first two columns of the matrix because columns to plot were not specified with the
using qualifier.
The clause using 1:3 in the second part of this plot command specifies that the first
and third columns of the matrix data should be taken as the values to plot.
In this example, the ranges have been explicitly specified to be a bit larger than the
actual range of the data so that the curves do not touch the border of the plot.
Commandgset options
Commandgshow options
Commandreplot options
In addition to the basic plotting commands, the whole range of gset and gshow
commands from gnuplot are available, as is replot.
Note that in Octave 2.0, the set and show commands were renamed to gset and gshow
in order to allow for compatibility with the Matlab graphics and GUI commands in
a future version of Octave. (For now, the old set and show commands do work, but
they print an annoying warning message to try to get people to switch to using gset
and gshow.)
The gset and gshow commands allow you to set and show gnuplot parameters. For
more information about the gset and gshow commands, see the documentation for
set and show in the gnuplot user’s guide (also available on line if you run gnuplot
directly, instead of running it from Octave).
The replot command allows you to force the plot to be redisplayed. This is useful
if you have changed something about the plot, such as the title or axis labels. The
replot command also accepts the same arguments as gplot or gsplot (except for
data ranges) so you can add additional lines to existing plots.
For example,
gset term tek40
gset output "/dev/plotter"
gset title "sine with lines and cosine with impulses"
replot "sin (x) w l"
will change the terminal type for plotting, add a title to the current plot, add a graph
of sin(x) to the plot, and force the new plot to be sent to the plot device. This last step
is normally required in order to update the plot. This default is reasonable for slow
terminals or hardcopy output devices because even when you are adding additional
lines with a replot command, gnuplot always redraws the entire plot, and you probably
don’t want to have a completely new plot generated every time something as minor
as an axis label changes.
The command shg is equivalent to executing replot without any arguments.
Built-in Variableautomatic replot
You can tell Octave to redisplay the plot each time anything about it changes by
setting the value of the builtin variable automatic_replot to a nonzero value. Since
this is fairly inefficient, the default value is 0.
Chapter 16: Plotting 133
Note that NaN values in the plot data are automatically omitted, and Inf values are
converted to a very large value before calling gnuplot.
The Matlab-style two-dimensional plotting commands are:
Function Fileplot (args)
This function produces two-dimensional plots. Many different combinations of arguments
are possible. The simplest form is
plot (y)
where the argument is taken as the set of y coordinates and the x coordinates are
taken to be the indices of the elements, starting with 1.
If more than one argument is given, they are interpreted as
plot (x, y, fmt ...)
where y and fmt are optional, and any number of argument sets may appear. The x
and y values are interpreted as follows:
• If a single data argument is supplied, it is taken as the set of y coordinates and
the x coordinates are taken to be the indices of the elements, starting with 1.
• If the first argument is a vector and the second is a matrix, the the vector is
plotted versus the columns (or rows) of the matrix. (using whichever combination
matches, with columns tried first.)
• If the first argument is a matrix and the second is a vector, the the columns (or
rows) of the matrix are plotted versus the vector. (using whichever combination
matches, with columns tried first.)
• If both arguments are vectors, the elements of y are plotted versus the elements
of x.
• If both arguments are matrices, the columns of y are plotted versus the columns
of x. In this case, both matrices must have the same number of rows and columns
and no attempt is made to transpose the arguments to make the number of rows
match.
If both arguments are scalars, a single point is plotted.
If the fmt argument is supplied, it is interpreted as follows. If fmt is missing, the
default gnuplot line style is assumed.
‘-’ Set lines plot style (default).
‘.’ Set dots plot style.
‘@’ Set points plot style.
‘-@’ Set linespoints plot style.
‘^’ Set impulses plot style.
‘L’ Set steps plot style.
‘#’ Set boxes plot style.
‘~’ Set errorbars plot style.
‘#~’ Set boxerrorbars plot style.
134 GNU Octave
‘n’ Interpreted as the plot color if n is an integer in the range 1 to 6.
‘nm’ If nm is a two digit integer and m is an integer in the range 1 to 6, m is
interpreted as the point style. This is only valid in combination with the
@ or -@ specifiers.
‘c’ If c is one of "r", "g", "b", "m", "c", or "w", it is interpreted as the plot
color (red, green, blue, magenta, cyan, or white).
‘+’
‘*’
‘o’
‘x’ Used in combination with the points or linespoints styles, set the point
style.
The color line styles have the following meanings on terminals that support color.
Number Gnuplot colors (lines)points style
1 red *
2 green +
3 blue o
4 magenta x
5 cyan house
6 brown there exists
The fmt argument can also be used to assign key titles. To do so, include the desired
title between semi-colons after the formatting sequence described above, e.g. "+3;Key
Title;" Note that the last semi-colon is required and will generate an error if it is left
out.
Here are some plot examples:
plot (x, y, "@12", x, y2, x, y3, "4", x, y4, "+")
This command will plot y with points of type 2 (displayed as ‘+’) and color 1 (red),
y2 with lines, y3 with lines of color 4 (magenta) and y4 with points displayed as ‘+’.
plot (b, "*")
This command will plot the data in the variable b will be plotted with points displayed
as ‘*’.
t = 0:0.1:6.3;
plot (t, cos(t), "-;cos(t);", t, sin(t), "+3;sin(t);");
This will plot the cosine and sine functions and label them accordingly in the key.
Built-in Functionhold args
Tell Octave to ‘hold’ the current data on the plot when executing subsequent plotting
commands. This allows you to execute a series of plot commands and have all the
lines end up on the same figure. The default is for each new plot command to clear
the plot device first. For example, the command
hold on
turns the hold state on. An argument of off turns the hold state off, and hold with
no arguments toggles the current hold state.
Chapter 16: Plotting 135
Built-in Functionishold
Return 1 if the next line will be added to the current plot, or 0 if the plot device will
be cleared before drawing the next line.
Built-in Functionclearplot
Built-in Functionclg
Clear the plot window and any titles or axis labels. The name clg is aliased to
clearplot for compatibility with Matlab.
The commands gplot clear, gsplot clear, and replot clear are equivalent to
clearplot. (Previously, commands like gplot clear would evaluate clear as an
ordinary expression and clear all the visible variables.)
Function Fileshg
Show the graph window. Currently, this is the same as executing replot without any
arguments.
Built-in Functioncloseplot
Close stream to the gnuplot subprocess. If you are using X11, this will close the plot
window.
Built-in Functionpurge tmp files
Delete the temporary files created by the plotting commands.
Octave creates temporary data files for gnuplot and then sends commands to gnuplot
through a pipe. Octave will delete the temporary files on exit, but if you are doing a
lot of plotting you may want to clean up in the middle of a session.
A future version of Octave will eliminate the need to use temporary files to hold the
plot data.
Function Fileaxis (limits)
Set axis limits for plots.
The argument limits should be a 2, 4, or 6 element vector. The first and second
elements specify the lower and upper limits for the x axis. The third and fourth
specify the limits for the y axis, and the fifth and sixth specify the limits for the z
axis.
If your plot is already drawn, then you need to use replot before the new axis limits
will take effect. You can get this to happen automatically by setting the built-in
variable automatic_replot to a nonzero value.
Without any arguments, axis turns autoscaling on.
The vector argument specifying limits is optional, and additional string arguments
may be used to specify various axis properties. For example,
axis ([1, 2, 3, 4], "square");
forces a square aspect ratio, and
136 GNU Octave
axis ("labely", "tic");
turns tic marks on for all axes and tic mark labels on for the y-axis only.
The following options control the aspect ratio of the axes.
"square" Force a square aspect ratio.
"equal" Force x distance to equal y-distance.
"normal" Restore the balance.
The following options control the way axis limits are interpreted.
"auto" Set the specified axes to have nice limits around the data or all if no axes
are specified.
"manual" Fix the current axes limits.
"tight" Fix axes to the limits of the data (not implemented).
The option "image" is equivalent to "tight" and "equal".
The following options affect the appearance of tic marks.
"on" Turn tic marks and labels on for all axes.
"off" Turn tic marks off for all axes.
"tic[xyz]"
Turn tic marks on for all axes, or turn them on for the specified axes and
off for the remainder.
"label[xyz]"
Turn tic labels on for all axes, or turn them on for the specified axes and
off for the remainder.
"nolabel"
Turn tic labels off for all axes.
Note, if there are no tic marks for an axis, there can be no labels.
The following options affect the direction of increasing values on the axes.
"ij" Reverse y-axis, so lower values are nearer the top.
"xy" Restore y-axis, so higher values are nearer the top.
16.2 Specialized Two-Dimensional Plots
Function Filebar (x, y)
Given two vectors of x-y data, bar produces a bar graph.
If only one argument is given, it is taken as a vector of y-values and the x coordinates
are taken to be the indices of the elements.
If two output arguments are specified, the data are generated but not plotted. For
example,
bar (x, y);
and
Chapter 16: Plotting 137
[xb, yb] = bar (x, y);
plot (xb, yb);
are equivalent.
Function Filecontour (z, n, x, y)
Make a contour plot of the three-dimensional surface described by z. Someone needs
to improve gnuplot’s contour routines before this will be very useful.
Function Filehist (y, x, norm)
Produce histogram counts or plots.
With one vector input argument, plot a histogram of the values with 10 bins. The
range of the histogram bins is determined by the range of the data.
Given a second scalar argument, use that as the number of bins.
Given a second vector argument, use that as the centers of the bins, with the width
of the bins determined from the adjacent values in the vector.
If third argument is provided, the histogram is normalised such that the sum of the
bars is equal to norm.
Extreme values are lumped in the first and last bins.
With two output arguments, produce the values nn and xx such that bar (xx, nn)
will plot the histogram.
Function Fileloglog (args)
Make a two-dimensional plot using log scales for both axes. See the description of
plot for a description of the arguments that loglog will accept.
Function Filepolar (theta, rho, fmt)
Make a two-dimensional plot given polar the coordinates theta and rho.
The optional third argument specifies the line type.
Function Filesemilogx (args)
Make a two-dimensional plot using a log scale for the x axis. See the description of
plot for a description of the arguments that semilogx will accept.
Function Filesemilogy (args)
Make a two-dimensional plot using a log scale for the y axis. See the description of
plot for a description of the arguments that semilogy will accept.
Function Filestairs (x, y)
Given two vectors of x-y data, bar produces a ‘stairstep’ plot.
If only one argument is given, it is taken as a vector of y-values and the x coordinates
are taken to be the indices of the elements.
If two output arguments are specified, the data are generated but not plotted. For
example,
138 GNU Octave
stairs (x, y);
and
[xs, ys] = stairs (x, y);
plot (xs, ys);
are equivalent.
16.3 Three-Dimensional Plotting
Commandgsplot ranges expression using title style
Generate a 3-dimensional plot.
The ranges, using, title, and style arguments are optional, and the using, title and
style qualifiers may appear in any order after the expression. You may plot multiple
expressions with a single command by separating them with commas. Each expression
may have its own set of qualifiers.
The optional item ranges has the syntax
[ x_lo : x_up ] [ y_lo : y_up ] [ z_lo : z_up ]
and may be used to specify the ranges for the axes of the plot, independent of the
actual range of the data. The range for the y and z axes and any of the individual
limits may be omitted. A range [:] indicates that the default limits should be used.
This normally means that a range just large enough to include all the data points
will be used.
The expression to be plotted must not contain any literal matrices (e.g. [ 1, 2; 3,
4 ]) since it is nearly impossible to distinguish a plot range from a matrix of data.
See the help for gnuplot for a description of the syntax for the optional items.
By default, the gsplot command plots each column of the expression as the z value,
using the row index as the x value, and the column index as the y value. The indices
are counted from zero, not one. For example,
gsplot rand (5, 2)
will plot a random surface, with the x and y values taken from the row and column
indices of the matrix.
If parametric plotting mode is set (using the command gset parametric, then gsplot
takes the columns of the matrix three at a time as the x, y and z values that define
a line in three space. Any extra columns are ignored, and the x and y values are
expected to be sorted. For example, with parametric set, it makes sense to plot a
matrix like 

1 1 3 2 1 6 3 1 9
1 2 2 2 2 5 3 2 8
1 3 1 2 3 4 3 3 7


but not rand (5, 30).
The Matlab-style three-dimensional plotting commands are:
Chapter 16: Plotting 139
Function Filemesh (x, y, z)
Plot a mesh given matrices x, and y from meshdom and a matrix z corresponding to
the x and y coordinates of the mesh. If x and y are vectors, then a typical vertex is
(x(j), y(i), z(i,j)). Thus, columns of z correspond to different x values and rows of z
correspond to different y values.
Function File[xx, yy] = meshgrid (x, y)
Function File[xx, yy] = meshgrid (x)
Given vectors of x and y coordinates, return two matrices corresponding to the x and
y coordinates of a mesh. The rows of xx are copies of x, and the columns of yy are
copies of y.
Function Filemeshdom (x, y)
Given vectors of x and y coordinates, return two matrices corresponding to the x and
y coordinates of the mesh.
Note: this function is provided for compatibility with older versions of Matlab. You
should use meshgrid instead.
16.4 Plot Annotations
Function Filegrid (arg)
For two-dimensional plotting, force the display of a grid on the plot. The argument
may be either "on" or "off". If it is omitted, "on" is assumed.
Function Filetitle (string)
Specify a title for a plot. If you already have a plot displayed, use the command
replot to redisplay it with the new title.
Function Filebottom title (string)
See top title.
Function Filexlabel (string)
Function Fileylabel (string)
Function Filezlabel (string)
Specify x, y, and z axis labels for the plot. If you already have a plot displayed, use
the command replot to redisplay it with the new labels.
140 GNU Octave
16.5 Multiple Plots on One Page
The following functions all require a version of gnuplot that supports the multiplot
feature.
Function Filemplot (x, y)
Function Filemplot (x, y, fmt)
Function Filemplot (x1, y1, x2, y2)
This is a modified version of the plot function that works with the multiplot version
of gnuplot to plot multiple plots per page. This plot version automatically advances
to the next subplot position after each set of arguments are processed.
See the description of the plot function for the various options.
Function Filemultiplot (xn, yn)
Sets and resets multiplot mode.
If the arguments are non-zero, multiplot will set up multiplot mode with xn, yn
subplots along the x and y axes. If both arguments are zero, multiplot closes
multiplot mode.
Function Fileoneplot ()
If in multiplot mode, switches to single plot mode.
Function Fileplot border (...)
Multiple arguments allowed to specify the sides on which the border is shown. Allowed
arguments include:
"blank" No borders displayed.
"all" All borders displayed
"north" North Border
"south" South Border
"east" East Border
"west" West Border
The arguments may be abbreviated to single characters. Without any arguments,
plot_border turns borders off.
Function Filesubplot (rows, cols, index)
Function Filesubplot (rcn)
Sets gnuplot in multiplot mode and plots in location given by index (there are cols
by rows subwindows).
Input:
rows Number of rows in subplot grid.
Chapter 16: Plotting 141
columns Number of columns in subplot grid.
index Index of subplot where to make the next plot.
If only one argument is supplied, then it must be a three digit value specifying the
location in digits 1 (rows) and 2 (columns) and the plot index in digit 3.
The plot index runs row-wise. First all the columns in a row are filled and then the
next row is filled.
For example, a plot with 4 by 2 grid will have plot indices running as follows:
1 2 3 4
5 6 7 8
Function Filesubwindow (xn, yn)
Sets the subwindow position in multiplot mode for the next plot. The multiplot
mode has to be previously initialized using the multiplot function, otherwise this
command just becomes an alias to multiplot
Function Filetop title (string)
Function Filebottom title (string)
Makes a title with text string at the top (bottom) of the plot.
16.6 Multiple Plot Windows
Function Filefigure (n)
Set the current plot window to plot window n. This function currently requires X11
and a version of gnuplot that supports multiple frames.
16.7 Interaction with gnuplot
Built-in Variablegnuplot binary
The name of the program invoked by the plot command. The default value is
"gnuplot". See Appendix C [Installation], page 305.
Built-in Variablegnuplot has frames
If the value of this variable is nonzero, Octave assumes that your copy of gnuplot
has support for multiple frames that is included in recent 3.6beta releases. It’s initial
value is determined by configure, but it can be changed in your startup script or
at the command line in case configure got it wrong, or if you upgrade your gnuplot
installation.
142 GNU Octave
Built-in Variablegnuplot has multiplot
If the value of this variable is nonzero, Octave assumes that your copy of gnuplot
has the multiplot support that is included in recent 3.6beta releases. It’s initial
value is determined by configure, but it can be changed in your startup script or
at the command line in case configure got it wrong, or if you upgrade your gnuplot
installation.
Built-in Functiongraw (string)
Send string directly to gnuplot subprocess.
Built-in Variablegnuplot command plot
Built-in Variablegnuplot command replot
Built-in Variablegnuplot command splot
Built-in Variablegnuplot command using
Built-in Variablegnuplot command with
Built-in Variablegnuplot command axes
Built-in Variablegnuplot command title
Built-in Variablegnuplot command end
Chapter 17: Matrix Manipulation 143
17 Matrix Manipulation
There are a number of functions available for checking to see if the elements of a matrix
meet some condition, and for rearranging the elements of a matrix. For example, Octave
can easily tell you if all the elements of a matrix are finite, or are less than some specified
value. Octave can also rotate the elements, extract the upper- or lower-triangular parts, or
sort the columns of a matrix.
17.1 Finding Elements and Checking Conditions
The functions any and all are useful for determining whether any or all of the elements
of a matrix satisfy some condition. The find function is also useful in determining which
elements of a matrix meet a specified condition.
Built-in Functionany (x)
For a vector argument, return 1 if any element of the vector is nonzero.
For a matrix argument, return a row vector of ones and zeros with each element
indicating whether any of the elements of the corresponding column of the matrix are
nonzero. For example,
any (eye (2, 4))
⇒ [ 1, 1, 0, 0 ]
To see if any of the elements of a matrix are nonzero, you can use a statement like
any (any (a))
Built-in Functionall (x)
The function all behaves like the function any, except that it returns true only if all
the elements of a vector, or all the elements in a column of a matrix, are nonzero.
Since the comparison operators (see Section 10.4 [Comparison Ops], page 69) return
matrices of ones and zeros, it is easy to test a matrix for many things, not just whether the
elements are nonzero. For example,
all (all (rand (5) < 0.9))
⇒ 0
tests a random 5 by 5 matrix to see if all of its elements are less than 0.9.
Note that in conditional contexts (like the test clause of if and while statements) Octave
treats the test as if you had typed all (all (condition)).
Mapping Functionxor (x, y)
Return the ‘exclusive or’ of the entries of x and y. For boolean expressions x and y,
xor (x, y) is true if and only if x or y is true, but not if both x and y are true.
Function Fileis duplicate entry (x)
Return non-zero if any entries in x are duplicates of one another.
144 GNU Octave
Function Filediff (x, k)
If x is a vector of length n, diff (x) is the vector of first differences x2 −x1, . . . , xn −
xn−1.
If x is a matrix, diff (x) is the matrix of column differences.
The second argument is optional. If supplied, diff (x, k), where k is a nonnegative
integer, returns the k-th differences.
Mapping Functionisinf (x)
Return 1 for elements of x that are infinite and zero otherwise. For example,
isinf ([13, Inf, NaN])
⇒ [ 0, 1, 0 ]
Mapping Functionisnan (x)
Return 1 for elements of x that are NaN values and zero otherwise. For example,
isnan ([13, Inf, NaN])
⇒ [ 0, 0, 1 ]
Mapping Functionfinite (x)
Return 1 for elements of x that are finite values and zero otherwise. For example,
finite ([13, Inf, NaN])
⇒ [ 1, 0, 0 ]
Loadable Functionfind (x)
Return a vector of indices of nonzero elements of a matrix. To obtain a single index
for each matrix element, Octave pretends that the columns of a matrix form one long
vector (like Fortran arrays are stored). For example,
find (eye (2))
⇒ [ 1; 4 ]
If two outputs are requested, find returns the row and column indices of nonzero
elements of a matrix. For example,
[i, j] = find (2 * eye (2))
⇒ i = [ 1; 2 ]
⇒ j = [ 1; 2 ]
If three outputs are requested, find also returns a vector containing the nonzero
values. For example,
[i, j, v] = find (3 * eye (2))
⇒ i = [ 1; 2 ]
⇒ j = [ 1; 2 ]
⇒ v = [ 3; 3 ]
Chapter 17: Matrix Manipulation 145
Function File[err, y1, ...] = common size (x1, ...)
Determine if all input arguments are either scalar or of common size. If so, err is
zero, and yi is a matrix of the common size with all entries equal to xi if this is a
scalar or xi otherwise. If the inputs cannot be brought to a common size, errorcode
is 1, and yi is xi. For example,
[errorcode, a, b] = common_size ([1 2; 3 4], 5)
⇒ errorcode = 0
⇒ a = [ 1, 2; 3, 4 ]
⇒ b = [ 5, 5; 5, 5 ]
This is useful for implementing functions where arguments can either be scalars or of
common size.
17.2 Rearranging Matrices
Function Filefliplr (x)
Return a copy of x with the order of the columns reversed. For example,
fliplr ([1, 2; 3, 4])
⇒ 2 1
4 3
Function Fileflipud (x)
Return a copy of x with the order of the rows reversed. For example,
flipud ([1, 2; 3, 4])
⇒ 3 4
1 2
Function Filerot90 (x, n)
Return a copy of x with the elements rotated counterclockwise in 90-degree increments.
The second argument is optional, and specifies how many 90-degree rotations
are to be applied (the default value is 1). Negative values of n rotate the matrix in a
clockwise direction. For example,
rot90 ([1, 2; 3, 4], -1)
⇒ 3 1
4 2
rotates the given matrix clockwise by 90 degrees. The following are all equivalent
statements:
rot90 ([1, 2; 3, 4], -1)
≡
rot90 ([1, 2; 3, 4], 3)
≡
rot90 ([1, 2; 3, 4], 7)
146 GNU Octave
Function Filereshape (a, m, n)
Return a matrix with m rows and n columns whose elements are taken from the
matrix a. To decide how to order the elements, Octave pretends that the elements of
a matrix are stored in column-major order (like Fortran arrays are stored).
For example,
reshape ([1, 2, 3, 4], 2, 2)
⇒ 1 3
2 4
If the variable do_fortran_indexing is nonzero, the reshape function is equivalent
to
retval = zeros (m, n);
retval (:) = a;
but it is somewhat less cryptic to use reshape instead of the colon operator. Note
that the total number of elements in the original matrix must match the total number
of elements in the new matrix.
Function Fileshift (x, b)
If x is a vector, perform a circular shift of length b of the elements of x.
If x is a matrix, do the same for each column of x.
Loadable Function[s, i] = sort (x)
Return a copy of x with the elements elements arranged in increasing order. For
matrices, sort orders the elements in each column.
For example,
sort ([1, 2; 2, 3; 3, 1])
⇒ 1 1
2 2
3 3
The sort function may also be used to produce a matrix containing the original row
indices of the elements in the sorted matrix. For example,
[s, i] = sort ([1, 2; 2, 3; 3, 1])
⇒ s = 1 1
2 2
3 3
⇒ i = 1 3
2 1
3 2
Since the sort function does not allow sort keys to be specified, it can’t be used to order
the rows of a matrix according to the values of the elements in various columns1
in a single
call. Using the second output, however, it is possible to sort all rows based on the values
in a given column. Here’s an example that sorts the rows of a matrix based on the values
in the second column.
1
For example, to first sort based on the values in column 1, and then, for any values that are repeated in
column 1, sort based on the values found in column 2, etc.
Chapter 17: Matrix Manipulation 147
a = [1, 2; 2, 3; 3, 1];
[s, i] = sort (a (:, 2));
a (i, :)
⇒ 3 1
1 2
2 3
Function Filetril (a, k)
Function Filetriu (a, k)
Return a new matrix formed by extracting extract the lower (tril) or upper (triu)
triangular part of the matrix a, and setting all other elements to zero. The second
argument is optional, and specifies how many diagonals above or below the main
diagonal should also be set to zero.
The default value of k is zero, so that triu and tril normally include the main
diagonal as part of the result matrix.
If the value of k is negative, additional elements above (for tril) or below (for triu)
the main diagonal are also selected.
The absolute value of k must not be greater than the number of sub- or super-
diagonals.
For example,
tril (ones (3), -1)
⇒ 0 0 0
1 0 0
1 1 0
and
tril (ones (3), 1)
⇒ 1 1 0
1 1 1
1 1 1
Function Filevec (x)
Return the vector obtained by stacking the columns of the matrix x one above the
other.
Function Filevech (x)
Return the vector obtained by eliminating all supradiagonal elements of the square
matrix x and stacking the result one column above the other.
Function Fileprepad (x, l, c)
Function Filepostpad (x, l, c)
Prepends (appends) the scalar value c to the vector x until it is of length l. If the
third argument is not supplied, a value of 0 is used.
If length (x) > l, elements from the beginning (end) of x are removed until a vector
of length l is obtained.
If x is a matrix, elements are prepended or removed from each row.
148 GNU Octave
17.3 Special Utility Matrices
Built-in Functioneye (x)
Built-in Functioneye (n, m)
Return an identity matrix. If invoked with a single scalar argument, eye returns
a square matrix with the dimension specified. If you supply two scalar arguments,
eye takes them to be the number of rows and columns. If given a vector with two
elements, eye uses the values of the elements as the number of rows and columns,
respectively. For example,
eye (3)
⇒ 1 0 0
0 1 0
0 0 1
The following expressions all produce the same result:
eye (2)
≡
eye (2, 2)
≡
eye (size ([1, 2; 3, 4])
For compatibility with Matlab, calling eye with no arguments is equivalent to calling
it with an argument of 1.
Built-in Functionones (x)
Built-in Functionones (n, m)
Return a matrix whose elements are all 1. The arguments are handled the same as
the arguments for eye.
If you need to create a matrix whose values are all the same, you should use an
expression like
val_matrix = val * ones (n, m)
Built-in Functionzeros (x)
Built-in Functionzeros (n, m)
Return a matrix whose elements are all 0. The arguments are handled the same as
the arguments for eye.
Loadable Functionrand (x)
Loadable Functionrand (n, m)
Loadable Functionrand ("seed", x)
Return a matrix with random elements uniformly distributed on the interval (0, 1).
The arguments are handled the same as the arguments for eye. In addition, you can
set the seed for the random number generator using the form
rand ("seed", x)
where x is a scalar value. If called as
rand ("seed")
rand returns the current value of the seed.
Chapter 17: Matrix Manipulation 149
Loadable Functionrandn (x)
Loadable Functionrandn (n, m)
Loadable Functionrandn ("seed", x)
Return a matrix with normally distributed random elements. The arguments are
handled the same as the arguments for eye. In addition, you can set the seed for the
random number generator using the form
randn ("seed", x)
where x is a scalar value. If called as
randn ("seed")
randn returns the current value of the seed.
The rand and randn functions use separate generators. This ensures that
rand ("seed", 13);
randn ("seed", 13);
u = rand (100, 1);
n = randn (100, 1);
and
rand ("seed", 13);
randn ("seed", 13);
u = zeros (100, 1);
n = zeros (100, 1);
for i = 1:100
u(i) = rand ();
n(i) = randn ();
end
produce equivalent results.
Normally, rand and randn obtain their initial seeds from the system clock, so that the
sequence of random numbers is not the same each time you run Octave. If you really do
need for to reproduce a sequence of numbers exactly, you can set the seed to a specific value.
If it is invoked without arguments, rand and randn return a single element of a random
sequence.
The rand and randn functions use Fortran code from Ranlib, a library of fortran
routines for random number generation, compiled by Barry W. Brown and James Lovato
of the Department of Biomathematics at The University of Texas, M.D. Anderson Cancer
Center, Houston, TX 77030.
Function Filerandperm (n)
Return a row vector containing a random permutation of the integers from 1 to n.
Built-in Functiondiag (v, k)
Return a diagonal matrix with vector v on diagonal k. The second argument is
optional. If it is positive, the vector is placed on the k-th super-diagonal. If it is
negative, it is placed on the -k-th sub-diagonal. The default value of k is 0, and the
vector is placed on the main diagonal. For example,
150 GNU Octave
diag ([1, 2, 3], 1)
⇒ 0 1 0 0
0 0 2 0
0 0 0 3
0 0 0 0
The functions linspace and logspace make it very easy to create vectors with evenly
or logarithmically spaced elements. See Section 4.2 [Ranges], page 35.
Built-in Functionlinspace (base, limit, n)
Return a row vector with n linearly spaced elements between base and limit. The
number of elements, n, must be greater than 1. The base and limit are always included
in the range. If base is greater than limit, the elements are stored in decreasing order.
If the number of points is not specified, a value of 100 is used.
The linspace function always returns a row vector, regardless of the value of prefer_
column_vectors.
Function Filelogspace (base, limit, n)
Similar to linspace except that the values are logarithmically spaced from 10base
to
10limit
.
If limit is equal to π, the points are between 10base
and π, not 10base
and 10π
, in order
to be compatible with the corresponding Matlab function.
Built-in Variabletreat neg dim as zero
If the value of treat_neg_dim_as_zero is nonzero, expressions like
eye (-1)
produce an empty matrix (i.e., row and column dimensions are zero). Otherwise, an
error message is printed and control is returned to the top level. The default value is
0.
Built-in Variableok to lose imaginary part
If the value of ok_to_lose_imaginary_part is nonzero, implicit conversions of complex
numbers to real numbers are allowed (for example, by fsolve). If the value is
"warn", the conversion is allowed, but a warning is printed. Otherwise, an error
message is printed and control is returned to the top level. The default value is
"warn".
17.4 Famous Matrices
The following functions return famous matrix forms.
Function Filehankel (c, r)
Return the Hankel matrix constructed given the first column c, and (optionally) the
last row r. If the last element of c is not the same as the first element of r, the last
Chapter 17: Matrix Manipulation 151
element of c is used. If the second argument is omitted, the last row is taken to be
the same as the first column.
A Hankel matrix formed from an m-vector c, and an n-vector r, has the elements
H(i, j) =
ci+j−1, i + j − 1 ≤ m;
ri+j−m, otherwise.
Function Filehilb (n)
Return the Hilbert matrix of order n. The i, j element of a Hilbert matrix is defined
as
H(i, j) =
1
(i + j − 1)
Function Fileinvhilb (n)
Return the inverse of a Hilbert matrix of order n. This is exact. Compare with the
numerical calculation of inverse (hilb (n)), which suffers from the ill-conditioning
of the Hilbert matrix, and the finite precision of your computer’s floating point arith-
metic.
Function Filesylvester matrix (k)
Return the Sylvester matrix of order n = 2k
.
Function Filetoeplitz (c, r)
Return the Toeplitz matrix constructed given the first column c, and (optionally) the
first row r. If the first element of c is not the same as the first element of r, the first
element of c is used. If the second argument is omitted, the first row is taken to be
the same as the first column.
A square Toeplitz matrix has the form







c0 r1 r2 . . . rn
c1 c0 r1 cn−1
c2 c1 c0 cn−2
...
...
cn cn−1 cn−2 . . . c0







.
Function Filevander (c)
Return the Vandermonde matrix whose next to last column is c.
A Vandermonde matrix has the form





cn
0 . . . c2
0 c0 1
cn
1 . . . c2
1 c1 1
...
...
...
...
cn
n . . . c2
n cn 1





.
152 GNU Octave
Chapter 18: Arithmetic 153
18 Arithmetic
Unless otherwise noted, all of the functions described in this chapter will work for real
and complex scalar or matrix arguments.
18.1 Utility Functions
The following functions are available for working with complex numbers. Each expects a
single argument. They are called mapping functions because when given a matrix argument,
they apply the given function to each element of the matrix.
Mapping Functionceil (x)
Return the smallest integer not less than x. If x is complex, return ceil (real (x))
+ ceil (imag (x)) * I.
Mapping Functionexp (x)
Compute the exponential of x. To compute the matrix exponential, see Chapter 19
[Linear Algebra], page 165.
Mapping Functionfix (x)
Truncate x toward zero. If x is complex, return fix (real (x)) + fix (imag (x))
* I.
Mapping Functionfloor (x)
Return the largest integer not greater than x. If x is complex, return floor (real
(x)) + floor (imag (x)) * I.
Mapping Functiongcd (x, ...)
Compute the greatest common divisor of the elements of x, or the list of all the
arguments. For example,
gcd (a1, ..., ak)
is the same as
gcd ([a1, ..., ak])
An optional second return value, v contains an integer vector such that
g = v(1) * a(k) + ... + v(k) * a(k)
Mapping Functionlcm (x, ...)
Compute the least common multiple of the elements elements of x, or the list of all
the arguments. For example,
lcm (a1, ..., ak)
is the same as
lcm ([a1, ..., ak]).
154 GNU Octave
Mapping Functionlog (x)
Compute the natural logarithm for each element of x. To compute the matrix logarithm,
see Chapter 19 [Linear Algebra], page 165.
Mapping Functionlog10 (x)
Compute the base-10 logarithm for each element of x.
Mapping Functionlog2 (x)
Mapping Function[f, e] log2 (x)
Compute the base-2 logarithm of x. With two outputs, returns f and e such that
1/2 <= |f| < 1 and x = f · 2e
.
For a vector argument, return the maximum value. For a matrix argument, return the
maximum value from each column, as a row vector. Thus,
max (max (x))
returns the largest element of x.
For complex arguments, the magnitude of the elements are used for comparison.
If called with two output arguments, also returns the index of the maximum value(s).
Thus,
[x, ix] = max([1, 3, 5, 2, 5])
returns x = 5 and ix = 3.
For a vector argument, return the minimum value. For a matrix argument, return the
minimum value from each column, as a row vector. Thus,
min (min (x))
returns the smallest element of x.
For complex arguments, the magnitude of the elements are used for comparison.
If called with two output arguments, also returns the index of the minimum value(s).
Thus,
[x, ix] = min ([1, 3, 0, 2, 5])
returns x = 0 and ix = 3.
Function Filenextpow2 (x)
If x is a scalar, returns the first integer n such that 2n
≥ |x|.
If x is a vector, return nextpow2 (length (x)).
Mapping Functionpow2 (x)
Mapping Functionpow2 (f, e)
With one argument, computes 2x
for each element of x. With two arguments, returns
f · 2e
.
Chapter 18: Arithmetic 155
Mapping Functionrem (x, y)
Return the remainder of x / y, computed using the expression
x - y .* fix (x ./ y)
An error message is printed if the dimensions of the arguments do not agree, or if
either of the arguments is complex.
Mapping Functionround (x)
Return the integer nearest to x. If x is complex, return round (real (x)) + round
(imag (x)) * I.
Mapping Functionsign (x)
Compute the signum function, which is defined as
sign(x) =



1, x > 0;
0, x = 0;
−1, x < 0.
For complex arguments, sign returns x ./ abs (x).
Mapping Functionsqrt (x)
Compute the square root of x. If x is negative, a complex result is returned. To
compute the matrix square root, see Chapter 19 [Linear Algebra], page 165.
18.2 Complex Arithmetic
The following functions are available for working with complex numbers. Each expects
a single argument. Given a matrix they work on an element by element basis. In the
descriptions of the following functions, z is the complex number x + iy, where i is defined
as
√
−1.
Mapping Functionabs (z)
Compute the magnitude of z, defined as |z| =
√
x2 + y2.
For example,
abs (3 + 4i)
⇒ 5
Mapping Functionarg (z)
Mapping Functionangle (z)
Compute the argument of z, defined as θ = tan−1
(y/x).
in radians.
For example,
arg (3 + 4i)
⇒ 0.92730
156 GNU Octave
Mapping Functionconj (z)
Return the complex conjugate of z, defined as ¯z = x − iy.
Mapping Functionimag (z)
Return the imaginary part of z as a real number.
Mapping Functionreal (z)
Return the real part of z.
18.3 Trigonometry
Octave provides the following trigonometric functions. Angles are specified in radians.
To convert from degrees to radians multipy by π/180 (e.g. sin (30 * pi/180) returns the
sine of 30 degrees).
Mapping Functionsin (x)
Compute the sin of each element of x.
Mapping Functioncos (x)
Compute the cosine of each element of x.
Mapping Functiontan (z)
Compute tanget of each element of x.
Mapping Functionsec (x)
Compute the secant of each element of x.
Mapping Functioncsc (x)
Compute the cosecant of each element of x.
Mapping Functioncot (x)
Compute the cotangent of each element of x.
Mapping Functionasin (x)
Compute the inverse sine of each element of x.
Mapping Functionacos (x)
Compute the inverse cosine of each element of x.
Mapping Functionatan (x)
Compute the inverse tangent of each element of x.
Chapter 18: Arithmetic 157
Mapping Functionasec (x)
Compute the inverse secant of each element of x.
Mapping Functionacsc (x)
Compute the inverse cosecant of each element of x.
Mapping Functionacot (x)
Compute the inverse cotangent of each element of x.
Mapping Functionsinh (x)
Compute the inverse hyperbolic sin of each element of x.
Mapping Functioncosh (x)
Compute the hyperbolic cosine of each element of x.
Mapping Functiontanh (x)
Compute hyperbolic tangent of each element of x.
Mapping Functionsech (x)
Compute the hyperbolic secant of each element of x.
Mapping Functioncsch (x)
Compute the hyperbolic cosecant of each element of x.
Mapping Functioncoth (x)
Compute the hyperbolic cotangent of each element of x.
Mapping Functionasinh (x)
Ompute the inverse hyperbolic sine of each element of x.
Mapping Functionacosh (x)
Compute the inverse hyperbolic cosine of each element of x.
Mapping Functionatanh (x)
Compute the inverse hyperbolic tanget of each element of x.
Mapping Functionasech (x)
Compute the inverse hyperbolic secant of each element of x.
Mapping Functionacsch (x)
Compute the inverse hyperbolic cosecant of each element of x.
158 GNU Octave
Mapping Functionacoth (x)
Compute the inverse hyperbolic cotangent of each element of x.
Each of these functions expect a single argument. For matrix arguments, they work on
an element by element basis. For example,
sin ([1, 2; 3, 4])
⇒ 0.84147 0.90930
0.14112 -0.75680
Mapping Functionatan2 (y, x)
Compute atan (y / x) for corresponding elements of y and x. The result is in range
-pi to pi.
18.4 Sums and Products
Built-in Functionsum (x)
Sum of elements.
Built-in Functionprod (x)
Products.
Built-in Functioncumsum (x)
Cumulative sums.
Built-in Functioncumprod (x)
Cumulative products.
Built-in Functionsumsq (x)
Sum of squares of elements.
This function is equivalent to computing
sum (X .* conj (X))
but it uses less memory and avoids calling conj if X is real.
18.5 Special Functions
Loadable Function[j, ierr] = besselj (alpha, x, opt)
Loadable Function[y, ierr] = bessely (alpha, x, opt)
Loadable Function[i, ierr] = besseli (alpha, x, opt)
Loadable Function[k, ierr] = besselk (alpha, x, opt)
Loadable Function[h, ierr] = besselh (alpha, k, x, opt)
Compute Bessel or Hankel functions of various kinds:
besselj Bessel functions of the first kind.
Chapter 18: Arithmetic 159
bessely Bessel functions of the second kind.
besseli Modified Bessel functions of the first kind.
besselk Modified Bessel functions of the second kind.
besselh Compute Hankel functions of the first (k = 1) or second (k = 2) kind.
If the argument opt is supplied, the result is scaled by the exp (-I*x) for k = 1 or
exp (I*x) for k = 2.
If alpha is a scalar, the result is the same size as x. If x is a scalar, the result is the
same size as alpha. If alpha is a row vector and x is a column vector, the result is a
matrix with length (x) rows and length (alpha) columns. Otherwise, alpha and x
must conform and the result will be the same size.
The value of alpha must be real. The value of x may be complex.
If requested, ierr contains the following status information and is the same size as the
result.
0. Normal return.
1. Input error, return NaN.
2. Overflow, return Inf.
3. Loss of significance by argument reduction results in less than half of machine
accuracy.
4. Complete loss of significance by argument reduction, return NaN.
5. Error—no computation, algorithm termination condition not met, return NaN.
Loadable Function[a, ierr] = airy (k, z, opt)
Compute Airy functions of the first and second kind, and their derivatives.
K Function Scale factor (if a third argument is supplied)
--- -------- ----------------------------------------------
0 Ai (Z) exp ((2/3) * Z * sqrt (Z))
1 dAi(Z)/dZ exp ((2/3) * Z * sqrt (Z))
2 Bi (Z) exp (-abs (real ((2/3) * Z *sqrt (Z))))
3 dBi(Z)/dZ exp (-abs (real ((2/3) * Z *sqrt (Z))))
The function call airy (z) is equivalent to airy (0, z).
The result is the same size as z.
If requested, ierr contains the following status information and is the same size as the
result.
0. Normal return.
1. Input error, return NaN.
2. Overflow, return Inf.
3. Loss of significance by argument reduction results in less than half of machine
accuracy.
4. Complete loss of significance by argument reduction, return NaN.
5. Error—no computation, algorithm termination condition not met, return NaN
160 GNU Octave
Mapping Functionbeta (a, b)
Return the Beta function,
B(a, b) =
Γ(a)Γ(b)
Γ(a + b)
.
Mapping Functionbetainc (x, a, b)
Return the incomplete Beta function,
β(a, b, x) = B(a, b)−1
x
0
t(a−z)
(1 − t)(b−1)
dt.
If x has more than one component, both a and b must be scalars. If x is a scalar, a
and b must be of compatible dimensions.
Mapping Functionbincoeff (n, k)
Return the binomial coefficient of n and k, defined as
n
k
=
n(n − 1)(n − 2) · · · (n − k + 1)
k!
For example,
bincoeff (5, 2)
⇒ 10
Mapping Functionerf (z)
Computes the error function,
erf(z) =
2
√
π
z
0
e−t2
dt
Mapping Functionerfc (z)
Computes the complementary error function, 1 − erf(z).
Mapping Functionerfinv (z)
Computes the inverse of the error function.
Mapping Functiongamma (z)
Computes the Gamma function,
Γ(z) =
∞
0
tz−1
e−t
dt.
Chapter 18: Arithmetic 161
Mapping Functiongammainc (x, a)
Computes the incomplete gamma function,
γ(x, a) =
x
0
e−t
ta−1
dt
Γ(a)
If a is scalar, then gammainc (x, a) is returned for each element of x and vice versa.
If neither x nor a is scalar, the sizes of x and a must agree, and gammainc is applied
element-by-element.
Mapping Functionlgamma (a, x)
Mapping Functiongammaln (a, x)
Return the natural logarithm of the gamma function.
Function Filecross (x, y)
Computes the vector cross product of the two 3-dimensional vectors x and y.
A row vector is returned if x and y are both row vectors; otherwise, a column vector
is returned.
cross ([1,1,0], [0,1,1])
⇒ [ 1; -1; 1 ]
Function Filecommutation matrix (m, n)
Return the commutation matrix Km,n which is the unique mn×mn matrix such that
Km,n · vec(A) = vec(AT
) for all m × n matrices A.
If only one argument m is given, Km,m is returned.
See Magnus and Neudecker (1988), Matrix differential calculus with applications in
statistics and econometrics.
Function Fileduplication matrix (n)
Return the duplication matrix Dn which is the unique n2
× n(n + 1)/2 matrix such
that Dn ∗ vech(A) = vec(A) for all symmetric n × n matrices A.
See Magnus and Neudecker (1988), Matrix differential calculus with applications in
statistics and econometrics.
18.6 Coordinate Transformations
162 GNU Octave
18.7 Mathematical Constants
Built-in VariableI
Built-in VariableJ
Built-in Variablei
Built-in Variablej
A pure imaginary number, defined as
√
−1. The I and J forms are true constants,
and cannot be modified. The i and j forms are like ordinary variables, and may be
used for other purposes. However, unlike other variables, they once again assume
their special predefined values if they are cleared See Section 9.2 [Status of Variables],
page 55.
Built-in VariableInf
Built-in Variableinf
Infinity. This is the result of an operation like 1/0, or an operation that results in a
floating point overflow.
Built-in VariableNaN
Built-in Variablenan
Not a number. This is the result of an operation like 0/0, or ∞−∞, or any operation
with a NaN.
Note that NaN always compares not equal to NaN. This behavior is specified by the
IEEE standard for floating point arithmetic. To find NaN values, you must use the
isnan function.
Built-in Variablepi
The ratio of the circumference of a circle to its diameter. Internally, pi is computed
as ‘4.0 * atan (1.0)’.
Built-in Variablee
The base of natural logarithms. The constant e satisfies the equation log(e) = 1.
Built-in Variableeps
The machine precision. More precisely, eps is the largest relative spacing between
any two adjacent numbers in the machine’s floating point system. This number is
obviously system-dependent. On machines that support 64 bit IEEE floating point
arithmetic, eps is approximately 2.2204 × 10−16
.
Built-in Variablerealmax
The largest floating point number that is representable. The actual value is systemdependent.
On machines that support 64 bit IEEE floating point arithmetic, realmax
is approximately 1.7977 × 10308
.
Chapter 18: Arithmetic 163
Built-in Variablerealmin
The smallest floating point number that is representable. The actual value is systemdependent.
On machines that support 64 bit IEEE floating point arithmetic, realmin
is approximately 2.2251 × 10−308
.
164 GNU Octave
Chapter 19: Linear Algebra 165
19 Linear Algebra
This chapter documents the linear algebra functions of Octave. Reference material for
many of these functions may be found in Golub and Van Loan, Matrix Computations, 2nd
Ed., Johns Hopkins, 1989, and in Lapack Users’ Guide, SIAM, 1992.
19.1 Basic Matrix Functions
Loadable Functionaa = balance (a, opt)
Loadable Function[dd, aa] = balance (a, opt)
Loadable Function[cc, dd, aa, bb] = balance (a, b, opt)
[dd, aa] = balance (a) returns aa = dd \ a * dd. aa is a matrix whose row and column
norms are roughly equal in magnitude, and dd = p * d, where p is a permutation
matrix and d is a diagonal matrix of powers of two. This allows the equilibration to be
computed without roundoff. Results of eigenvalue calculation are typically improved
by balancing first.
[cc, dd, aa, bb] = balance (a, b) returns aa = cc*a*dd and bb = cc*b*dd),
where aa and bb have non-zero elements of approximately the same magnitude and
cc and dd are permuted diagonal matrices as in dd for the algebraic eigenvalue
problem.
The eigenvalue balancing option opt is selected as follows:
"N", "n" No balancing; arguments copied, transformation(s) set to identity.
"P", "p" Permute argument(s) to isolate eigenvalues where possible.
"S", "s" Scale to improve accuracy of computed eigenvalues.
"B", "b" Permute and scale, in that order. Rows/columns of a (and b) that are
isolated by permutation are not scaled. This is the default behavior.
Algebraic eigenvalue balancing uses standard Lapack routines.
Generalized eigenvalue problem balancing uses Ward’s algorithm (SIAM Journal on
Scientific and Statistical Computing, 1981).
Function Filecond (a)
Compute the (two-norm) condition number of a matrix. cond (a) is defined as norm
(a) * norm (inv (a)), and is computed via a singular value decomposition.
Loadable Functiondet (a)
Compute the determinant of a using Linpack.
Function Filedmult (a, b)
If a is a vector of length rows (b), return diag (a) * b (but computed much more
efficiently).
166 GNU Octave
Function Filedot (x, y)
Computes the dot product of two vectors.
Loadable Functionlambda = eig (a)
Loadable Function[v, lambda] = eig (a)
The eigenvalues (and eigenvectors) of a matrix are computed in a several step process
which begins with a Hessenberg decomposition, followed by a Schur decomposition,
from which the eigenvalues are apparent. The eigenvectors, when desired, are computed
by further manipulations of the Schur decomposition.
Loadable Functiong = givens (x, y)
Loadable Function[c, s] = givens (x, y)
Return a 2 × 2 orthogonal matrix
G =
c s
−s c
such that
G
x
y
=
∗
0
with x and y scalars.
For example,
givens (1, 1)
⇒ 0.70711 0.70711
-0.70711 0.70711
Loadable Functioninv (a)
Loadable Functioninverse (a)
Compute the inverse of the square matrix a.
Function Filenorm (a, p)
Compute the p-norm of the matrix a. If the second argument is missing, p = 2 is
assumed.
If a is a matrix:
p = 1 1-norm, the largest column sum of a.
p = 2 Largest singular value of a.
p = Inf Infinity norm, the largest row sum of a.
p = "fro"
Frobenius norm of a, sqrt (sum (diag (a’ * a))).
If a is a vector or a scalar:
p = Inf max (abs (a)).
p = -Inf min (abs (a)).
other p-norm of a, (sum (abs (a) .^ p)) ^ (1/p).
Chapter 19: Linear Algebra 167
Function Filenull (a, tol)
Return an orthonormal basis of the null space of a.
The dimension of the null space is taken as the number of singular values of a not
greater than tol. If the argument tol is missing, it is computed as
max (size (a)) * max (svd (a)) * eps
Function Fileorth (a, tol)
Return an orthonormal basis of the range space of a.
The dimension of the range space is taken as the number of singular values of a greater
than tol. If the argument tol is missing, it is computed as
max (size (a)) * max (svd (a)) * eps
Loadable Functionpinv (x, tol)
Return the pseudoinverse of x. Singular values less than tol are ignored.
If the second argument is omitted, it is assumed that
tol = max (size (x)) * sigma_max (x) * eps,
where sigma_max (x) is the maximal singular value of x.
Function Filerank (a, tol)
Compute the rank of a, using the singular value decomposition. The rank is taken
to be the number of singular values of a that are greater than the specified tolerance
tol. If the second argument is omitted, it is taken to be
tol = max (size (a)) * sigma(1) * eps;
where eps is machine precision and sigma(1) is the largest singular value of a.
Function Filetrace (a)
Compute the trace of a, sum (diag (a)).
19.2 Matrix Factorizations
Loadable Functionchol (a)
Compute the Cholesky factor, r, of the symmetric positive definite matrix a, where
RT
R = A.
Loadable Functionh = hess (a)
Loadable Function[p, h] = hess (a)
Compute the Hessenberg decomposition of the matrix a.
The Hessenberg decomposition is usually used as the first step in an eigenvalue computation,
but has other applications as well (see Golub, Nash, and Van Loan, IEEE
Transactions on Automatic Control, 1979. The Hessenberg decomposition is
A = PHPT
where P is a square unitary matrix (PH
P = I), and H is upper Hessenberg (Hi,j =
0, ∀i ≥ j + 1).
168 GNU Octave
Loadable Function[l, u, p] = lu (a)
Compute the LU decomposition of a, using subroutines from Lapack. The result is
returned in a permuted form, according to the optional return value p. For example,
given the matrix a = [1, 2; 3, 4],
[l, u, p] = lu (a)
returns
l =
1.00000 0.00000
0.33333 1.00000
u =
3.00000 4.00000
0.00000 0.66667
p =
0 1
1 0
Loadable Function[q, r, p] = qr (a)
Compute the QR factorization of a, using standard Lapack subroutines. For example,
given the matrix a = [1, 2; 3, 4],
[q, r] = qr (a)
returns
q =
-0.31623 -0.94868
-0.94868 0.31623
r =
-3.16228 -4.42719
0.00000 -0.63246
The qr factorization has applications in the solution of least squares problems
min
x
Ax − b 2
for overdetermined systems of equations (i.e., A is a tall, thin matrix). The QR
factorization is QR = A where Q is an orthogonal matrix and R is upper triangular.
The permuted QR factorization [q, r, p] = qr (a) forms the QR factorization such
that the diagonal entries of r are decreasing in magnitude order. For example, given
the matrix a = [1, 2; 3, 4],
[q, r, p] = qr(a)
returns
Chapter 19: Linear Algebra 169
q =
-0.44721 -0.89443
-0.89443 0.44721
r =
-4.47214 -3.13050
0.00000 0.44721
p =
0 1
1 0
The permuted qr factorization [q, r, p] = qr (a) factorization allows the construction
of an orthogonal basis of span (a).
Loadable Functionlambda = qz (a, b)
Generalized eigenvalue problem Ax = sBx, QZ decomposition. Three ways to call:
1. lambda = qz(A,B)
Computes the generalized eigenvalues lambda of (A − sB).
2. [AA, BB, Q, Z, V, W, lambda] = qz (A, B)
Computes qz decomposition, generalized eigenvectors, and generalized eigenvalues
of (A − sB)
A V = B V diag(lambda)
W’ A = diag(lambda) W’ B
AA = Q’*A*Z, BB = Q’*B*Z with Q, Z orthogonal (unitary)= I
3. [AA,BB,Z{,lambda}] = qz(A,B,opt)
As in form [2], but allows ordering of generalized eigenpairs for (e.g.) solution
of discrete time algebraic Riccati equations. Form 3 is not available for complex
matrices and does not compute the generalized eigenvectors V, W, nor the
orthogonal matrix Q.
opt for ordering eigenvalues of the GEP pencil. The leading block of the
revised pencil contains all eigenvalues that satisfy:
"N" = unordered (default)
"S" = small: leading block has all |lambda| <=1
"B" = big: leading block has all |lambda >= 1
"-" = negative real part: leading block has all eigenvalues in
the open left half-plant
"+" = nonnegative real part: leading block has all eigenvalues
in the closed right half-plane
Note: qz performs permutation balancing, but not scaling (see balance). Order of
output arguments was selected for compatibility with MATLAB
See also: balance, dare, eig, schur
170 GNU Octave
Function File[aa, bb, q, z] = qzhess (a, b)
Compute the Hessenberg-triangular decomposition of the matrix pencil (a, b), returning
aa = q * a * z, bb = q * b * z, with q and z orthogonal. For example,
[aa, bb, q, z] = qzhess ([1, 2; 3, 4], [5, 6; 7, 8])
⇒ aa = [ -3.02244, -4.41741; 0.92998, 0.69749 ]
⇒ bb = [ -8.60233, -9.99730; 0.00000, -0.23250 ]
⇒ q = [ -0.58124, -0.81373; -0.81373, 0.58124 ]
⇒ z = [ 1, 0; 0, 1 ]
The Hessenberg-triangular decomposition is the first step in Moler and Stewart’s QZ
decomposition algorithm.
Algorithm taken from Golub and Van Loan, Matrix Computations, 2nd edition.
Loadable Functions = schur (a)
Loadable Function[u, s] = schur (a, opt)
The Schur decomposition is used to compute eigenvalues of a square matrix, and
has applications in the solution of algebraic Riccati equations in control (see are
and dare). schur always returns S = UT
AU where U is a unitary matrix (UT
U is
identity) and S is upper triangular. The eigenvalues of A (and S) are the diagonal
elements of S If the matrix A is real, then the real Schur decomposition is computed,
in which the matrix U is orthogonal and S is block upper triangular with blocks of
size at most 2 × 2 along the diagonal. The diagonal elements of S (or the eigenvalues
of the 2 × 2 blocks, when appropriate) are the eigenvalues of A and S.
The eigenvalues are optionally ordered along the diagonal according to the value of
opt. opt = "a" indicates that all eigenvalues with negative real parts should be moved
to the leading block of S (used in are), opt = "d" indicates that all eigenvalues with
magnitude less than one should be moved to the leading block of S (used in dare),
and opt = "u", the default, indicates that no ordering of eigenvalues should occur.
The leading k columns of U always span the A-invariant subspace corresponding to
the k leading eigenvalues of S.
Loadable Functions = svd (a)
Loadable Function[u, s, v] = svd (a)
Compute the singular value decomposition of a
A = UΣV H
The function svd normally returns the vector of singular values. If asked for three
return values, it computes U, S, and V . For example,
svd (hilb (3))
returns
ans =
1.4083189
0.1223271
0.0026873
and
Chapter 19: Linear Algebra 171
[u, s, v] = svd (hilb (3))
returns
u =
-0.82704 0.54745 0.12766
-0.45986 -0.52829 -0.71375
-0.32330 -0.64901 0.68867
s =
1.40832 0.00000 0.00000
0.00000 0.12233 0.00000
0.00000 0.00000 0.00269
v =
-0.82704 0.54745 0.12766
-0.45986 -0.52829 -0.71375
-0.32330 -0.64901 0.68867
If given a second argument, svd returns an economy-sized decomposition, eliminating
the unnecessary rows or columns of u or v.
Function File[housv, beta, zer] = housh (x, j, z)
Computes householder reflection vector housv to reflect x to be jth column of identity,
i.e., (I - beta*housv*housv’)x =e(j) inputs x: vector j: index into vector z: threshold
for zero (usually should be the number 0) outputs: (see Golub and Van Loan) beta: If
beta = 0, then no reflection need be applied (zer set to 0) housv: householder vector
Function File[u, h, nu] = krylov (a, v, k, eps1, pflg);
construct orthogonal basis U of block Krylov subspace; [v a*v a^2*v ... a^(k+1)*v];
method used: householder reflections to guard against loss of orthogonality eps1:
threshhold for 0 (default: 1e-12) pflg: flag to use row pivoting (improves numerical
behavior) 0 [default]: no pivoting; prints a warning message if trivial null space is
corrupted 1 : pivoting performed
outputs: u: orthogonal basis of block krylov subspace h: Hessenberg matrix; if v
is a vector then a u = u h otherwise h is meaningless nu: dimension of span of
krylov subspace (based on eps1) if b is a vector and k > m-1, krylov returns h = the
Hessenberg decompostion of a.
Reference: Hodel and Misra, "Partial Pivoting in the Computation of Krylov Subspaces",
to be submitted to Linear Algebra and its Applications
19.3 Functions of a Matrix
172 GNU Octave
Loadable Functionexpm (a)
Return the exponential of a matrix, defined as the infinite Taylor series
exp(A) = I + A +
A2
2!
+
A3
3!
+ · · ·
The Taylor series is not the way to compute the matrix exponential; see Moler and
Van Loan, Nineteen Dubious Ways to Compute the Exponential of a Matrix, SIAM
Review, 1978. This routine uses Ward’s diagonal Pad´e approximation method with
three step preconditioning (SIAM Journal on Numerical Analysis, 1977). Diagonal
Pad´e approximations are rational polynomials of matrices Dq(a)−1
Nq(a) whose Taylor
series matches the first 2q + 1 terms of the Taylor series above; direct evaluation of
the Taylor series (with the same preconditioning steps) may be desirable in lieu of
the Pad´e approximation when Dq(a) is ill-conditioned.
Loadable Functionlogm (a)
Compute the matrix logarithm of the square matrix a. Note that this is currently
implemented in terms of an eigenvalue expansion and needs to be improved to be
more robust.
Loadable Functionsqrtm (a)
Compute the matrix square root of the square matrix a. Note that this is currently
implemented in terms of an eigenvalue expansion and needs to be improved to be
more robust.
Function Filekron (a, b)
Form the kronecker product of two matrices, defined block by block as
x = [a(i, j) b]
For example,
kron (1:4, ones (3, 1))
⇒ 1 2 3 4
1 2 3 4
1 2 3 4
Loadable Functionx = syl (a, b, c)
Solve the Sylvester equation
AX + XB + C = 0
using standard Lapack subroutines. For example,
syl ([1, 2; 3, 4], [5, 6; 7, 8], [9, 10; 11, 12])
⇒ [ -0.50000, -0.66667; -0.66667, -0.50000 ]
Chapter 20: Nonlinear Equations 173
20 Nonlinear Equations
Octave can solve sets of nonlinear equations of the form
f(x) = 0
using the function fsolve, which is based on the Minpack subroutine hybrd.
Loadable Function[x, info] = fsolve (fcn, x0)
Given fcn, the name of a function of the form f (x) and an initial starting point x0,
fsolve solves the set of equations such that f(x) == 0.
Loadable Functionfsolve options (opt, val)
When called with two arguments, this function allows you set options parameters for
the function fsolve. Given one argument, fsolve_options returns the value of the
corresponding option. If no arguments are supplied, the names of all the available
options and their current values are displayed.
Here is a complete example. To solve the set of equations
−2x2
+ 3xy + 4 sin(y) − 6 = 0
3x2
− 2xy2
+ 3 cos(x) + 4 = 0
you first need to write a function to compute the value of the given function. For example:
function y = f (x)
y(1) = -2*x(1)^2 + 3*x(1)*x(2) + 4*sin(x(2)) - 6;
y(2) = 3*x(1)^2 - 2*x(1)*x(2)^2 + 3*cos(x(1)) + 4;
endfunction
Then, call fsolve with a specified initial condition to find the roots of the system of
equations. For example, given the function f defined above,
[x, info] = fsolve ("f", [1; 2])
results in the solution
x =
0.57983
2.54621
info = 1
A value of info = 1 indicates that the solution has converged.
The function perror may be used to print English messages corresponding to the numeric
error codes. For example,
perror ("fsolve", 1)
solution converged to requested tolerance
174 GNU Octave
Chapter 21: Quadrature 175
21 Quadrature
21.1 Functions of One Variable
Loadable Function[v, ier, nfun, err] = quad (f, a, b, tol, sing)
Integrate a nonlinear function of one variable using Quadpack. The first argument is
the name of the function to call to compute the value of the integrand. It must have
the form
y = f (x)
where y and x are scalars.
The second and third arguments are limits of integration. Either or both may be
infinite.
The optional argument tol is a vector that specifies the desired accuracy of the result.
The first element of the vector is the desired absolute tolerance, and the second
element is the desired relative tolerance. To choose a relative test only, set the absolute
tolerance to zero. To choose an absolute test only, set the relative tolerance to zero.
The optional argument sing is a vector of values at which the integrand is known to
be singular.
The result of the integration is returned in v and ier contains an integer error code
(0 indicates a successful integration). The value of nfun indicates how many function
evaluations were required, and err contains an estimate of the error in the solution.
Loadable Functionquad options (opt, val)
When called with two arguments, this function allows you set options parameters
for the function quad. Given one argument, quad_options returns the value of the
corresponding option. If no arguments are supplied, the names of all the available
options and their current values are displayed.
Here is an example of using quad to integrate the function
f(x) = x sin(1/x) |1 − x|
from x = 0 to x = 3.
This is a fairly difficult integration (plot the function over the range of integration to see
why).
The first step is to define the function:
function y = f (x)
y = x .* sin (1 ./ x) .* sqrt (abs (1 - x));
endfunction
Note the use of the ‘dot’ forms of the operators. This is not necessary for the call to
quad, but it makes it much easier to generate a set of points for plotting (because it makes
it possible to call the function with a vector argument to produce a vector result).
Then we simply call quad:
176 GNU Octave
[v, ier, nfun, err] = quad ("f", 0, 3)
⇒ 1.9819
⇒ 1
⇒ 5061
⇒ 1.1522e-07
Although quad returns a nonzero value for ier, the result is reasonably accurate (to see
why, examine what happens to the result if you move the lower bound to 0.1, then 0.01,
then 0.001, etc.).
21.2 Orthogonal Collocation
Loadable Function[r, amat, bmat, q] = colloc (n, "left", "right")
Compute derivative and integral weight matrices for orthogonal collocation using
the subroutines given in J. Villadsen and M. L. Michelsen, Solution of Differential
Equation Models by Polynomial Approximation.
Here is an example of using colloc to generate weight matrices for solving the second
order differential equation u −αu = 0 with the boundary conditions u(0) = 0 and u(1) = 1.
First, we can generate the weight matrices for n points (including the endpoints of the
interval), and incorporate the boundary conditions in the right hand side (for a specific
value of α).
n = 7;
alpha = 0.1;
[r, a, b] = colloc (n-2, "left", "right");
at = a(2:n-1,2:n-1);
bt = b(2:n-1,2:n-1);
rhs = alpha * b(2:n-1,n) - a(2:n-1,n);
Then the solution at the roots r is
u = [ 0; (at - alpha * bt) \ rhs; 1]
⇒ [ 0.00; 0.004; 0.01 0.00; 0.12; 0.62; 1.00 ]
Chapter 22: Differential Equations 177
22 Differential Equations
Octave has two built-in functions for solving differential equations. Both are based on
reliable ODE solvers written in Fortran.
22.1 Ordinary Differential Equations
The function lsode can be used to solve ODEs of the form
dx
dt
= f(x, t)
using Hindmarsh’s ODE solver Lsode.
Loadable Functionlsode (fcn, x0, t, t crit)
Return a matrix of x as a function of t, given the initial state of the system x0. Each
row in the result matrix corresponds to one of the elements in the vector t. The first
element of t corresponds to the initial state x0, so that the first row of the output is
x0.
The first argument, fcn, is a string that names the function to call to compute the
vector of right hand sides for the set of equations. It must have the form
xdot = f (x, t)
where xdot and x are vectors and t is a scalar.
The fourth argument is optional, and may be used to specify a set of times that
the ODE solver should not integrate past. It is useful for avoiding difficulties with
singularities and points where there is a discontinuity in the derivative.
Here is an example of solving a set of three differential equations using lsode. Given
the function
function xdot = f (x, t)
xdot = zeros (3,1);
xdot(1) = 77.27 * (x(2) - x(1)*x(2) + x(1) \
- 8.375e-06*x(1)^2);
xdot(2) = (x(3) - x(1)*x(2) - x(2)) / 77.27;
xdot(3) = 0.161*(x(1) - x(3));
endfunction
and the initial condition x0 = [ 4; 1.1; 4 ], the set of equations can be integrated using
the command
t = linspace (0, 500, 1000);
y = lsode ("f", x0, t);
If you try this, you will see that the value of the result changes dramatically between t
= 0 and 5, and again around t = 305. A more efficient set of output points might be
t = [0, logspace (-1, log10(303), 150), \
logspace (log10(304), log10(500), 150)];
178 GNU Octave
Loadable Functionlsode options (opt, val)
When called with two arguments, this function allows you set options parameters for
the function lsode. Given one argument, lsode_options returns the value of the
corresponding option. If no arguments are supplied, the names of all the available
options and their current values are displayed.
See Alan C. Hindmarsh, ODEPACK, A Systematized Collection of ODE Solvers, in
Scientific Computing, R. S. Stepleman, editor, (1983) for more information about the inner
workings of lsode.
22.2 Differential-Algebraic Equations
The function dassl can be used to solve DAEs of the form
0 = f(˙x, x, t), x(t = 0) = x0, ˙x(t = 0) = ˙x0
using Petzold’s DAE solver Dassl.
Loadable Function[x, xdot] = dassl (fcn, x0, xdot0, t, t crit)
Return a matrix of states and their first derivatives with respect to t. Each row in the
result matrices correspond to one of the elements in the vector t. The first element
of t corresponds to the initial state x0 and derivative xdot0, so that the first row of
the output x is x0 and the first row of the output xdot is xdot0.
The first argument, fcn, is a string that names the function to call to compute the
vector of residuals for the set of equations. It must have the form
res = f (x, xdot, t)
where x, xdot, and res are vectors, and t is a scalar.
The second and third arguments to dassl specify the initial condition of the states
and their derivatives, and the fourth argument specifies a vector of output times at
which the solution is desired, including the time corresponding to the initial condition.
The set of initial states and derivatives are not strictly required to be consistent. In
practice, however, Dassl is not very good at determining a consistent set for you, so
it is best if you ensure that the initial values result in the function evaluating to zero.
The fifth argument is optional, and may be used to specify a set of times that the DAE
solver should not integrate past. It is useful for avoiding difficulties with singularities
and points where there is a discontinuity in the derivative.
Loadable Functiondassl options (opt, val)
When called with two arguments, this function allows you set options parameters for
the function lsode. Given one argument, dassl_options returns the value of the
corresponding option. If no arguments are supplied, the names of all the available
options and their current values are displayed.
See K. E. Brenan, et al., Numerical Solution of Initial-Value Problems in DifferentialAlgebraic
Equations, North-Holland (1989) for more information about the implementation
of Dassl.
Chapter 23: Optimization 179
23 Optimization
23.1 Quadratic Programming
23.2 Nonlinear Programming
23.3 Linear Least Squares
Function File[beta, v, r] = gls (y, x, o)
Generalized least squares estimation for the multivariate model y = xb+e with ¯e = 0
and cov(vec(e)) = (s2
)o, where y is a t × p matrix, x is a t × k matrix, b is a k × p
matrix, e is a t × p matrix, and o is a tp × tp matrix.
Each row of y and x is an observation and each column a variable. The return values
beta, v, and r are defined as follows.
beta The GLS estimator for b.
v The GLS estimator for sˆ2.
r The matrix of GLS residuals, r = y − xbeta.
Function File[beta, sigma, r] = ols (y, x)
Ordinary least squares estimation for the multivariate model y = xb + e with ¯e = 0,
and cov(vec(e)) = kron (s, I) where y is a t × p matrix, x is a t × k matrix, b is a
k × p matrix, and e is a t × p matrix.
Each row of y and x is an observation and each column a variable.
The return values beta, sigma, and r are defined as follows.
beta The OLS estimator for b, beta = pinv (x) * y, where pinv (x) denotes
the pseudoinverse of x.
sigma The OLS estimator for the matrix s,
sigma = (y-x*beta)’
* (y-x*beta)
/ (t-rank(x))
r The matrix of OLS residuals, r = y - x * beta.
180 GNU Octave
Chapter 24: Statistics 181
24 Statistics
I hope that someday Octave will include more statistics functions. If you would like to
help improve Octave in this area, please contact bug-octave@bevo.che.wisc.edu.
24.1 Basic Statistical Functions
Function Filemean (x, opt)
If x is a vector, compute the mean of the elements of x
mean(x) = ¯x =
1
N
N
i=1
xi
If x is a matrix, compute the mean for each column and return them in a row vector.
With the optional argument opt, the kind of mean computed can be selected. The
following options are recognized:
"a" Compute the (ordinary) arithmetic mean. This is the default.
"g" Computer the geometric mean.
"h" Compute the harmonic mean.
Function Filemedian (x)
If x is a vector, compute the median value of the elements of x.
median(x) =
x( N/2 ), N odd;
(x(N/2) + x(N/2 + 1))/2, N even.
If x is a matrix, compute the median value for each column and return them in a row
vector.
Function Filestd (x)
If x is a vector, compute the standard deviation of the elements of x.
std(x) = σ(x) =
N
i=1(xi − ¯x)
N − 1
If x is a matrix, compute the standard deviation for each column and return them in
a row vector.
Function Filecov (x, y)
If each row of x and y is an observation and each column is a variable, the (i,j)-th
entry of cov (x, y) is the covariance between the i-th variable in x and the j-th
variable in y. If called with one argument, compute cov (x, x).
182 GNU Octave
Function Filecorrcoef (x, y)
If each row of x and y is an observation and each column is a variable, the (i,j)-th
entry of corrcoef (x, y) is the correlation between the i-th variable in x and the
j-th variable in y. If called with one argument, compute corrcoef (x, x).
Function Filekurtosis (x)
If x is a vector of length N, return the kurtosis
kurtosis(x) =
1
Nσ(x)4
N
i=1
(xi − ¯x)4
− 3
of x. If x is a matrix, return the row vector containing the kurtosis of each column.
Function Filemahalanobis (x, y)
Return the Mahalanobis’ D-square distance between the multivariate samples x and
y, which must have the same number of components (columns), but may have a
different number of observations (rows).
Function Fileskewness (x)
If x is a vector of length n, return the skewness
skewness(x) =
1
Nσ(x)3
N
i=1
(xi − ¯x)3
of x. If x is a matrix, return the row vector containing the skewness of each column.
Function Filevalues (x)
Return the different values in a column vector, arranged in ascending order.
Function Filevar (x)
For vector arguments, return the (real) variance of the values. For matrix arguments,
return a row vector contaning the variance for each column.
Function File[t, l x] = table (x)
Function File[t, l x, l y] = table (x, y)
Create a contingency table t from data vectors. The l vectors are the corresponding
levels.
Currently, only 1- and 2-dimensional tables are supported.
Function Filestudentize (x)
If x is a vector, subtract its mean and divide by its standard deviation.
If x is a matrix, do the above for each column.
Chapter 24: Statistics 183
Function Filestatistics (x)
If x is a matrix, return a matrix with the minimum, first quartile, median, third
quartile, maximum, mean, standard deviation, skewness and kurtosis of the columns
of x as its rows.
If x is a vector, treat it as a column vector.
Function Filespearman (x, y)
Compute Spearman’s rank correlation coefficient rho for each of the variables specified
by the input arguments.
For matrices, each row is an observation and each column a variable; vectors are
always observations and may be row or column vectors.
spearman (x) is equivalent to spearman (x, x).
For two data vectors x and y, Spearman’s rho is the correlation of the ranks of x and
y.
If x and y are drawn from independent distributions, rho has zero mean and variance
1 / (n - 1), and is asymptotically normally distributed.
Function Filerun count (x, n)
Count the upward runs in the columns of x of length 1, 2, ..., n-1 and greater than
or equal to n.
Function Fileranks (x)
If x is a vector, return the (column) vector of ranks of x adjusted for ties.
If x is a matrix, do the above for each column of x.
Function Filerange (x)
If x is a vector, return the range, i.e., the difference between the maximum and the
minimum, of the input data.
If x is a matrix, do the above for each column of x.
Function File[q, s] = qqplot (x, dist, params)
Perform a QQ-plot (quantile plot).
If F is the CDF of the distribution dist with parameters params and G its inverse,
and x a sample vector of length n, the QQ-plot graphs ordinate s(i) = i-th largest
element of x versus abscissa q(if) = G((i - 0.5)/n).
If the sample comes from F except for a transformation of location and scale, the
pairs will approximately follow a straight line.
The default for dist is the standard normal distribution. The optional argument
params contains a list of parameters of dist. For example, for a quantile plot of the
uniform distribution on [2,4] and x, use
qqplot (x, "uniform", 2, 4)
If no output arguments are given, the data are plotted directly.
184 GNU Octave
Function Fileprobit (p)
For each component of p, return the probit (the quantile of the standard normal
distribution) of p.
Function File[p, y] = ppplot (x, dist, params)
Perform a PP-plot (probability plot).
If F is the CDF of the distribution dist with parameters params and x a sample vector
of length n, the PP-plot graphs ordinate y(i) = F (i-th largest element of x) versus
abscissa p(i) = (i - 0.5)/n. If the sample comes from F, the pairs will approximately
follow a straight line.
The default for dist is the standard normal distribution. The optional argument
params contains a list of parameters of dist. For example, for a probability plot of
the uniform distribution on [2,4] and x, use
ppplot (x, "uniform", 2, 4)
If no output arguments are given, the data are plotted directly.
Function Filemoment (x, p, opt)
If x is a vector, compute the p-th moment of x.
If x is a matrix, return the row vector containing the p-th moment of each column.
With the optional string opt, the kind of moment to be computed can be specified. If
opt contains "c" or "a", central and/or absolute moments are returned. For example,
moment (x, 3, "ac")
computes the third central absolute moment of x.
Function Filemeansq (x)
For vector arguments, return the mean square of the values. For matrix arguments,
return a row vector contaning the mean square of each column.
Function Filelogit (p)
For each component of p, return the logit log (p / (1-p)) of p.
Function Filekendall (x, y)
Compute Kendall’s tau for each of the variables specified by the input arguments.
For matrices, each row is an observation and each column a variable; vectors are
always observations and may be row or column vectors.
kendall (x) is equivalent to kendall (x, x).
For two data vectors x, y of common length n, Kendall’s tau is the correlation of the
signs of all rank differences of x and y; i.e., if both x and y have distinct entries, then
τ =
1
n(n − 1) i,j
sign(qi − qj)sign(ri − rj)
in which the qi and ri are the ranks of x and y, respectively.
If x and y are drawn from independent distributions, Kendall’s tau is asymptotically
normal with mean 0 and variance (2 * (2n+5)) / (9 * n * (n-1)).
Chapter 24: Statistics 185
Function Fileiqr (x)
If x is a vector, return the interquartile range, i.e., the difference between the upper
and lower quartile, of the input data.
If x is a matrix, do the above for each column of x.
Function Filecut (x, breaks)
Create categorical data out of numerical or continuous data by cutting into intervals.
If breaks is a scalar, the data is cut into that many equal-width intervals. If breaks
is a vector of break points, the category has length (breaks) - 1 groups.
The returned value is a vector of the same size as x telling which group each point in
x belongs to. Groups are labelled from 1 to the number of groups; points outside the
range of breaks are labelled by NaN.
Function Filecor (x, y)
The (i,j)-th entry of cor (x, y) is the correlation between the i-th variable in x and
the j-th variable in y.
For matrices, each row is an observation and each column a variable; vectors are
always observations and may be row or column vectors.
cor (x) is equivalent to cor (x, x).
Function Filecloglog (x)
Return the complementary log-log function of x, defined as
- log (- log (x))
Function Filecenter (x)
If x is a vector, subtract its mean. If x is a matrix, do the above for each column.
24.2 Tests
Function File[pval, f, df b, df w] = anova (y, g)
Perform a one-way analysis of variance (ANOVA). The goal is to test whether the
population means of data taken from k different groups are all equal.
Data may be given in a single vector y with groups specified by a corresponding
vector of group labels g (e.g., numbers from 1 to k). This is the general form which
does not impose any restriction on the number of data in each group or the group
labels.
If y is a matrix and g is omitted, each column of y is treated as a group. This form
is only appropriate for balanced ANOVA in which the numbers of samples from each
group are all equal.
Under the null of constant means, the statistic f follows an F distribution with df b
and df w degrees of freedom.
The p-value (1 minus the CDF of this distribution at f ) is returned in pval.
If no output argument is given, the standard one-way ANOVA table is printed.
186 GNU Octave
Function File[pval, chisq, df ] = bartlett test (x1, ...)
Perform a Bartlett test for the homogeneity of variances in the data vectors x1, x2,
. . ., xk, where k > 1.
Under the null of equal variances, the test statistic chisq approximately ollows a
chi-square distribution with df degrees of freedom.
The p-value (1 minus the CDF of this distribution at chisq) is returned in pval.
If no output argument is given, the p-value is displayed.
Function File[pval, chisq, df ] = chisquare test homogeneity (x, y, c)
Given two samples x and y, perform a chisquare test for homogeneity of the null
hypothesis that x and y come from the same distribution, based on the partition
induced by the (strictly increasing) entries of c.
For large samples, the test statistic chisq approximately follows a chisquare distribution
with df = length (c) degrees of freedom.
The p-value (1 minus the CDF of this distribution at chisq) is returned in pval.
If no output argument is given, the p-value is displayed.
Function File[pval, chisq, df ] = chisquare test independence (x)
Perform a chi-square test for indepence based on the contingency table x. Under the
null hypothesis of independence, chisq approximately has a chi-square distribution
with df degrees of freedom.
The p-value (1 minus the CDF of this distribution at chisq) of the test is returned in
pval.
If no output argument is given, the p-value is displayed.
Function Filecor test (x, y, alt, method)
Test whether two samples x and y come from uncorrelated populations.
The optional argument string alt describes the alternative hypothesis, and can be
"!=" or "<>" (non-zero), ">" (greater than 0), or "<" (less than 0). The default is
the two-sided case.
The optional argument string method specifies on which correlation coefficient the test
should be based. If method is "pearson" (default), the (usual) Pearson’s product
moment correlation coefficient is used. In this case, the data should come from a
bivariate normal distribution. Otherwise, the other two methods offer nonparametric
alternatives. If method is "kendall", then Kendall’s rank correlation tau is used. If
method is "spearman", then Spearman’s rank correlation rho is used. Only the first
character is necessary.
The output is a structure with the following elements:
pval The p-value of the test.
stat The value of the test statistic.
dist The distribution of the test statistic.
Chapter 24: Statistics 187
params The parameters of the null distribution of the test statistic.
alternative
The alternative hypothesis.
method The method used for testing.
If no output argument is given, the p-value is displayed.
Function File[pval, f, df num, df den] = f test regression (y, x, rr, r)
Perform an F test for the null hypothesis rr * b = r in a classical normal regression
model y = X * b + e.
Under the null, the test statistic f follows an F distribution with df num and df den
degrees of freedom.
The p-value (1 minus the CDF of this distribution at f ) is returned in pval.
If not given explicitly, r = 0.
If no output argument is given, the p-value is displayed.
Function File[pval, tsq] = hotelling test (x, m)
For a sample x from a multivariate normal distribution with unknown mean and
covariance matrix, test the null hypothesis that mean (x) == m.
Hotelling’s T^2 is returned in tsq. Under the null, (n − p)Tˆ2/(p(n − 1)) has an F
distribution with p and n − p degrees of freedom, where n and p are the numbers of
samples and variables, respectively.
The p-value of the test is returned in pval.
If no output argument is given, the p-value of the test is displayed.
Function File[pval, tsq] = hotelling test 2 (x, y)
For two samples x from multivariate normal distributions with the same number of
variables (columns), unknown means and unknown equal covariance matrices, test
the null hypothesis mean (x) == mean (y).
Hotelling’s two-sample T^2 is returned in tsq. Under the null,
(n_x+n_y-p-1) T^2 / (p(n_x+n_y-2))
has an F distribution with p and n x+n y − p − 1 degrees of freedom, where n x and
n y are the sample sizes and p is the number of variables.
The p-value of the test is returned in pval.
If no output argument is given, the p-value of the test is displayed.
Function File[pval, ks] = kolmogorov smirnov test (x, dist, params, alt)
Perform a Kolmogorov-Smirnov test of the null hypothesis that the sample x comes
from the (continuous) distribution dist. I.e., if F and G are the CDFs corresponding
to the sample and dist, respectively, then the null is that F == G.
The optional argument params contains a list of parameters of dist. For example, to
test whether a sample x comes from a uniform distribution on [2,4], use
188 GNU Octave
kolmogorov_smirnov_test(x, "uniform", 2, 4)
With the optional argument string alt, the alternative of interest can be selected. If
alt is "!=" or "<>", the null is tested against the two-sided alternative F != G. In this
case, the test statistic ks follows a two-sided Kolmogorov-Smirnov distribution. If alt
is ">", the one-sided alternative F > G is considered. Similarly for "<", the one-sided
alternative F > G is considered. In this case, the test statistic ks has a one-sided
Kolmogorov-Smirnov distribution. The default is the two-sided case.
The p-value of the test is returned in pval.
If no output argument is given, the p-value is displayed.
Function File[pval, ks, d] = kolmogorov smirnov test 2 (x, y, alt)
Perform a 2-sample Kolmogorov-Smirnov test of the null hypothesis that the samples
x and y come from the same (continuous) distribution. I.e., if F and G are the CDFs
corresponding to the x and y samples, respectively, then the null is that F == G.
With the optional argument string alt, the alternative of interest can be selected. If
alt is "!=" or "<>", the null is tested against the two-sided alternative F != G. In this
case, the test statistic ks follows a two-sided Kolmogorov-Smirnov distribution. If alt
is ">", the one-sided alternative F > G is considered. Similarly for "<", the one-sided
alternative F < G is considered. In this case, the test statistic ks has a one-sided
Kolmogorov-Smirnov distribution. The default is the two-sided case.
The p-value of the test is returned in pval.
The third returned value, d, is the test statistic, the maximum vertical distance
between the two cumulative distribution functions.
If no output argument is given, the p-value is displayed.
Function File[pval, k, df ] = kruskal wallis test (x1, ...)
Perform a Kruskal-Wallis one-factor "analysis of variance".
Suppose a variable is observed for k > 1 different groups, and let x1, . . ., xk be the
corresponding data vectors.
Under the null hypothesis that the ranks in the pooled sample are not affected by the
group memberships, the test statistic k is approximately chi-square with df = k - 1
degrees of freedom.
The p-value (1 minus the CDF of this distribution at k) is returned in pval.
If no output argument is given, the p-value is displayed.
Function Filemanova (y, g)
Perform a one-way multivariate analysis of variance (MANOVA). The goal is to test
whether the p-dimensional population means of data taken from k different groups
are all equal. All data are assumed drawn independently from p-dimensional normal
distributions with the same covariance matrix.
The data matrix is given by y. As usual, rows are observations and columns are
variables. The vector g specifies the corresponding group labels (e.g., numbers from
1 to k).
Chapter 24: Statistics 189
The LR test statistic (Wilks’ Lambda) and approximate p-values are computed and
displayed.
Function File[pval, chisq, df ] = mcnemar test (x)
For a square contingency table x of data cross-classified on the row and column
variables, McNemar’s test can be used for testing the null hypothesis of symmetry of
the classification probabilities.
Under the null, chisq is approximately distributed as chisquare with df degrees of
freedom.
The p-value (1 minus the CDF of this distribution at chisq) is returned in pval.
If no output argument is given, the p-value of the test is displayed.
Function File[pval, z] = prop test 2 (x1, n1, x2, n2, alt)
If x1 and n1 are the counts of successes and trials in one sample, and x2 and n2
those in a second one, test the null hypothesis that the success probabilities p1 and
p2 are the same. Under the null, the test statistic z approximately follows a standard
normal distribution.
With the optional argument string alt, the alternative of interest can be selected. If
alt is "!=" or "<>", the null is tested against the two-sided alternative p1 != p2. If
alt is ">", the one-sided alternative p1 > p2 is used. Similarly for "<", the one-sided
alternative p1 < p2 is used. The default is the two-sided case.
The p-value of the test is returned in pval.
If no output argument is given, the p-value of the test is displayed.
Function File[pval, chisq] = run test (x)
Perform a chi-square test with 6 degrees of freedom based on the upward runs in the
columns of x. Can be used to test whether x contains independent data.
The p-value of the test is returned in pval.
If no output argument is given, the p-value is displayed.
Function File[pval, b, n] = sign test (x, y, alt)
For two matched-pair samples x and y, perform a sign test of the null hypothesis
PROB (x > y) == PROB (x < y) == 1/2. Under the null, the test statistic b
roughly follows a binomial distribution with parameters n = sum (x != y) and p =
1/2.
With the optional argument alt, the alternative of interest can be selected. If alt is
"!=" or "<>", the null hypothesis is tested against the two-sided alternative PROB
(x < y) != 1/2. If alt is ">", the one-sided alternative PROB (x > y) > 1/2 ("x
is stochastically greater than y") is considered. Similarly for "<", the one-sided
alternative PROB (x > y) < 1/2 ("x is stochastically less than y") is considered. The
default is the two-sided case.
The p-value of the test is returned in pval.
If no output argument is given, the p-value of the test is displayed.
190 GNU Octave
Function File[pval, t, df ] = t test (x, m, alt)
For a sample x from a normal distribution with unknown mean and variance, perform
a t-test of the null hypothesis mean (x) == m. Under the null, the test statistic t
follows a Student distribution with df = length (x) - 1 degrees of freedom.
With the optional argument string alt, the alternative of interest can be selected. If
alt is "!=" or "<>", the null is tested against the two-sided alternative mean (x) != m.
If alt is ">", the one-sided alternative mean (x) > m is considered. Similarly for "<",
the one-sided alternative mean (x) < m is considered, The default is the two-sided
case.
The p-value of the test is returned in pval.
If no output argument is given, the p-value of the test is displayed.
Function File[pval, t, df ] = t test 2 (x, y, alt)
For two samples x and y from normal distributions with unknown means and unknown
equal variances, perform a two-sample t-test of the null hypothesis of equal means.
Under the null, the test statistic t follows a Student distribution with df degrees of
freedom.
With the optional argument string alt, the alternative of interest can be selected.
If alt is "!=" or "<>", the null is tested against the two-sided alternative mean (x)
!= mean (y). If alt is ">", the one-sided alternative mean (x) > mean (y) is used.
Similarly for "<", the one-sided alternative mean (x) < mean (y) is used. The default
is the two-sided case.
The p-value of the test is returned in pval.
If no output argument is given, the p-value of the test is displayed.
Function File[pval, t, df ] = t test regression (y, x, rr, r, alt)
Perform an t test for the null hypothesis rr * b = r in a classical normal regression
model y = x * b + e. Under the null, the test statistic t follows a t distribution with
df degrees of freedom.
If r is omitted, a value of 0 is assumed.
With the optional argument string alt, the alternative of interest can be selected.
If alt is "!=" or "<>", the null is tested against the two-sided alternative rr * b !=
r. If alt is ">", the one-sided alternative rr * b > r is used. Similarly for "<", the
one-sided alternative rr * b < r is used. The default is the two-sided case.
The p-value of the test is returned in pval.
If no output argument is given, the p-value of the test is displayed.
Function File[pval, z] = u test (x, y, alt)
For two samples x and y, perform a Mann-Whitney U-test of the null hypothesis
PROB (x > y) == 1/2 == PROB (x < y). Under the null, the test statistic z
approximately follows a standard normal distribution. Note that this test is equivalent
to the Wilcoxon rank-sum test.
Chapter 24: Statistics 191
With the optional argument string alt, the alternative of interest can be selected. If
alt is "!=" or "<>", the null is tested against the two-sided alternative PROB (x >
y) != 1/2. If alt is ">", the one-sided alternative PROB (x > y) > 1/2 is considered.
Similarly for "<", the one-sided alternative PROB (x > y) < 1/2 is considered, The
default is the two-sided case.
The p-value of the test is returned in pval.
If no output argument is given, the p-value of the test is displayed.
Function File[pval, f, df num, df den] = var test (x, y, alt)
For two samples x and y from normal distributions with unknown means and unknown
variances, perform an F-test of the null hypothesis of equal variances. Under the
null, the test statistic f follows an F-distribution with df num and df den degrees of
freedom.
With the optional argument string alt, the alternative of interest can be selected. If
alt is "!=" or "<>", the null is tested against the two-sided alternative var (x) != var
(y). If alt is ">", the one-sided alternative var (x) > var (y) is used. Similarly for
"<", the one-sided alternative var (x) > var (y) is used. The default is the two-sided
case.
The p-value of the test is returned in pval.
If no output argument is given, the p-value of the test is displayed.
Function File[pval, t, df ] = welch test (x, y, alt)
For two samples x and y from normal distributions with unknown means and unknown
and not necessarily equal variances, perform a Welch test of the null hypothesis of
equal means. Under the null, the test statistic t approximately follows a Student
distribution with df degrees of freedom.
With the optional argument string alt, the alternative of interest can be selected. If
alt is "!=" or "<>", the null is tested against the two-sided alternative mean (x) !=
m. If alt is ">", the one-sided alternative mean(x) > m is considered. Similarly for
"<", the one-sided alternative mean(x) < m is considered. The default is the two-sided
case.
The p-value of the test is returned in pval.
If no output argument is given, the p-value of the test is displayed.
Function File[pval, z] = wilcoxon test (x, y, alt)
For two matched-pair sample vectors x and y, perform a Wilcoxon signed-rank test
of the null hypothesis PROB (x > y) == 1/2. Under the null, the test statistic z
approximately follows a standard normal distribution.
With the optional argument string alt, the alternative of interest can be selected. If
alt is "!=" or "<>", the null is tested against the two-sided alternative PROB (x >
y) != 1/2. If alt is ">", the one-sided alternative PROB (x > y) > 1/2 is considered.
Similarly for "<", the one-sided alternative PROB (x > y) < 1/2 is considered. The
default is the two-sided case.
The p-value of the test is returned in pval.
If no output argument is given, the p-value of the test is displayed.
192 GNU Octave
Function File[pval, z] = z test (x, m, v, alt)
Perform a Z-test of the null hypothesis mean (x) == m for a sample x from a normal
distribution with unknown mean and known variance v. Under the null, the test
statistic z follows a standard normal distribution.
With the optional argument string alt, the alternative of interest can be selected. If
alt is "!=" or "<>", the null is tested against the two-sided alternative mean (x) != m.
If alt is ">", the one-sided alternative mean (x) > m is considered. Similarly for "<",
the one-sided alternative mean (x) < m is considered. The default is the two-sided
case.
The p-value of the test is returned in pval.
If no output argument is given, the p-value of the test is displayed along with some
information.
Function File[pval, z] = z test 2 (x, y, v x, v y, alt)
For two samples x and y from normal distributions with unknown means and known
variances v x and v y, perform a Z-test of the hypothesis of equal means. Under the
null, the test statistic z follows a standard normal distribution.
With the optional argument string alt, the alternative of interest can be selected.
If alt is "!=" or "<>", the null is tested against the two-sided alternative mean (x)
!= mean (y). If alt is ">", the one-sided alternative mean (x) > mean (y) is used.
Similarly for "<", the one-sided alternative mean (x) < mean (y) is used. The default
is the two-sided case.
The p-value of the test is returned in pval.
If no output argument is given, the p-value of the test is displayed along with some
information.
24.3 Models
Functio File[theta, beta, dev, dl, d2l, p] = logistic regression (y, x,
print, theta, beta)
Perform ordinal logistic regression.
Suppose y takes values in k ordered categories, and let gamma_i (x) be the cumulative
probability that y falls in one of the first i categories given the covariate x. Then
[theta, beta] = logistic_regression (y, x)
fits the model
logit (gamma_i (x)) = theta_i - beta’ * x, i = 1, ..., k-1
The number of ordinal categories, k, is taken to be the number of distinct values of
round (y). If k equals 2, y is binary and the model is ordinary logistic regression.
The matrix x is assumed to have full column rank.
Given y only, theta = logistic_regression (y) fits the model with baseline logit
odds only.
The full form is
Chapter 24: Statistics 193
[theta, beta, dev, dl, d2l, gamma]
= logistic_regression (y, x, print, theta, beta)
in which all output arguments and all input arguments except y are optional.
Stting print to 1 requests summary information about the fitted model to be displayed.
Setting print to 2 requests information about convergence at each iteration. Other
values request no information to be displayed. The input arguments theta and beta
give initial estimates for theta and beta.
The returned value dev holds minus twice the log-likelihood.
The returned values dl and d2l are the vector of first and the matrix of second
derivatives of the log-likelihood with respect to theta and beta.
p holds estimates for the conditional distribution of y given x.
24.4 Distributions
Function Filebeta cdf (x, a, b)
For each element of x, returns the CDF at x of the beta distribution with parameters
a and b, i.e., PROB (beta (a, b) <= x).
Function Filebeta inv (x, a, b)
For each component of x, compute the quantile (the inverse of the CDF) at x of the
Beta distribution with parameters a and b.
Function Filebeta pdf (x, a, b)
For each element of x, returns the PDF at x of the beta distribution with parameters
a and b.
Function Filebeta rnd (a, b, r, c)
Return an r by c matrix of random samples from the Beta distribution with parameters
a and b. Both a and b must be scalar or of size r by c.
If r and c are omitted, the size of the result matrix is the common size of a and b.
Function Filebinomial cdf (x, n, p)
For each element of x, compute the CDF at x of the binomial distribution with
parameters n and p.
Function Filebinomial inv (x, n, p)
For each element of x, compute the quantile at x of the binomial distribution with
parameters n and p.
Function Filebinomial pdf (x, n, p)
For each element of x, compute the probability density function (PDF) at x of the
binomial distribution with parameters n and p.
194 GNU Octave
Function Filebinomial rnd (n, p, r, c)
Return an r by c matrix of random samples from the binomial distribution with
parameters n and p. Both n and p must be scalar or of size r by c.
If r and c are omitted, the size of the result matrix is the common size of n and p.
Function Filecauchy cdf (x, lambda, sigma)
For each element of x, compute the cumulative distribution function (CDF) at x of
the Cauchy distribution with location parameter lambda and scale parameter sigma.
Default values are lambda = 0, sigma = 1.
Function Filecauchy inv (x, lambda, sigma)
For each element of x, compute the quantile (the inverse of the CDF) at x of the
Cauchy distribution with location parameter lambda and scale parameter sigma. Default
values are lambda = 0, sigma = 1.
Function Filecauchy pdf (x, lambda, sigma)
For each element of x, compute the probability density function (PDF) at x of the
Cauchy distribution with location parameter lambda and scale parameter sigma > 0.
Default values are lambda = 0, sigma = 1.
Function Filecauchy rnd (lambda, sigma, r, c)
Return an r by c matrix of random samples from the Cauchy distribution with parameters
lambda and sigma which must both be scalar or of size r by c.
If r and c are omitted, the size of the result matrix is the common size of lambda and
sigma.
Function Filechisquare cdf (x, n)
For each element of x, compute the cumulative distribution function (CDF) at x of
the chisquare distribution with n degrees of freedom.
Function Filechisquare inv (x, n)
For each element of x, compute the quantile (the inverse of the CDF) at x of the
chisquare distribution with n degrees of freedom.
Function Filechisquare pdf (x, n)
For each element of x, compute the probability density function (PDF) at x of the
chisquare distribution with k degrees of freedom.
Function Filechisquare rnd (n, r, c)
Return an r by c matrix of random samples from the chisquare distribution with n
degrees of freedom. n must be a scalar or of size r by c.
If r and c are omitted, the size of the result matrix is the size of n.
Chapter 24: Statistics 195
Function Filediscrete cdf (x, v, p)
For each element of x, compute the cumulative distribution function (CDF) at x of a
univariate discrete distribution which assumes the values in v with probabilities p.
Function Filediscrete inv (x, v, p)
For each component of x, compute the quantile (the inverse of the CDF) at x of the
univariate distribution which assumes the values in v with probabilities p.
Function Filediscrete pdf (x, v, p)
For each element of x, compute the probability density function (pDF) at x of a
univariate discrete distribution which assumes the values in v with probabilities p.
Function Filediscrete rnd (n, v, p)
Generate a row vector containing a random sample of size n from the univariate
distribution which assumes the values in v with probabilities p.
Currently, n must be a scalar.
Function Fileempirical cdf (x, data)
For each element of x, compute the cumulative distribution function (CDF) at x of
the empirical distribution obtained from the univariate sample data.
Function Fileempirical inv (x, data)
For each element of x, compute the quantile (the inverse of the CDF) at x of the
empirical distribution obtained from the univariate sample data.
Function Fileempirical pdf (x, data)
For each element of x, compute the probability density function (PDF) at x of the
empirical distribution obtained from the univariate sample data.
Function Fileempirical rnd (n, data)
Generate a bootstrap sample of size n from the empirical distribution obtained from
the univariate sample data.
Function Fileexponential cdf (x, lambda)
For each element of x, compute the cumulative distribution function (CDF) at x of
the exponential distribution with parameter lambda.
The arguments can be of common size or scalar.
Function Fileexponential inv (x, lambda)
For each element of x, compute the quantile (the inverse of the CDF) at x of the
exponential distribution with parameter lambda.
196 GNU Octave
Function Fileexponential pdf (x, lambda)
For each element of x, compute the probability density function (PDF) of the exponential
distribution with parameter lambda.
Function Fileexponential rnd (lambda, r, c)
Return an r by c matrix of random samples from the exponential distribution with
parameter lambda, which must be a scalar or of size r by c.
If r and c are omitted, the size of the result matrix is the size of lambda.
Function Filef cdf (x, m, n)
For each element of x, compute the CDF at x of the F distribution with m and n
degrees of freedom, i.e., PROB (F (m, n) <= x).
Function Filef inv (x, m, n)
For each component of x, compute the quantile (the inverse of the CDF) at x of the
F distribution with parameters m and n.
Function Filef pdf (x, m, n)
For each element of x, compute the probability density function (PDF) at x of the F
distribution with m and n degrees of freedom.
Function Filef rnd (m, n, r, c)
Return an r by c matrix of random samples from the F distribution with m and n
degrees of freedom. Both m and n must be scalar or of size r by c.
If r and c are omitted, the size of the result matrix is the common size of m and n.
Function Filegamma cdf (x, a, b)
For each element of x, compute the cumulative distribution function (CDF) at x of
the Gamma distribution with parameters a and b.
Function Filegamma inv (x, a, b)
For each component of x, compute the quantile (the inverse of the CDF) at x of the
Gamma distribution with parameters a and b.
Function Filegamma pdf (x, a, b)
For each element of x, return the probability density function (PDF) at x of the
Gamma distribution with parameters a and b.
Function Filegamma rnd (a, b, r, c)
Return an r by c matrix of random samples from the Gamma distribution with
parameters a and b. Both a and b must be scalar or of size r by c.
If r and c are omitted, the size of the result matrix is the common size of a and b.
Chapter 24: Statistics 197
Function Filegeometric cdf (x, p)
For each element of x, compute the CDF at x of the geometric distribution with
parameter p.
Function Filegeometric inv (x, p)
For each element of x, compute the quantile at x of the geometric distribution with
parameter p.
Function Filegeometric pdf (x, p)
For each element of x, compute the probability density function (PDF) at x of the
geometric distribution with parameter p.
Function Filegeometric rnd (p, r, c)
Return an r by c matrix of random samples from the geometric distribution with
parameter p, which must be a scalar or of size r by c.
If r and c are omitted, the size of the result matrix is the size of p.
Function Filehypergeometric cdf (x, m, t, n)
Compute the cumulative distribution function (CDF) at x of the hypergeometric
distribution with parameters m, t, and n. This is the probability of obtaining not more
than x marked items when randomly drawing a sample of size n without replacement
from a population of total size t containing m marked items.
The parameters m, t, and n must positive integers with m and n not greater than t.
Function Filehypergeometric inv (x, m, t, n)
For each element of x, compute the quantile at x of the hypergeometric distribution
with parameters m, t, and n.
The parameters m, t, and n must positive integers with m and n not greater than t.
Function Filehypergeometric pdf (x, m, t, n)
Compute the probability density function (PDF) at x of the hypergeometric distribution
with parameters m, t, and n. This is the probability of obtaining x marked items
when randomly drawing a sample of size n without replacement from a population of
total size t containing m marked items.
The arguments must be of common size or scalar.
Function Filehypergeometric rnd (n size, m, t, n)
Generate a row vector containing a random sample of size n size from the hypergeometric
distribution with parameters m, t, and n.
The parameters m, t, and n must positive integers with m and n not greater than t.
198 GNU Octave
Function Filekolmogorov smirnov cdf (x, tol)
Return the CDF at x of the Kolmogorov-Smirnov distribution,
Q(x) = sum∞
k=−∞(−1)k
exp(−2k2
x2
)
for x > 0.
The optional parameter tol specifies the precision up to which the series should be
evaluated; the default is tol = eps.
Function Filelaplace cdf (x)
For each element of x, compute the cumulative distribution function (CDF) at x of
the Laplace distribution.
Function Filelaplace inv (x)
For each element of x, compute the quantile (the inverse of the CDF) at x of the
Laplace distribution.
Function Filelaplace pdf (x)
For each element of x, compute the probability density function (PDF) at x of the
Laplace distribution.
Function Filelaplace rnd (r, c)
Return an r by c matrix of random numbers from the Laplace distribution.
Function Filelogistic cdf (x)
For each component of x, compute the CDF at x of the logistic distribution.
Function Filelogistic inv (x)
For each component of x, compute the quantile (the inverse of the CDF) at x of the
logistic distribution.
Function Filelogistic pdf (x)
For each component of x, compute the PDF at x of the logistic distribution.
Function Filelogistic rnd (r, c)
Return an r by c matrix of random numbers from the logistic distribution.
Function Filelognormal cdf (x, a, v)
For each element of x, compute the cumulative distribution function (CDF) at x of
the lognormal distribution with parameters a and v. If a random variable follows this
distribution, its logarithm is normally distributed with mean log (a) and variance v.
Default values are a = 1, v = 1.
Chapter 24: Statistics 199
Function Filelognormal inv (x, a, v)
For each element of x, compute the quantile (the inverse of the CDF) at x of the
lognormal distribution with parameters a and v. If a random variable follows this
distribution, its logarithm is normally distributed with mean log (a) and variance v.
Default values are a = 1, v = 1.
Function Filelognormal pdf (x, a, v)
For each element of x, compute the probability density function (PDF) at x of the
lognormal distribution with parameters a and v. If a random variable follows this
distribution, its logarithm is normally distributed with mean log (a) and variance v.
Default values are a = 1, v = 1.
Function Filelognormal rnd (a, v, r, c)
Return an r by c matrix of random samples from the lognormal distribution with
parameters a and v. Both a and v must be scalar or of size r by c.
If r and c are omitted, the size of the result matrix is the common size of a and v.
Function Filenormal cdf (x, m, v)
For each element of x, compute the cumulative distribution function (CDF) at x of
the normal distribution with mean m and variance v.
Default values are m = 0, v = 1.
Function Filenormal inv (x, m, v)
For each element of x, compute the quantile (the inverse of the CDF) at x of the
normal distribution with mean m and variance v.
Default values are m = 0, v = 1.
Function Filenormal pdf (x, m, v)
For each element of x, compute the probability density function (PDF) at x of the
normal distribution with mean m and variance v.
Default values are m = 0, v = 1.
Function Filenormal rnd (m, v, r, c)
Return an r by c matrix of random samples from the normal distribution with parameters
m and v. Both m and v must be scalar or of size r by c.
If r and c are omitted, the size of the result matrix is the common size of m and v.
Function Filepascal cdf (x, n, p)
For each element of x, compute the CDF at x of the Pascal (negative binomial)
distribution with parameters n and p.
The number of failures in a Bernoulli experiment with success probability p before
the n-th success follows this distribution.
200 GNU Octave
Function Filepascal inv (x, n, p)
For each element of x, compute the quantile at x of the Pascal (negative binomial)
distribution with parameters n and p.
The number of failures in a Bernoulli experiment with success probability p before
the n-th success follows this distribution.
Function Filepascal pdf (x, n, p)
For each element of x, compute the probability density function (PDF) at x of the
Pascal (negative binomial) distribution with parameters n and p.
The number of failures in a Bernoulli experiment with success probability p before
the n-th success follows this distribution.
Function Filepascal rnd (n, p, r, c)
Return an r by c matrix of random samples from the Pascal (negative binomial)
distribution with parameters n and p. Both n and p must be scalar or of size r by c.
If r and c are omitted, the size of the result matrix is the common size of n and p.
Function Filepoisson cdf (x, lambda)
For each element of x, compute the cumulative distribution function (CDF) at x of
the Poisson distribution with parameter lambda.
Function Filepoisson inv (x, lambda)
For each component of x, compute the quantile (the inverse of the CDF) at x of the
Poisson distribution with parameter lambda.
Function Filepoisson pdf (x, lambda)
For each element of x, compute the probability density function (PDF) at x of the
poisson distribution with parameter lambda.
Function Filepoisson rnd (lambda, r, c)
Return an r by c matrix of random samples from the Poisson distribution with parameter
lambda, which must be a scalar or of size r by c.
If r and c are omitted, the size of the result matrix is the size of lambda.
Function Filestdnormal cdf (x)
For each component of x, compute the CDF of the standard normal distribution at
x.
Function Filestdnormal inv (x)
For each component of x, compute compute the quantile (the inverse of the CDF) at
x of the standard normal distribution.
Chapter 24: Statistics 201
Function Filestdnormal pdf (x)
For each element of x, compute the probability density function (PDF) of the standard
normal distribution at x.
Function Filestdnormal rnd (r, c)
Return an r by c matrix of random numbers from the standard normal distribution.
Function Filet cdf (x, n)
For each element of x, compute the CDF at x of the t (Student) distribution with n
degrees of freedom, i.e., PROB (t(n) <= x).
Function Filet inv (x, n)
For each component of x, compute the quantile (the inverse of the CDF) at x of the
t (Student) distribution with parameter n.
Function Filet pdf (x, n)
For each element of x, compute the probability density function (PDF) at x of the t
(Student) distribution with n degrees of freedom.
Function Filet rnd (n, r, c)
Return an r by c matrix of random samples from the t (Student) distribution with n
degrees of freedom. n must be a scalar or of size r by c.
If r and c are omitted, the size of the result matrix is the size of n.
Function Fileuniform cdf (x, a, b)
Return the CDF at x of the uniform distribution on [a, b], i.e., PROB (uniform (a,
b) <= x).
Default values are a = 0, b = 1.
Function Fileuniform inv (x, a, b)
For each element of x, compute the quantile (the inverse of the CDF) at x of the
uniform distribution on [a, b].
Default values are a = 0, b = 1.
Function Fileuniform pdf (x, a, b)
For each element of x, compute the PDF at x of the uniform distribution on [a, b].
Default values are a = 0, b = 1.
Function Fileuniform rnd (a, b, r, c)
Return an r by c matrix of random samples from the uniform distribution on [a, b].
Both a and b must be scalar or of size r by c.
If r and c are omitted, the size of the result matrix is the common size of a and b.
202 GNU Octave
Function Fileweibull cdf (x, alpha, sigma)
Compute the cumulative distribution function (CDF) at x of the Weibull distribution
with shape parameter alpha and scale parameter sigma, which is
1 - exp(-(x/sigma)^alpha)
for x >= 0.
Function Fileweibull inv (x, lambda, alpha)
Compute the quantile (the inverse of the CDF) at x of the Weibull distribution with
shape parameter alpha and scale parameter sigma.
Function Fileweibull pdf (x, alpha, sigma)
Compute the probability density function (PDF) at x of the Weibull distribution with
shape parameter alpha and scale parameter sigma which is given by
alpha * sigma^(-alpha) * x^(alpha-1) * exp(-(x/sigma)^alpha)
for x > 0.
Function Fileweibull rnd (alpha, sigma, r, c)
Return an r by c matrix of random samples from the Weibull distribution with parameters
alpha and sigma which must be scalar or of size r by c.
If r and c are omitted, the size of the result matrix is the common size of alpha and
sigma.
Function Filewiener rnd (t, d, n)
Return a simulated realization of the d-dimensional Wiener Process on the interval
[0,t]. If d is omitted, d = 1 is used. The first column of the return matrix contains
time, the remaining columns contain the Wiener process.
The optional parameter n gives the number of summands used for simulating the
process over an interval of length 1. If n is omitted, n = 1000 is used.
Chapter 25: Financial Functions 203
25 Financial Functions
Function Filefv (r, n, p, l, method)
Return the future value at the end of period n of an investment which consists of n
payments of p in each period, assuming an interest rate r.
The optional argument l may be used to specify an additional lump-sum payment.
The optional argument method may be used ot specify whether the payments are
made at the end ("e", default) or at the beginning ("b") of each period.
Note that the rate r is specified as a fraction (i.e., 0.05, not 5 percent).
Function Filefvl (r, n, l)
Return the future value at the end of n periods of an initial lump sum investment l,
given a per-period interest rate r.
Note that the rate r is specified as a fraction (i.e., 0.05, not 5 percent).
Function Fileirr (p, i)
Return the internal rate of return of a series of payments p from an initial investment
i (i.e., the solution of npv (r, p) = i. If the second argument is omitted, a value of
0 is used.
Function Filenper (r, p, a, l, method)
Return the number of regular payments of p necessary to amortize a loan of amount
a and interest r.
The optional argument l may be used to specify an additional lump-sum payment of
l made at the end of the amortization time.
The optional argument method may be used to specify whether payments are made
at the end ("e", default) or at the beginning ("b") of each period.
Note that the rate r is specified as a fraction (i.e., 0.05, not 5 percent).
Function Filenpv (r, p, i)
Returns the net present value of a series of irregular (i.e., not necessarily identical)
payments p which occur at the ends of n consecutive periods. r specifies the oneperiod
interest rates and can either be a scalar (constant rates) or a vector of the
same length as p.
The optional argument i may be used to specify an initial investment.
Note that the rate r is specified as a fraction (i.e., 0.05, not 5 percent).
Function Filepmt (r, n, a, l, method)
Return the amount of periodic payment necessary to amortize a loan of amount a
with interest rate r in n periods.
The optional argument l may be used to specify an initial lump-sum payment.
The optional argument method may be used to specify whether payments are made
at the end ("e", default) or at the beginning ("b") of each period.
204 GNU Octave
Function Filepv (r, n, p, l, method)
Returns the present value of an investment that will pay off p for n consecutive
periods, assuming an interest r.
The optional argument l may be used to specify an additional lump-sum payment
made at the end of n periods.
The optional argument method may be used to specify whether payments are made
at the end ("e", default) or at the beginning ("b") of each period.
Note that the rate r is specified as a fraction (i.e., 0.05, not 5 percent).
Function Filepvl (r, n, p)
Return the present value of an investment that will pay off p in one lump sum at the
end of n periods, given the interest rate r.
Note that the rate r is specified as a fraction (i.e., 0.05, not 5 percent).
Function Filerate (n, p, v, l, method)
Return the rate of return on an investment of present value v which pays p in n
consecutive periods.
The optional argument l may be used to specify an additional lump-sum payment
made at the end of n periods.
The optional string argument method may be used to specify whether payments are
made at the end ("e", default) or at the beginning ("b") of each period.
Function Filevol (x, m, n)
Return the volatility of each column of the input matrix x. The number of data sets
per period is given by m (e.g. the number of data per year if you want to compute
the volatility per year). The optional parameter n gives the number of past periods
used for computation, if it is omitted, a value of 1 is used. If t is the number of rows
of x, vol returns the volatility from n*m to t.
Chapter 26: Sets 205
26 Sets
Octave has a limited set of functions for managing sets of data, where a set is defined as
a collection unique elements.
Function Filecreate set (x)
Return a row vector containing the unique values in x, sorted in ascending order. For
example,
create_set ([ 1, 2; 3, 4; 4, 2 ])
⇒ [ 1, 2, 3, 4 ]
Function Fileunion (x, y)
Return the set of elements that are in either of the sets x and y. For example,
union ([ 1, 2, 4 ], [ 2, 3, 5 ])
⇒ [ 1, 2, 3, 4, 5 ]
Function Fileintersection (x, y)
Return the set of elements that are in both sets x and y. For example,
intersection ([ 1, 2, 3 ], [ 2, 3, 5 ])
⇒ [ 2, 3 ]
Function Filecomplement (x, y)
Return the elements of set y that are not in set x. For example,
complement ([ 1, 2, 3 ], [ 2, 3, 5 ])
⇒ 5
206 GNU Octave
Chapter 27: Polynomial Manipulations 207
27 Polynomial Manipulations
In Octave, a polynomial is represented by its coefficients (arranged in descending order).
For example, a vector of length N + 1 corresponds to the following polynomial of order N
p(x) = c1xN
+ ... + cN x + cN+1.
Function Filecompan (c)
Compute the companion matrix corresponding to polynomial coefficient vector c.
The companion matrix is
A =







−c2/c1 −c3/c1 · · · −cN /c1 −cN+1/c1
1 0 · · · 0 0
0 1 · · · 0 0
...
...
...
...
...
0 0 · · · 1 0







.
The eigenvalues of the companion matrix are equal to the roots of the polynomial.
Function Fileconv (a, b)
Convolve two vectors.
y = conv (a, b) returns a vector of length equal to length (a) + length (b) - 1. If
a and b are polynomial coefficient vectors, conv returns the coefficients of the product
polynomial.
Function Filedeconv (y, a)
Deconvolve two vectors.
[b, r] = deconv (y, a) solves for b and r such that y = conv (a, b) + r.
If y and a are polynomial coefficient vectors, b will contain the coefficients of the
polynomial quotient and r will be a remander polynomial of lowest order.
Function Filepoly (a)
If a is a square N-by-N matrix, poly (a) is the row vector of the coefficients of det
(z * eye (N) - a), the characteristic polynomial of a. If x is a vector, poly (x) is a
vector of coefficients of the polynomial whose roots are the elements of x.
Function Filepolyderiv (c)
Return the coefficients of the derivative of the polynomial whose coefficients are given
by vector c.
208 GNU Octave
Function File[p, yf ] = polyfit (x, y, n)
Return the coefficients of a polynomial p(x) of degree n that minimizes
N
i=1
(p(xi) − yi)2
to best fit the data in the least squares sense.
The polynomial coefficients are returned in a row vector if x and y are both row
vectors; otherwise, they are returned in a column vector.
If two output arguments are requested, the second contains the values of the polynomial
for each value of x.
Function Filepolyinteg (c)
Return the coefficients of the integral of the polynomial whose coefficients are represented
by the vector c.
The constant of integration is set to zero.
Function Filepolyreduce (c)
Reduces a polynomial coefficient vector to a minimum number of terms by stripping
off any leading zeros.
Function Filepolyval (c, x)
Evaluate a polynomial.
polyval (c, x) will evaluate the polynomial at the specified value of x.
If x is a vector or matrix, the polynomial is evaluated at each of the elements of x.
Function Filepolyvalm (c, x)
Evaluate a polynomial in the matrix sense.
polyvalm (c, x) will evaluate the polynomial in the matrix sense, i.e. matrix multiplication
is used instead of element by element multiplication as is used in polyval.
The argument x must be a square matrix.
Function Fileresidue (b, a, tol)
If b and a are vectors of polynomial coefficients, then residue calculates the partial
fraction expansion corresponding to the ratio of the two polynomials.
The function residue returns r, p, k, and e, where the vector r contains the residue
terms, p contains the pole values, k contains the coefficients of a direct polynomial
term (if it exists) and e is a vector containing the powers of the denominators in the
partial fraction terms.
Assuming b and a represent polynomials P(s) and Q(s) we have:
P(s)
Q(s)
=
M
m=1
rm
(s − pm)e
m
+
N
i=1
kisN−i
.
Chapter 27: Polynomial Manipulations 209
where M is the number of poles (the length of the r, p, and e vectors) and N is the
length of the k vector.
The argument tol is optional, and if not specified, a default value of 0.001 is assumed.
The tolerance value is used to determine whether poles with small imaginary components
are declared real. It is also used to determine if two poles are distinct. If
the ratio of the imaginary part of a pole to the real part is less than tol, the imaginary
part is discarded. If two poles are farther apart than tol they are distinct. For
example,
b = [1, 1, 1];
a = [1, -5, 8, -4];
[r, p, k, e] = residue (b, a);
⇒ r = [-2, 7, 3]
⇒ p = [2, 2, 1]
⇒ k = [](0x0)
⇒ e = [1, 2, 1]
which implies the following partial fraction expansion
s2
+ s + 1
s3 − 5s2 + 8s − 4
=
−2
s − 2
+
7
(s − 2)2
+
3
s − 1
Function Fileroots (v)
For a vector v with N components, return the roots of the polynomial
v1zN−1
+ · · · + vN−1z + vN .
Function Filepolyout (c, x)
Write formatted polynomial
c(x) = c(1) * x^n + ... + c(n) x + c(n+1)
and return it as a string or write it to the screen (if nargout is zero). x defaults to
the string "s"
210 GNU Octave
Chapter 28: Control Theory 211
28 Control Theory
The Octave Control Systems Toolbox (OCST) was initially developed by Dr. A. Scottedward
Hodel a.s.hodel@eng.auburn.edu with the assistance of his students
• R. Bruce Tenison btenison@dibbs.net,
• David C. Clem,
• John E. Ingram John.Ingram@sea.siemans.com, and
• Kristi McGowan.
This development was supported in part by NASA’s Marshall Space Flight Center as
part of an in-house CACSD environment. Additional important contributions were made
by Dr. Kai Mueller mueller@ifr.ing.tu-bs.de and Jose Daniel Munoz Frias (place.m).
An on-line menu-driven tutorial is available via DEMOcontrol; beginning OCST users
should start with this program.
Function FileDEMOcontrol
Octave Control Systems Toolbox demo/tutorial program. The demo allows the user
to select among several categories of OCST function:
octave:1> DEMOcontrol
O C T A V E C O N T R O L S Y S T E M S T O O L B O X
Octave Controls System Toolbox Demo
[ 1] System representation
[ 2] Block diagram manipulations
[ 3] Frequency response functions
[ 4] State space analysis functions
[ 5] Root locus functions
[ 6] LQG/H2/Hinfinity functions
[ 7] End
Command examples are interactively run for users to observe the use of OCST func-
tions.
28.1 System Data Structure
The OCST stores all dynamic systems in a single data structure format that can represent
continuous systems, discrete-systems, and mixed (hybrid) systems in state-space form, and
can also represent purely continuous/discrete systems in either transfer function or polezero
form. In order to provide more flexibility in treatment of discrete/hybrid systems, the
OCST also keeps a record of which system outputs are sampled.
Octave structures are accessed with a syntax much like that used by the C programming
language. For consistency in use of the data structure used in the OCST, it is recommended
that the system structure access m-files be used (see Section 28.2 [sysinterface], page 213).
Some elements of the data structure are absent depending on the internal system representation(s)
used. More than one system representation can be used for SISO systems; the
OCST m-files ensure that all representations used are consistent with one another.
212 GNU Octave
Function Filesysrepdemo
Tutorial for the use of the system data structure functions.
28.1.1 Variables common to all OCST system formats
The data structure elements (and variable types) common to all system representations
are listed below; examples of the initialization and use of the system data structures are
given in subsequent sections and in the online demo DEMOcontrol.
n
nz The respective number of continuous and discrete states in the system (scalar)
inname
outname list of name(s) of the system input, output signal(s). (list of strings)
sys System status vector. (vector)
This vector indicates both what representation was used to initialize the system
data structure (called the primary system type) and which other representations
are currently up-to-date with the primary system type (see Section 28.2.5
[structaccess], page 219).
The value of the first element of the vector indicates the primary system type.
0 for tf form (initialized with tf2sys or fir2sys)
1 for zp form (initialized with zp2sys)
2 for ss form (initialized with ss2sys)
The next three elements are boolean flags that indicate whether tf, zp, or ss,
respectively, are “up to date" (whether it is safe to use the variables associated
with these representations). These flags are changed when calls are made to
the sysupdate command.
tsam Discrete time sampling period (nonnegative scalar). tsam is set to 0 for continuous
time systems.
yd Discrete-time output list (vector)
indicates which outputs are discrete time (i.e., produced by D/A converters)
and which are continuous time. yd(ii) = 0 if output ii is continuous, = 1 if
discrete.
The remaining variables of the system data structure are only present if the corresponding
entry of the sys vector is true (=1).
28.1.2 tf format variables
num numerator coefficients (vector)
den denominator coefficients (vector)
Chapter 28: Control Theory 213
28.1.3 zp format variables
zer system zeros (vector)
pol system poles (vector)
k leading coefficient (scalar)
28.1.4 ss format variables
a
b
c
d The usual state-space matrices. If a system has both continuous and discrete
states, they are sorted so that continuous states come first, then discrete states
Note some functions (e.g., bode, hinfsyn) will not accept systems with both
discrete and continuous states/outputs
stname names of system states (list of strings)
28.2 System Construction and Interface Functions
Construction and manipulations of the OCST system data structure (see Section 28.1
[sysstruct], page 211) requires attention to many details in order to ensure that data structure
contents remain consistent. Users are strongly encouraged to use the system interface
functions in this section. Functions for the formatted display in of system data structures
are given in Section 28.3 [sysdisp], page 223.
28.2.1 Finite impulse response system interface functions
Function Filefir2sys (num, tsam, inname, outname)
construct a system data structure from FIR description
Inputs:
num vector of coefficients [c 0c 1...c n] of the SISO FIR transfer function
C(z) = c0 + c1 ∗ z−1
+ c2 ∗ z−2
+ ... + znz−n
tsam sampling time (default: 1)
inname name of input signal; may be a string or a list with a single entry.
outname name of output signal; may be a string or a list with a single entry.
Outputs sys (system data structure)
Example
214 GNU Octave
octave:1> sys = fir2sys([1 -1 2 4],0.342,"A/D input","filter output");
octave:2> sysout(sys)
Input(s)
1: A/D input
Output(s):
1: filter output (discrete)
Sampling interval: 0.342
transfer function form:
1*z^3 - 1*z^2 + 2*z^1 + 4
-------------------------
1*z^3 + 0*z^2 + 0*z^1 + 0
Function File[c, tsam, input, output] = sys2fir (sys)
Extract FIR data from system data structure; see fir2sys for parameter descriptions.
28.2.2 State space system interface functions
Function Filess2sys (a, b, c, d, tsam, n, nz, stname, inname, outname,
outlist)
Create system structure from state-space data. May be continous, discrete, or mixed
(sampeled-data)
Inputs
a
b
c
d usual state space matrices.
default: d = zero matrix
tsam sampling rate. Default: tsam = 0 (continuous system)
n
nz number of continuous, discrete states in the system
If tsam is 0, n = rows(a), nz = 0.
If tsam is greater than zero, n = 0, nz = rows(a)
see below for system partitioning
stname list of strings of state signal names
default (stname=[] on input): x_n for continuous states, xd_n for discrete
states
inname list of strings of input signal names
default (inname = [] on input): u_n
outname list of strings of input signal names
default (outname = [] on input): y_n
Chapter 28: Control Theory 215
outlist
list of indices of outputs y that are sampled
If tsam is 0, outlist = [].
If tsam is greater than 0, outlist = 1 : rows(c).
Unlike states, discrete/continous outputs may appear in any order.
Note sys2ss returns a vector yd where yd(outlist) = 1; all other entries of yd are 0.
Outputs outsys = system data structure
System partitioning
Suppose for simplicity that outlist specified that the first several outputs were continuous
and the remaining outputs were discrete. Then the system is partitioned
as
x = [ xc ] (n x 1)
[ xd ] (nz x 1 discrete states)
a = [ acc acd ] b = [ bc ]
[ adc add ] [ bd ]
c = [ ccc ccd ] d = [ dc ]
[ cdc cdd ] [ dd ]
(cdc = c(outlist,1:n), etc.)
with dynamic equations:
d
dt
xc(t) = accxc(t) + acdxd(k ∗ tsam) + bc ∗ u(t)
xd((k + 1) ∗ tsam) = adcxc(ktsam) + addxd(ktsam) + bdu(ktsam)
yc(t) = cccxc(t) + ccdxd(ktsam) + dcu(t)
yd(ktsam) = cdcxc(ktsam) + cddxd(ktsam) + ddu(ktsam)
Signal partitions
| continuous | discrete |
----------------------------------------------------
states | stname(1:n,:) | stname((n+1):(n+nz),:) |
----------------------------------------------------
outputs | outname(cout,:) | outname(outlist,:) |
----------------------------------------------------
where cout is the list of in 1:rows(p) that are not contained in outlist.
(Discrete/continuous outputs may be entered in any order desired by the user.)
Example
octave:1> a = [1 2 3; 4 5 6; 7 8 10];
octave:2> b = [0 0 ; 0 1 ; 1 0];
octave:3> c = eye(3);
octave:4> sys = ss2sys(a,b,c,[],0,3,0,list("volts","amps","joules"));
octave:5> sysout(sys);
Input(s)
1: u_1
216 GNU Octave
2: u_2
Output(s):
1: y_1
2: y_2
3: y_3
state-space form:
3 continuous states, 0 discrete states
State(s):
1: volts
2: amps
3: joules
A matrix: 3 x 3
1 2 3
4 5 6
7 8 10
B matrix: 3 x 2
0 0
0 1
1 0
C matrix: 3 x 3
1 0 0
0 1 0
0 0 1
D matrix: 3 x 3
0 0
0 0
0 0
Notice that the D matrix is constructed by default to the correct dimensions. Default
input and output signals names were assigned since none were given.
Function File[a, b, c, d, tsam, n, nz, stname, inname, outname, yd] =
sys2ss (sys)
Extract state space representation from system data structure.
Inputs sys system data structure
Outputs
a
b
c
d state space matrices for sys
tsam sampling time of sys (0 if continuous)
n
nz number of continuous, discrete states (discrete states come last in state
vector x)
Chapter 28: Control Theory 217
stname
inname
outname signal names (lists of strings); names of states, inputs, and outputs, re-
spectively
yd binary vector; yd(ii) is 1 if output y(ii)$ is discrete (sampled); otherwise
yd(ii) 0.
A warning massage is printed if the system is a mixed continuous and discrete system
Example
octave:1> sys=tf2sys([1 2],[3 4 5]);
octave:2> [a,b,c,d] = sys2ss(sys)
a =
0.00000 1.00000
-1.66667 -1.33333
b =
0
1
c = 0.66667 0.33333
d = 0
28.2.3 Transfer function system interface functions
Function Filetf2sys (num, den, tsam, inname, outname)
build system data structure from transfer function format data
Inputs
num
den coefficients of numerator/denominator polynomials
tsam sampling interval. default: 0 (continuous time)
inname
outname input/output signal names; may be a string or list with a single string
entry.
Outputs sys = system data structure
Example
octave:1> sys=tf2sys([2 1],[1 2 1],0.1);
octave:2> sysout(sys)
Input(s)
1: u_1
Output(s):
1: y_1 (discrete)
Sampling interval: 0.1
transfer function form:
2*z^1 + 1
-----------------
1*z^2 + 2*z^1 + 1
218 GNU Octave
Function File[num, den, tsam, inname, outname] = sys2tf (sys)
Extract transfer function data from a system data structure
See tf2sys for parameter descriptions.
Example
octave:1> sys=ss2sys([1 -2; -1.1,-2.1],[0;1],[1 1]);
octave:2> [num,den] = sys2tf(sys)
num = 1.0000 -3.0000
den = 1.0000 1.1000 -4.3000
28.2.4 Zero-pole system interface functions
Function Filezp2sys (zer, pol, k, tsam, inname, outname)
Create system data structure from zero-pole data.
Inputs
zer vector of system zeros
pol vector of system poles
k scalar leading coefficient
tsam sampling period. default: 0 (continuous system)
inname
outname input/output signal names (lists of strings)
Outputs sys: system data structure
Example
octave:1> sys=zp2sys([1 -1],[-2 -2 0],1);
octave:2> sysout(sys)
Input(s)
1: u_1
Output(s):
1: y_1
zero-pole form:
1 (s - 1) (s + 1)
-----------------
s (s + 2) (s + 2)
Function File[zer, pol, k, tsam, inname, outname] = sys2zp (sys)
Extract zero/pole/leading coefficient information from a system data structure
See zp2sys for parameter descriptions.
Example
octave:1> sys=ss2sys([1 -2; -1.1,-2.1],[0;1],[1 1]);
octave:2> [zer,pol,k] = sys2zp(sys)
zer = 3.0000
pol =
-2.6953
1.5953
k = 1
Chapter 28: Control Theory 219
28.2.5 Data structure access functions
Function Filesyschnames (sys, opt, list, names)
Superseded by syssetsignals
Function Filesyschtsam (sys, tsam)
This function changes the sampling time (tsam) of the system. Exits with an error if
sys is purely continuous time.
Function File[n, nz, m, p, yd] = sysdimensions (sys, opt)
return the number of states, inputs, and/or outputs in the system sys.
Inputs
sys system data structure
opt String indicating which dimensions are desired. Values:
"all" (default) return all parameters as specified under Outputs
below.
"cst" return n= number of continuous states
"dst" return n= number of discrete states
"in" return n= number of inputs
"out" return n= number of outputs
Outputs
n number of continuous states (or individual requested dimension as specified
by opt).
nz number of discrete states
m number of system inputs
p number of system outputs
yd binary vector; yd(ii) is nonzero if output ii is discrete. yd(ii) = 0 if
output ii is continous
Function File[stname, inname, outname, yd] = sysgetsignals (sys)
Function Filesiglist = sysgetsignals (sys, sigid)
Function Filesigname = sysgetsignals (sys, sigid, signum, strflg)
Get signal names from a system
Inputs
sys system data structure for the state space system
sigid signal id. String. Must be one of
"in" input signals
220 GNU Octave
"out" output signals
"st" stage signals
"yd" value of logical vector yd
signum index(indices) or name(s) or signals; see sysidx
strflg flag to return a string instead of a list; Values:
0 (default) return a list (even if signum specifies an individual
signal)
1 return a string. Exits with an error if signum does not specify
an individual signal.
Outputs
•If sigid is not specified
stname
inname
outname signal names (lists of strings); names of states, inputs, and
outputs, respectively
yd binary vector; yd(ii) is nonzero if output ii is discrete.
•If sigid is specified but signum is not specified, then
sigid="in"
siglist is set to the list of input names
sigid="out"
siglist is set to the list of output names
sigid="st"
siglist is set to the list of state names
stage signals
sigid="yd"
siglist is set to logical vector indicating discrete outputs;
siglist(ii) = 0 indicates that output ii is continuous (unsampled),
otherwise it is discrete.
•if the first three input arguments are specified, then signame is
a list of the specified signal names (sigid is "in", "out", or "st"), or
else the logical flag indicating whether output(s) signum is(are) discrete
(sigval=1) or continuous (sigval=0).
Examples (From sysrepdemo)
octave> sys=ss2sys(rand(4),rand(4,2),rand(3,4));
octave> [Ast,Ain,Aout,Ayd] = sysgetsignals(sys) i # get all signal names
Ast =
(
[1] = x_1
[2] = x_2
[3] = x_3
Chapter 28: Control Theory 221
[4] = x_4
)
Ain =
(
[1] = u_1
[2] = u_2
)
Aout =
(
[1] = y_1
[2] = y_2
[3] = y_3
)
Ayd =
0 0 0
octave> Ain = sysgetsignals(sys,"in") # get only input signal names
Ain =
(
[1] = u_1
[2] = u_2
)
octave> Aout = sysgetsignals(sys,"out",2) # get name of output 2 (in list)
Aout =
(
[1] = y_2
)
octave> Aout = sysgetsignals(sys,"out",2,1) # get name of output 2 (as string
Aout = y_2
Function Filesysgettype (sys)
return the initial system type of the system
Inputs sys: system data structure
Outputs systype: string indicating how the structure was initially constructed: values:
"ss", "zp", or "tf"
Note FIR initialized systems return systype="tf".
Function Filesyssetsignals (sys, opt, names, sig idx)
change the names of selected inputs, outputs and states. Inputs
sys system data structure
opt change default name (output)
"out" change selected output names
"in" change selected input names
"st" change selected state names
222 GNU Octave
"yd" change selected outputs from discrete to continuous or from
continuous to discrete.
names
opt = "out", "in", or "st"
string or string array containing desired signal names or val-
ues.
opt = "yd"
To desired output continuous/discrete flag. Set name to 0 for
continuous, or 1 for discrete.
sig idx indices or names of outputs, yd, inputs, or states whose respective
names/values should be changed.
Default: replace entire list of names/entire yd vector.
Outputs retsys=sys with appropriate signal names changed (or yd values, where ap-
propriate)
Example
octave:1> sys=ss2sys([1 2; 3 4],[5;6],[7 8]);
octave:2> sys = syssetsignals(sys,"st",str2mat("Posx","Velx"));
octave:3> sysout(sys)
Input(s)
1: u_1
Output(s):
1: y_1
state-space form:
2 continuous states, 0 discrete states
State(s):
1: Posx
2: Velx
A matrix: 2 x 2
1 2
3 4
B matrix: 2 x 1
5
6
C matrix: 1 x 2
7 8
D matrix: 1 x 1
0
Function Filesysupdate (sys, opt)
Update the internal representation of a system.
Inputs
sys: system data structure
opt string:
Chapter 28: Control Theory 223
"tf" update transfer function form
"zp" update zero-pole form
"ss" update state space form
"all" all of the above
Outputs retsys: contains union of data in sys and requested data. If requested data
in sys is already up to date then retsys=sys.
Conversion to tf or zp exits with an error if the system is mixed continuous/digital.
function [systype, nout, nin, ncstates, ndstates] = minfo(inmat)
MINFO: Determines the type of system matrix. INMAT can be a varying(*), system,
constant, and empty matrix.
Returns: systype can be one of: varying, system, constant, and empty nout is the number
of outputs of the system nin is the number of inputs of the system ncstates is the number
of continuous states of the system ndstates is the number of discrete states of the system
Function Filesysgettsam (sys)
Return the sampling time of the system sys.
28.2.6 Data structure internal functions
28.3 System display functions
Function Filesysout (sys, opt)
print out a system data structure in desired format
sys system data structure
opt Display option
[] primary system form (default)
"ss" state space form
"tf" transfer function form
"zp" zero-pole form
"all" all of the above
Function Filetfout (num, denom, x)
Print formatted transfer function n(s)/d(s) to the screen. x defaults to the string
"s"
Function Filezpout (zer, pol, k, x)
print formatted zero-pole form to the screen. x defaults to the string "s"
224 GNU Octave
28.4 Block Diagram Manipulations
See Section 28.7 [systime], page 240.
Unless otherwise noted, all parameters (input,output) are system data structures.
Function Filebddemo (inputs)
Octave Controls toolbox demo: Block Diagram Manipulations demo
Function Filebuildssic (clst, ulst, olst, ilst, s1, s2, s3, s4, s5, s6, s7, s8)
Form an arbitrary complex (open or closed loop) system in state-space form from
several systems. "buildssic" can easily (despite it’s cryptic syntax) integrate transfer
functions from a complex block diagram into a single system with one call. This
function is especially useful for building open loop interconnections for H infinity and
H2 designs or for closing loops with these controllers.
Although this function is general purpose, the use of "sysgroup" "sysmult",
"sysconnect" and the like is recommended for standard operations since they can
handle mixed discrete and continuous systems and also the names of inputs, outputs,
and states.
The parameters consist of 4 lists that describe the connections outputs and inputs
and up to 8 systems s1-s8. Format of the lists:
clst connection list, describes the input signal of each system. The maximum
number of rows of Clst is equal to the sum of all inputs of s1-s8.
Example: [1 2 -1; 2 1 0] ==> new input 1 is old inpout 1 + output 2
- output 1, new input 2 is old input 2 + output 1. The order of rows is
arbitrary.
ulst if not empty the old inputs in vector Ulst will be appended to the outputs.
You need this if you want to "pull out" the input of a system. Elements
are input numbers of s1-s8.
olst output list, specifiy the outputs of the resulting systems. Elements are
output numbers of s1-s8. The numbers are alowed to be negative and
may appear in any order. An empty matrix means all outputs.
ilst input list, specifiy the inputs of the resulting systems. Elements are input
numbers of s1-s8. The numbers are alowed to be negative and may appear
in any order. An empty matrix means all inputs.
Example: Very simple closed loop system.
w e +-----+ u +-----+
--->o--*-->| K |--*-->| G |--*---> y
^ | +-----+ | +-----+ |
- | | | |
| | +----------------> u
| | |
| +-------------------------|---> e
| |
+----------------------------+
The closed loop system GW can be optained by
Chapter 28: Control Theory 225
GW = buildssic([1 2; 2 -1], 2, [1 2 3], 2, G, K);
clst (1. row) connect input 1 (G) with output 2 (K). (2. row) connect input
2 (K) with neg. output 1 (G).
ulst append input of (2) K to the number of outputs.
olst Outputs are output of 1 (G), 2 (K) and appended output 3 (from Ulst).
ilst the only input is 2 (K).
Here is a real example:
+----+
-------------------->| W1 |---> v1
z | +----+
----|-------------+ || GW || => min.
| | vz infty
| +---+ v +----+
*--->| G |--->O--*-->| W2 |---> v2
| +---+ | +----+
| |
| v
u y
The closed loop system GW from [z; u]’ to [v1; v2; y]’ can be obtained by (all SISO
systems):
GW = buildssic([1, 4; 2, 4; 3, 1], 3, [2, 3, 5],
[3, 4], G, W1, W2, One);
where "One" is a unity gain (auxillary) function with order 0. (e.g. One = ugain(1);)
Function Filejet707 ()
Creates linearized state space model of a Boeing 707-321 aircraft at v=80m/s. (M
= 0.26, Ga0 = -3 deg, alpha0 = 4 deg, kappa = 50 deg) System inputs: (1) thrust
and (2) elevator angle System outputs: (1) airspeed and (2) pitch angle Ref: R.
Brockhaus: Flugregelung (Flight Control), Springer, 1994
Function Fileord2 (nfreq, damp, gain)
Creates a continuous 2nd order system with parameters: Inputs
nfreq natural frequency [Hz]. (not in rad/s)
damp damping coefficient
gain dc-gain This is steady state value only for damp > 0. gain is assumed to
be 1.0 if ommitted.
Outputs outsys system data structure has representation with w = 2 ∗ pi ∗ nfreq:
/ \
| / -2w*damp -w \ / w \ |
G = | | |, | |, [ 0 gain ], 0 |
| \ w 0 / \ 0 / |
\ /
See also jet707 (MIMO example, Boeing 707-321 aircraft model)
226 GNU Octave
Function Filesysadd (gsys, hsys)
returns sys = gsys + hsys.
• Exits with an error if gsys and hsys are not compatibly dimensioned.
• Prints a warning message is system states have identical names; duplicate names
are given a suffix to make them unique.
• sys input/output names are taken from gsys.
________
----| gsys |---
u | ---------- +|
----- (_)----> y
| ________ +|
----| hsys |---
--------
Function Filesysappend (sys, b, c, d, outname, inname, yd)
appends new inputs and/or outputs to a system
Inputs
sys system data structure
b matrix to be appended to sys "B" matrix (empty if none)
c matrix to be appended to sys "C" matrix (empty if none)
d revised sys d matrix (can be passed as [] if the revised d is all zeros)
outname list of names for new outputs
inname list of names for new inputs
yd binary vector; yd(ii) = 0 indicates a continuous output; yd(ii) = 1 indicates
a discrete output.
Outputs sys
sys.b := [sys.b , b]
sys.c := [sys.c ]
[ c ]
sys.d := [sys.d | D12 ]
[D21 | D22 ]
where D12, D21, and D22 are the appropriate dimensioned blocks of the input parameter
d.
• The leading block D11 of d is ignored.
• If inname and outname are not given as arguments, the new inputs and outputs
are be assigned default names.
• yd is a binary vector of length rows(c) that indicates continuous/sampled outputs.
Default value for yd is:
• sys = continuous or mixed yd = zeros(1,rows(c))
• sys = discrete yd = ones(1,rows(c))
Chapter 28: Control Theory 227
Function Filesysconnect (sys, out idx, in idx, order, tol)
Close the loop from specified outputs to respective specified inputs
Inputs
sys system data structure
out idx
in idx names or indices of signals to connect (see sysidx). The output specified
by out idx(ii) is connected to the input specified by in idx(ii).
order logical flag (default = 0)
0 leave inputs and outputs in their original order
1 permute inputs and outputs to the order shown in the diagram
below
tol tolerance for singularities in algebraic loops default: 200eps
Outputs sys: resulting closed loop system.
Method sysconnect internally permutes selected inputs, outputs as shown below,
closes the loop, and then permutes inputs and outputs back to their original order
____________________
u_1 ----->| |----> y_1
| sys |
old u_2 | |
u_2* ---->(+)--->| |----->y_2
(in_idx) ^ -------------------| | (out_idx)
| |
-------------------------------
The input that has the summing junction added to it has an * added to the end of
the input name.
Function File[csys, acd, ccd] = syscont (sys)
Extract the purely continuous subsystem of an input system.
Inputs sys is a system data structure
Outputs
csys is the purely continuous input/output connections of sys
acd
ccd connections from discrete states to continuous states, discrete states to
continuous outputs, respectively.
returns csys empty if no continuous/continous path exists
Function File[dsys, adc, cdc] = sysdisc (sys)
Inputs sys = system data structure
Outputs
dsys purely discrete portion of sys (returned empty if there is no purely discrete
path from inputs to outputs)
228 GNU Octave
adc
cdc connections from continuous states to discrete states and discrete outputs,
respectively.
Function Filesysdup (asys, out idx, in idx)
Duplicate specified input/output connections of a system
Inputs
asys system data structure
out idx
in idx indices or names of desired signals (see sigidx). duplicates are made of
y(out_idx(ii)) and u(in_idx(ii)).
Outputs retsys: resulting closed loop system: duplicated i/o names are appended
with a "+" suffix.
Method sysdup creates copies of selected inputs and outputs as shown below. u1/y1
is the set of original inputs/outputs, and u2,y2 is the set of duplicated inputs/outputs
in the order specified in in idx, out idx, respectively
____________________
u1 ----->| |----> y1
| asys |
u2 ------>| |----->y2
(in_idx) -------------------| (out_idx)
Function Filesysgroup (asys, bsys)
Combines two systems into a single system
Inputs asys, bsys: system data structures
Outputs sys = blockdiag(asys, bsys)
__________________
| ________ |
u1 ----->|--> | asys |--->|----> y1
| -------- |
| ________ |
u2 ----->|--> | bsys |--->|----> y2
| -------- |
------------------
Ksys
The function also rearranges the internal state-space realization of sys so that the
continuous states come first and the discrete states come last. If there are duplicate
names, the second name has a unique suffix appended on to the end of the name.
Function Filesysmult (asys, bsys)
Compute sys = Asys ∗ Bsys (series connection):
Chapter 28: Control Theory 229
u ---------- ----------
--->| bsys |---->| asys |--->
---------- ----------
A warning occurs if there is direct feed-through from an input of Bsys or a continuous
state of bsys through a discrete output of Bsys to a continuous state or output in
asys (system data structure does not recognize discrete inputs).
Function Filesysprune (asys, out idx, in idx)
Extract specified inputs/outputs from a system
Inputs
asys system data structure
out idx
in idx
Indices or signal names of the outputs and inputs to be kept in the returned
system; remaining connections are "pruned" off. May select as []
(empty matrix) to specify all outputs/inputs.
retsys = sysprune(Asys,[1:3,4],"u_1");
retsys = sysprune(Asys,list("tx","ty","tz"), 4);
Outputs retsys: resulting system
____________________
u1 ------->| |----> y1
(in_idx) | Asys | (out_idx)
u2 ------->| |----| y2
(deleted)-------------------- (deleted)
Function Filesysreorder (vlen, list)
Inputs vlen=vector length, list= a subset of [1:vlen],
Outputs pv: a permutation vector to order elements of [1:vlen] in list to the end
of a vector.
Used internally by sysconnect to permute vector elements to their desired locations.
Function Filesysscale (sys, outscale, inscale, outname, inname)
scale inputs/outputs of a system.
Inputs sys: structured system outscale, inscale: constant matrices of appropriate
dimension
Outputs sys: resulting open loop system:
----------- ------- -----------
u --->| inscale |--->| sys |--->| outscale |---> y
----------- ------- -----------
If the input names and output names (each a list of strings) are not given and the
scaling matrices are not square, then default names will be given to the inputs and/or
outputs.
230 GNU Octave
A warning message is printed if outscale attempts to add continuous system outputs
to discrete system outputs; otherwise yd is set appropriately in the returned value of
sys.
Function Filesyssub (gsys, hsys)
Return sys = Gsys − Hsys.
Method: gsys and hsys are connected in parallel The input vector is connected to
both systems; the outputs are subtracted. Returned system names are those of gsys.
+--------+
+--->| gsys |---+
| +--------+ |
| +|
u --+ (_)--> y
| -|
| +--------+ |
+--->| hsys |---+
+--------+
Function Fileugain (n)
Creates a system with unity gain, no states. This trivial system is sometimes needed
to create arbitrary complex systems from simple systems with buildssic. Watch out if
you are forming sampled systems since "ugain" does not contain a sampling period.
Function Filewgt1o (vl, vh, fc)
State space description of a first order weighting function.
Weighting function are needed by the H2/H infinity design procedure. These function
are part of thye augmented plant P (see hinfdemo for an applicattion example).
vl = Gain at low frequencies
vh = Gain at high frequencies
fc = Corner frequency (in Hz, *not* in rad/sec)
Function Fileparallel (asys, bsys)
Forms the parallel connection of two systems.
| | u —–>|—-> | asys |—>|—-> y1 | | ——– | | |
| |—>|—-> | bsys |—>|—-> y2 | ——– | ——————– ksys
Function File[retsys, nc, no] = sysmin (sys, flg)
return a minimal (or reduced order) system inputs: sys: system data structure flg:
0 [default] return minimal system; state names lost : 1 return system with physical
states removed that are either uncontrollable or unobservable (cannot reduce further
without discarding physical meaning of states) outputs: retsys: returned system nc:
number of controllable states in the returned system no: number of observable states
in the returned system cflg: is controllable(retsys) oflg: is observable(retsys)
Chapter 28: Control Theory 231
28.5 Numerical Functions
Function Fileare (a, b, c, opt)
Solve the algebraic Riccati equation
AT
X + XA − XBX + C = 0
Inputs for identically dimensioned square matrices
a nxn matrix.
b nxn matrix or nxm matrix; in the latter case b is replaced by b := b ∗ b .
c nxn matrix or pxm matrix; in the latter case c is replaced by c := c ∗ c.
opt (optional argument; default = "B"): String option passed to balance
prior to ordered Schur decomposition.
Outputs x: solution of the ARE.
Method Laub’s Schur method (IEEE Transactions on Automatic Control, 1979) is
applied to the appropriate Hamiltonian matrix.
Function Filedare (a, b, c, r, opt)
Return the solution, x of the discrete-time algebraic Riccati equation
AT
XA − X + AT
XB(R + BT
XB)−1
BT
XA + C = 0
Inputs
a n by n.
b n by m.
c n by n, symmetric positive semidefinite, or p by n. In the latter case
c := c ∗ c is used.
r m by m, symmetric positive definite (invertible).
opt (optional argument; default = "B"): String option passed to balance
prior to ordered QZ decomposition.
Outputs x solution of DARE.
Method Generalized eigenvalue approach (Van Dooren; SIAM J. Sci. Stat. Comput.,
Vol 2) applied to the appropriate symplectic pencil.
See also: Ran and Rodman, "Stable Hermitian Solutions of Discrete Algebraic Riccati
Equations," Mathematics of Control, Signals and Systems, Vol 5, no 2 (1992) pp 165-
194.
232 GNU Octave
Function File[tvals, plist] = dre (sys, q, r, qf, t0, tf, ptol, maxits);
Solve the differential Riccati equation
−
dP
dt
= AT
P + PA − PBR−1
BT
P + Q
P(tf ) = Qf
for the LTI system sys. Solution of standard LTI state feedback optimization
min
tf
t0
xT
Qx + uT
Rudt + x(tf )T
Qfx(tf )
optimal input is
u = −R−1
BT
P(t)x
Inputs
sys continuous time system data structure
q state integral penalty
r input integral penalty
qf state terminal penalty
t0
tf limits on the integral
ptol tolerance (used to select time samples; see below); default = 0.1
maxits number of refinement iterations (default=10)
Outputs
tvals time values at which p(t) is computed
plist list values of p(t); nth (plist, ii) is p(tvals(ii)).
tvals
is selected so that || nth(Plist,ii) - nth(Plist,ii-1) || < Ptol
for ii=2:length(tvals)
Function Filedgram (a, b)
Return controllability grammian of discrete time system
x(k+1) = a x(k) + b u(k)
Inputs
a n by n matrix
b n by m matrix
Outputs m (n by n) satisfies
a m a’ - m + b*b’ = 0
Chapter 28: Control Theory 233
Function Filedlyap (a, b)
Solve the discrete-time Lyapunov equation
Inputs
a n by n matrix
b Matrix: n by n, n by m, or p by n.
Outputs x: matrix satisfying appropriate discrete time Lyapunov equation. Options:
• b is square: solve a x a’ - x + b = 0
• b is not square: x satisfies either
a x a’ - x + b b’ = 0
or
a’ x a - x + b’ b = 0,
whichever is appropriate.
Method Uses Schur decomposition method as in Kitagawa, An Algorithm for Solving
the Matrix Equation X = FXF +S, International Journal of Control, Volume 25,
Number 5, pages 745–753 (1977).
Column-by-column solution method as suggested in Hammarling, Numerical Solution
of the Stable, Non-Negative Definite Lyapunov Equation, IMA Journal of Numerical
Analysis, Volume 2, pages 303–323 (1982).
Function Filegram (a, b)
Return controllability grammian m of the continuous time system dx/dt = ax+bu.
m satisfies am+ma +bb = 0.
Function Filelyap (a, b, c)
Function Filelyap (a, b)
Solve the Lyapunov (or Sylvester) equation via the Bartels-Stewart algorithm (Communications
of the ACM, 1972).
If a, b, and c are specified, then lyap returns the solution of the Sylvester equation
AX + XB + C = 0
If only (a, b) are specified, then lyap returns the solution of the Lyapunov equation
AT
X + XA + B = 0
If b is not square, then lyap returns the solution of either
AT
X + XA + BT
B = 0
or
AX + XAT
+ BBT
= 0
whichever is appropriate.
Solves by using the Bartels-Stewart algorithm (1972).
234 GNU Octave
Function Fileqzval (a, b)
Compute generalized eigenvalues of the matrix pencil (A − λB).
a and b must be real matrices.
Note qzval is obsolete; use qz instead.
Function Filezgfmul (a, b, c, d, x)
Compute product of zgep incidence matrix F with vector x. Used by zgepbal (in
zgscal) as part of generalized conjugate gradient iteration.
Function Filezgfslv (n, m, p, b)
Solve system of equations for dense zgep problem.
Function Filezginit (a, b, c, d)
Construct right hand side vector zz for the zero-computation generalized eigenvalue
problem balancing procedure. Called by zgepbal.
Function Filezgreduce (sys, meps)
Implementation of procedure REDUCE in (Emami-Naeini and Van Dooren, Automatica,
# 1982).
Function File[nonz, zer] = zgrownorm (mat, meps)
Return nonz = number of rows of mat whose two norm exceeds meps, and zer =
number of rows of mat whose two norm is less than meps.
Function Filezgscal (f, z, n, m, p)
Generalized conjugate gradient iteration to solve zero-computation generalized eigenvalue
problem balancing equation fx = z; called by zgepbal
Function File[a, b] = zgsgiv (c, s, a, b)
Apply givens rotation c,s to row vectors a, b. No longer used in zero-balancing
( zgpbal ); kept for backward compatibility.
Function Filezgshsr (y)
apply householder vector based on eˆ(m) to (column vector) y. Called by zgfslv
References:
ZGEP Hodel, "Computation of Zeros with Balancing," 1992, Linear Algebra and its
Applications
Generalized CG
Golub and Van Loan, "Matrix Computations, 2nd ed" 1989
Chapter 28: Control Theory 235
28.6 System Analysis-Properties
Function Fileanaldemo ()
Octave Controls toolbox demo: State Space analysis demo
Function File[n, m, p] = abcddim (a, b, c, d)
Check for compatibility of the dimensions of the matrices defining the linear system
[A, B, C, D] corresponding to
dx
dt
= Ax + Bu
y = Cx + Du
or a similar discrete-time system.
If the matrices are compatibly dimensioned, then abcddim returns
n The number of system states.
m The number of system inputs.
p The number of system outputs.
Otherwise abcddim returns n = m = p = −1.
Note: n = 0 (pure gain block) is returned without warning.
Function Filectrb (sys, b)
Function Filectrb (a, b)
Build controllability matrix
2 n-1
Qs = [ B AB A B ... A B ]
of a system data structure or the pair (a, b).
Note ctrb forms the controllability matrix. The numerical properties of
is_controllable are much better for controllability tests.
Function Filh2norm (sys)
Computes the H2 norm of a system data structure (continuous time only)
Reference: Doyle, Glover, Khargonekar, Francis, “State Space Solutions to Standard
H2 and Hinf Control Problems", IEEE TAC August 1989
Function File[g, gmin, gmax] = hinfnorm (sys, tol, gmin, gmax, ptol)
Computes the H infinity norm of a system data structure.
Inputs
sys system data structure
tol H infinity norm search tolerance (default: 0.001)
236 GNU Octave
gmin minimum value for norm search (default: 1e-9)
gmax maximum value for norm search (default: 1e+9)
ptol pole tolerance:
• if sys is continuous, poles with |real(pole)| < ptol*||H|| (H is appropriate
Hamiltonian) are considered to be on the imaginary axis.
• if sys is discrete, poles with |abs(pole)-1| < ptol*||[s1,s2]|| (appropriate
symplectic pencil) are considered to be on the unit circle
• Default: 1e-9
Outputs
g Computed gain, within tol of actual gain. g is returned as Inf if the
system is unstable.
gmin
gmax Actual system gain lies in the interval [gmin, gmax]
References: Doyle, Glover, Khargonekar, Francis, "State space solutions to standard
H2 and Hinf control problems", IEEE TAC August 1989 Iglesias and Glover, "StateSpace
approach to discrete-time Hinf control," Int. J. Control, vol 54, #5, 1991 Zhou,
Doyle, Glover, "Robust and Optimal Control," Prentice-Hall, 1996
Function Fileobsv (sys, c)
Build observability matrix
| C |
| CA |
Qb = | CA^2 |
| ... |
| CA^(n-1) |
of a system data structure or the pair (A, C).
Note: obsv() forms the observability matrix.
The numerical properties of is observable() are much better for observability tests.
Function File[zer, pol]= pzmap (sys)
Plots the zeros and poles of a system in the complex plane. Inputs sys system data
structure
Outputs if omitted, the poles and zeros are plotted on the screen. otherwise, pol, zer
are returned as the system poles and zeros. (see sys2zp for a preferable function call)
Function Fileis abcd (a, b, c, d)
Returns retval = 1 if the dimensions of a, b, c, d are compatible, otherwise retval =
0 with an appropriate diagnostic message printed to the screen. The matrices b, c,
or d may be omitted.
Chapter 28: Control Theory 237
Function File[retval, u] = is controllable (sys, tol)
Function File[retval, u] = is controllable (a, b, tol)
Logical check for system controllability.
Inputs
sys system data structure
a
b n by n, n by m matrices, respectively
tol optional roundoff paramter. default value: 10*eps
Outputs
retval Logical flag; returns true (1) if the system sys or the pair (a,b) is controllable,
whichever was passed as input arguments.
U U is an orthogonal basis of the controllable subspace.
Method Controllability is determined by applying Arnoldi iteration with complete
re-orthogonalization to obtain an orthogonal basis of the Krylov subspace
span ([b,a*b,...,a^{n-1}*b]).
The Arnoldi iteration is executed with krylov if the system has a single input; otherwise
a block Arnoldi iteration is performed with krylovb.
Function File[retval, u] = is detectable (a, c, tol)
Function File[retval, u] = is detectable (sys, tol)
Test for detactability (observability of unstable modes) of (a,c).
Returns 1 if the system a or the pair (a,c)is detectable, 0 if not.
See is_stabilizable for detailed description of arguments and computational
method.
Default: tol = 10*norm(a,’fro’)*eps
Function File[retval, dgkf struct ] = is dgkf (asys, nu, ny, tol )
Determine whether a continuous time state space system meets assumptions of DGKF
algorithm. Partitions system into:
[dx/dt] = [A | Bw Bu ][w]
[ z ] [Cz | Dzw Dzu ][u]
[ y ] [Cy | Dyw Dyu ]
or similar discrete-time system. If necessary, orthogonal transformations qw, qz and
nonsingular transformations ru, ry are applied to respective vectors w, z, u, y in order
to satisfy DGKF assumptions. Loop shifting is used if dyu block is nonzero.
Inputs
asys system data structure
nu number of controlled inputs
ny number of measured outputs
238 GNU Octave
tol threshhold for 0. Default: 200eps
Outputs
retval true(1) if system passes check, false(0) otherwise
dgkf struct
data structure of is_dgkf results. Entries:
nw
nz dimensions of w, z
a system A matrix
bw (n x nw) qw-transformed disturbance input matrix
bu (n x nu) ru-transformed controlled input matrix;
Note B = [BwBu]
cz (nz x n) Qz-transformed error output matrix
cy (ny x n) ry-transformed measured output matrix
Note C = [Cz; Cy]
dzu
dyw off-diagonal blocks of transformed system D matrix that enter
z, y from u, w respectively
ru controlled input transformation matrix
ry observed output transformation matrix
dyu nz nonzero if the dyu block is nonzero.
dyu untransformed dyu block
dflg nonzero if the system is discrete-time
is_dgkf exits with an error if the system is mixed discrete/continuous
References
[1] Doyle, Glover, Khargonekar, Francis, "State Space Solutions to Standard
H2 and Hinf Control Problems," IEEE TAC August 1989
[2] Maciejowksi, J.M.: "Multivariable feedback design,"
Function Fileis digital (sys)
Return nonzero if system is digital; inputs: sys: system data structure eflg: 0 [default]
exit with an error if system is mixed (continuous and discrete components) : 1 print
a warning if system is mixed (continuous and discrete) : 2 silent operation outputs:
DIGITAL: 0: system is purely continuous : 1: system is purely discrete : -1: system
is mixed continuous and discrete Exits with an error of sys is a mixed (continuous
and discrete) system
Chapter 28: Control Theory 239
Function File[retval, u] = is observable (a, c, tol)
Function File[retval, u] = is observable (sys, tol)
Logical check for system observability.
Default: tol = 10*norm(a,’fro’)*eps
Returns 1 if the system sys or the pair (a,c) is observable, 0 if not.
See is_controllable for detailed description of arguments and default values.
Function Fileis sample (ts)
Return true if ts is a valid sampling time (real,scalar, > 0)
Function Fileis siso (sys)
return nonzero if the system data structure sys is single-input, single-output.
Function File[retval, u] = is stabilizable (sys, tol)
Function File[retval, u] = is stabilizable (a, b, tol)
Logical check for system stabilizability (i.e., all unstable modes are controllable).
Test for stabilizability is performed via an ordered Schur decomposition that reveals
the unstable subspace of the system a matrix.
Returns retval = 1 if the system, a, is stabilizable, if the pair (a, b) is stabilizable,
or 0 if not. u = orthogonal basis of controllable subspace.
Controllable subspace is determined by applying Arnoldi iteration with complete reorthogonalization
to obtain an orthogonal basis of the Krylov subspace.
span ([b,a*b,...,a^ b]).
tol is a roundoff paramter, set to 200*eps if omitted.
Function Fileis signal list (mylist)
Return true if mylist is a list of individual strings.
Function Fileis stable (a, tol, dflg)
Function Fileis stable (sys, tol)
Returns 1 if the matrix a or the system sys is stable, or 0 if not.
Inputs
tol is a roundoff paramter, set to 200*eps if omitted.
dflg Digital system flag (not required for system data structure):
dflg != 0 stable if eig(a) in unit circle
dflg == 0 stable if eig(a) in open LHP (default)
240 GNU Octave
28.7 System Analysis-Time Domain
Function Filec2d (sys, opt, t)
Function Filec2d (sys, t)
Inputs
sys system data structure (may have both continuous time and discrete time
subsystems)
opt string argument; conversion option (optional argument; may be omitted
as shown above)
"ex" use the matrix exponential (default)
"bi" use the bilinear transformation
2(z-1)
s = -----
T(z+1)
FIXME: This option exits with an error if sys is not purely continuous.
(The ex option can handle mixed systems.)
t sampling time; required if sys is purely continuous.
Note If the 2nd argument is not a string, c2d assumes that the 2nd
argument is t and performs appropriate argument checks.
Outputs dsys discrete time equivalent via zero-order hold, sample each t sec.
converts the system data structure describing
.
x = Ac x + Bc u
into a discrete time equivalent model
x[n+1] = Ad x[n] + Bd u[n]
via the matrix exponential or bilinear transform
Note This function adds the suffix _d to the names of the new discrete states.
Function Filed2c (sys, tol)
Function Filed2c (sys, opt)
Convert discrete (sub)system to a purely continuous system. Sampling time used is
sysgettsam(sys)
Inputs
sys system data structure with discrete components
tol Scalar value. tolerance for convergence of default "log" option (see be-
low)
opt conversion option. Choose from:
Chapter 28: Control Theory 241
"log" (default) Conversion is performed via a matrix logarithm.
Due to some problems with this computation, it is followed
by a steepest descent algorithm to identify continuous time
a, b, to get a better fit to the original data.
If called as d2c (sys, tol), with tol positive scalar, the "log"
option is used. The default value for tol is 1e-8.
"bi" Conversion is performed via bilinear transform
z = (1+sT/2)/(1 − sT/2) where T is the system sampling
time (see sysgettsam).
FIXME: bilinear option exits with an error if sys is not purely
discrete
Outputs csys continuous time system (same dimensions and signal names as in sys).
Function File[dsys, fidx] = dmr2d (sys, idx, sprefix, ts2, cuflg)
convert a multirate digital system to a single rate digital system states specified by
idx, sprefix are sampled at ts2, all others are assumed sampled at ts1 = sysgettsam
(sys).
Inputs
sys discrete time system; dmr2d exits with an error if sys is not discrete
idx indices or names of states with sampling time sysgettsam(sys) (may be
empty); see listidx
sprefix list of string prefixes of states with sampling time sysgettsam(sys) (may
be empty)
ts2 sampling time of states not specified by idx, sprefix must be an integer
multiple of sysgettsam(sys)
cuflg "constant u flag" if cuflg is nonzero then the system inputs are assumed
to be constant over the revised sampling interval ts2. Otherwise, since the
inputs can change during the interval t in [kts2, (k+1)ts2], an additional
set of inputs is included in the revised B matrix so that these intersample
inputs may be included in the single-rate system. default cuflg = 1.
Outputs
dsys equivalent discrete time system with sampling time ts2.
The sampling time of sys is updated to ts2.
if cuflg=0 then a set of additional inputs is added to the system with
suffixes d1, ..., dn to indicate their delay from the starting time k ts2,
i.e. u = [u 1; u 1 d1; ..., u 1 dn] where u 1 dk is the input k*ts1 units
of time after u 1 is sampled. (ts1 is the original sampling time of the
discrete time system and ts2 = (n+1)*ts1)
fidx indices of "formerly fast" states specified by idx and sprefix; these states
are updated to the new (slower) sampling interval ts2.
WARNING Not thoroughly tested yet; especially when cuflg == 0.
242 GNU Octave
Function Filedamp (p, tsam)
Displays eigenvalues, natural frequencies and damping ratios of the eigenvalues of a
matrix p or the A-matrix of a system p, respectively. If p is a system, tsam must not
be specified. If p is a matrix and tsam is specified, eigenvalues of p are assumed to
be in z-domain.
Function Filedcgain (sys, tol)
Returns dc-gain matrix. If dc-gain is infinite an empty matrix is returned. The
argument tol is an optional tolerance for the condition number of the A-Matrix in sys
(default tol = 1.0e-10)
Function File[y, t] = impulse (sys, inp, tstop, n)
Impulse response for a linear system. The system can be discrete or multivariable (or
both). If no output arguments are specified, impulse produces a plot or the impulse
response data for system sys.
Inputs
sys System data structure.
inp Index of input being excited
tstop The argument tstop (scalar value) denotes the time when the simulation
should end.
n the number of data values.
Both parameters tstop and n can be omitted and will be computed from
the eigenvalues of the A-Matrix.
Outputs y, t: impulse response
Function File[y, t] = step (sys, inp, tstop, n)
Step response for a linear system. The system can be discrete or multivariable (or
both). If no output arguments are specified, step produces a plot or the step response
data for system sys.
Inputs
sys System data structure.
inp Index of input being excited
tstop The argument tstop (scalar value) denotes the time when the simulation
should end.
n the number of data values.
Both parameters tstop and n can be omitted and will be computed from
the eigenvalues of the A-Matrix.
Outputs y, t: impulse response
When invoked with the output paramter y the plot is not displayed.
Chapter 28: Control Theory 243
28.8 System Analysis-Frequency Domain
Demonstration/tutorial script
Function Filefrdemo ()
Octave Controls toolbox demo: Frequency Response demo
Function File[mag, phase, w] = bode (sys, w, out idx, in idx)
If no output arguments are given: produce Bode plots of a system; otherwise, compute
the frequency response of a system data structure
Inputs
sys a system data structure (must be either purely continuous or discrete; see
is digital)
w frequency values for evaluation.
if sys is continuous, then bode evaluates G(jw) where G(s) is the system
transfer function.
if sys is discrete, then bode evaluates G(exp(jwT)), where
• T is the system sampling time
• G(z) is the system transfer function.
Default the default frequency range is selected as follows: (These steps
are NOT performed if w is specified)
1. via routine bodquist , isolate all poles and zeros away from w=0
(jw=0 or exp(jwT)=1) and select the frequency range based on the
breakpoint locations of the frequencies.
2. if sys is discrete time, the frequency range is limited to jwT in
[0, 2π/T]
3. A "smoothing" routine is used to ensure that the plot phase does
not change excessively from point to point and that singular points
(e.g., crossovers from +/- 180) are accurately shown.
out idx
in idx
The names or indices of outputs and inputs to be used in the frequency
response. See sysprune.
Example
bode(sys,[],"y_3",list("u_1","u_4");
Outputs
mag
phase the magnitude and phase of the frequency response G(jw) or
G(exp(jwT)) at the selected frequency values.
w the vector of frequency values used
Notes
244 GNU Octave
1. If no output arguments are given, e.g.,
bode(sys);
bode plots the results to the screen. Descriptive labels are automatically placed.
Failure to include a concluding semicolon will yield some garbage being printed
to the screen (ans = []).
2. If the requested plot is for an MIMO system, mag is set to ||G(jw)|| or
||G(exp(jwT))|| and phase information is not computed.
Function File[wmin, wmax] = bode bounds (zer, pol, dflg, tsam)
Get default range of frequencies based on cutoff frequencies of system poles and zeros.
Frequency range is the interval [10^wmin,10^wmax]
Used internally in freqresp (bode, nyquist)
Function Filefreqchkw (w)
Used by __freqresp__ to check that input frequency vector w is valid. Returns
boolean value.
Function Fileltifr (a, b, w)
Function Fileltifr (sys, w)
Linear time invariant frequency response of single input systems Inputs
a
b coefficient matrices of dx/dt = Ax+Bu
sys system data structure
w vector of frequencies
Outputs out
-1
G(s) = (jw I-A) B
for complex frequencies s = jw.
Function File[realp, imagp, w] = nyquist (sys, w, out idx, in idx, atol)
Function Filenyquist (sys, w, out idx, in idx, atol)
Produce Nyquist plots of a system; if no output arguments are given, Nyquist plot is
printed to the screen.
Compute the frequency response of a system. Inputs (pass as empty to get default
values)
sys system data structure (must be either purely continuous or discrete; see
is digital)
w frequency values for evaluation. if sys is continuous, then bode evaluates
G(jw) if sys is discrete, then bode evaluates G(exp(jwT)), where T is
the system sampling time.
Chapter 28: Control Theory 245
default the default frequency range is selected as follows: (These steps are NOT
performed if w is specified)
1. via routine bodquist , isolate all poles and zeros away from w=0 (jw=0 or
exp(jwT) = 1) and select the frequency range based on the breakpoint locations
of the frequencies.
2. if sys is discrete time, the frequency range is limited to jwT in $[0,2p*\pi]$
3. A "smoothing" routine is used to ensure that the plot phase does not change
excessively from point to point and that singular points (e.g., crossovers from +/-
180) are accurately shown.
outputs, inputs: names or indices of the output(s) and input(s) to be used in the
frequency response; see sysprune.
Inputs (pass as empty to get default values)
atol for interactive nyquist plots: atol is a change-in-slope tolerance for the of
asymptotes (default = 0; 1e-2 is a good choice). This allows the user to
“zoom in” on portions of the Nyquist plot too small to be seen with large
asymptotes.
Outputs
realp
imagp the real and imaginary parts of the frequency response G(jw) or
G(exp(jwT)) at the selected frequency values.
w the vector of frequency values used
If no output arguments are given, nyquist plots the results to the screen. If atol != 0
and asymptotes are detected then the user is asked interactively if they wish to zoom
in (remove asymptotes) Descriptive labels are automatically placed.
Note: if the requested plot is for an MIMO system, a warning message is presented;
the returned information is of the magnitude ||G(jw)|| or ||G(exp(jwT))|| only;
phase information is not computed.
Function Filetzero (a, b, c, d, opt)
Function Filetzero (sys, opt)
Compute transmission zeros of a continuous
.
x = Ax + Bu
y = Cx + Du
or discrete
x(k+1) = A x(k) + B u(k)
y(k) = C x(k) + D u(k)
system. Outputs
zer transmission zeros of the system
gain leading coefficient (pole-zero form) of SISO transfer function returns
gain=0 if system is multivariable
246 GNU Octave
References
1. Emami-Naeini and Van Dooren, Automatica, 1982.
2. Hodel, "Computation of Zeros with Balancing," 1992 Lin. Alg. Appl.
Function Filetzero2 (a, b, c, d, bal)
Compute the transmission zeros of a, b, c, d.
bal = balancing option (see balance); default is "B".
Needs to incorporate mvzero algorithm to isolate finite zeros; use tzero instead.
28.9 Controller Design
Function Filedgkfdemo ()
Octave Controls toolbox demo: H2/Hinfinity options demos
Function Filehinfdemo ()
H infinity design demos for continuous SISO and MIMO systems and a discrete system.
The SISO system is difficult to control because it is non minimum phase and
unstable. The second design example controls the "jet707" plant, the linearized state
space model of a Boeing 707-321 aircraft at v=80m/s (M = 0.26, Ga0 = -3 deg,
alpha0 = 4 deg, kappa = 50 deg). Inputs: (1) thrust and (2) elevator angle outputs:
(1) airspeed and (2) pitch angle. The discrete system is a stable and second order.
SISO plant
s - 2
G(s) = ————–
(s + 2)(s - 1)
+—-+
——————–>| W1 |—> v1
z | +—-+
—-|————-+ || T || => min.
| | vz infty
| +—+ v y +—-+
u *—>| G |—>O–*–>| W2 |—> v2
| +—+ | +—-+
| |
| +—+ |
—–| K |<——-
+—+
W1 und W2 are the robustness and performance weighting functions
MIMO plant
The optimal controller minimizes the H infinity norm of the augmented
plant P (mixed-sensitivity problem):
Chapter 28: Control Theory 247
w
1 ———–+
| +—-+
+———————->| W1 |—-> z1
w | | +—-+
2 ————————+
| | |
| v +—-+ v +—-+
+–*–>o–>| G |–>o–*–>| W2 |—> z2
| +—-+ | +—-+
| |
^ v
u (from y (to K)
controller
K)
+ + + +
| z | | w |
| 1 | | 1 |
| z | = [ P ] * | w |
| 2 | | 2 |
| y | | u |
+ + + +
DISCRETE SYSTEM
This is not a true discrete design. The design is carried out in continuous
time while the effect of sampling is described by a bilinear transformation
of the sampled system. This method works quite well if the sampling
period is "small" compared to the plant time constants.
The continuous plant
1
G (s) = ————–
k (s + 2)(s + 1)
is discretised with a ZOH (Sampling period = Ts = 1 second):
248 GNU Octave
0.199788z + 0.073498
G(s) = ————————–
(z - 0.36788)(z - 0.13534)
+—-+
——————–>| W1 |—> v1
z | +—-+
—-|————-+ || T || => min.
| | vz infty
| +—+ v +—-+
*—>| G |—>O–*–>| W2 |—> v2
| +—+ | +—-+
| |
| +—+ |
—–| K |<——-
+—+
W1 and W2 are the robustness and performancs weighting functions
Function File[l, m, p, e] = dlqe (a, g, c, sigw, sigv, z)
Construct the linear quadratic estimator (Kalman filter) for the discrete time system
xk+1 = Axk + Buk + Gwk
yk = Cxk + Duk + vk
where w, v are zero-mean gaussian noise processes with respective intensities sigw =
cov (w, w) and sigv = cov (v, v).
If specified, z is cov (w, v). Otherwise cov (w, v) = 0.
The observer structure is
zk|k = zk|k−1 + l(yk − Czk|k−1 − Duk)
zk+1|k = Azk|k + Buk
The following values are returned:
l The observer gain, (A − ALC). is stable.
m The Riccati equation solution.
p The estimate error covariance after the measurement update.
e The closed loop poles of (A − ALC).
Function File[k, p, e] = dlqr (a, b, q, r, z)
Construct the linear quadratic regulator for the discrete time system
xk+1 = Axk + Buk
Chapter 28: Control Theory 249
to minimize the cost functional
J = xT
Qx + uT
Ru
z omitted or
J = xT
Qx + uT
Ru + 2xT
Zu
z included.
The following values are returned:
k The state feedback gain, (A − BK) is stable.
p The solution of algebraic Riccati equation.
e The closed loop poles of (A − BK).
Function File[Lp, Lf, P, Z] = dkalman (A, G, C, Qw, Rv, S)
Construct the linear quadratic estimator (Kalman predictor) for the discrete time
system
xk+1 = Axk + Buk + Gwk
yk = Cxk + Duk + vk
where w, v are zero-mean gaussian noise processes with respective intensities Qw =
cov (w, w) and Rv = cov (v, v).
If specified, S is cov (w, v). Otherwise cov (w, v) = 0.
The observer structure is xk+1|k = Axk|k−1 + Buk + Lp(yk − Cxk|k−1 − Duk) xk|k =
xk|k + Lf (yk − Cxk|k−1 − Duk)
The following values are returned:
Lp The predictor gain, (A − LpC). is stable.
Lf The filter gain.
P The Riccati solution. P = E{(x − xn|n−1)(x − xn|n−1) }
Z The updated error covariance matrix. Z = E{(x − xn|n)(x − xn|n) }
Function File[K, gain, kc, kf, pc, pf ] = h2syn (asys, nu, ny, tol)
Design H2 optimal controller per procedure in Doyle, Glover, Khargonekar, Francis,
"State Space Solutions to Standard H2 and Hinf Control Problems", IEEE TAC
August 1989
Discrete time control per Zhou, Doyle, and Glover, ROBUST AND OPTIMAL CONTROL,
Prentice-Hall, 1996
Inputs input system is passed as either
asys system data structure (see ss2sys, sys2ss)
• controller is implemented for continuous time systems
• controller is NOT implemented for discrete time systems
nu number of controlled inputs
250 GNU Octave
ny number of measured outputs
tol threshhold for 0. Default: 200*eps
Outputs
k system controller
gain optimal closed loop gain
kc full information control (packed)
kf state estimator (packed)
pc ARE solution matrix for regulator subproblem
pf ARE solution matrix for filter subproblem
Function Filehinf ctr (dgs, f, h, z, g)
Called by hinfsyn to compute the H inf optimal controller.
Inputs
dgs data structure returned by is_dgkf
f
h feedback and filter gain (not partitioned)
g final gamma value
Outputs controller (system data structure)
Do not attempt to use this at home; no argument checking performed.
Function File[k, g, gw, xinf, yinf ] = hinfsyn (asys, nu, ny, gmin, gmax,
gtol, ptol, tol)
Inputs input system is passed as either
asys system data structure (see ss2sys, sys2ss)
• controller is implemented for continuous time systems
• controller is NOT implemented for discrete time systems (see bilinear
transforms in c2d, d2c)
nu number of controlled inputs
ny number of measured outputs
gmin initial lower bound on H-infinity optimal gain
gmax initial upper bound on H-infinity optimal gain
gtol gain threshhold. Routine quits when gmax/gmin < 1+tol
ptol poles with abs(real(pole)) < ptol*||H|| (H is appropriate Hamiltonian)
are considered to be on the imaginary axis. Default: 1e-9
tol threshhold for 0. Default: 200*eps
gmax, min, tol, and tol must all be postive scalars.
Chapter 28: Control Theory 251
Outputs
k system controller
g designed gain value
gw closed loop system
xinf ARE solution matrix for regulator subproblem
yinf ARE solution matrix for filter subproblem
1. Doyle, Glover, Khargonekar, Francis, "State Space Solutions to Standard H2 and
Hinf Control Problems," IEEE TAC August 1989
2. Maciejowksi, J.M., "Multivariable feedback design," Addison-Wesley, 1989, ISBN
0-201-18243-2
3. Keith Glover and John C. Doyle, "State-space formulae for all stabilizing controllers
that satisfy and h-infinity-norm bound and relations to risk sensitivity,"
Systems & Control Letters 11, Oct. 1988, pp 167-172.
Function File[retval, pc, pf ] = hinfsyn chk (a, b1, b2, c1, c2, d12, d21, g,
ptol)
Called by hinfsyn to see if gain g satisfies conditions in Theorem 3 of Doyle, Glover,
Khargonekar, Francis, "State Space Solutions to Standard H2 and Hinf Control Problems",
IEEE TAC August 1989
Warning Do not attempt to use this at home; no argument checking performed.
Inputs as returned by is_dgkf, except for:
g candidate gain level
ptol as in hinfsyn
Outputs
retval 1 if g exceeds optimal Hinf closed loop gain, else 0
pc solution of "regulator" H-inf ARE
pf solution of "filter" H-inf ARE
Do not attempt to use this at home; no argument checking performed.
Function File[xinf, x ha err] = hinfsyn ric (a, bb, c1, d1dot, r, ptol)
Forms
xx = ([BB; -C1’*d1dot]/R) * [d1dot’*C1 BB’];
Ha = [A 0*A; -C1’*C1 -A’] - xx;
and solves associated Riccati equation. The error code x ha err indicates one of the
following conditions:
0 successful
1 xinf has imaginary eigenvalues
2 hx not Hamiltonian
252 GNU Octave
3 xinf has infinite eigenvalues (numerical overflow)
4 xinf not symmetric
5 xinf not positive definite
6 r is singular
Function File[k, p, e] = lqe (a, g, c, sigw, sigv, z)
Construct the linear quadratic estimator (Kalman filter) for the continuous time sys-
tem
dx
dt
= Ax + Bu
y = Cx + Du
where w and v are zero-mean gaussian noise processes with respective intensities
sigw = cov (w, w)
sigv = cov (v, v)
The optional argument z is the cross-covariance cov (w, v). If it is omitted, cov
(w, v) = 0 is assumed.
Observer structure is dz/dt = A z + B u + k (y - C z - D u)
The following values are returned:
k The observer gain, (A − KC) is stable.
p The solution of algebraic Riccati equation.
e The vector of closed loop poles of (A − KC).
Function File[k, q1, p1, ee, er] = lqg (sys, sigw, sigv, q, r, in idx)
Design a linear-quadratic-gaussian optimal controller for the system
dx/dt = A x + B u + G w [w]=N(0,[Sigw 0 ])
y = C x + v [v] ( 0 Sigv ])
or
x(k+1) = A x(k) + B u(k) + G w(k) [w]=N(0,[Sigw 0 ])
y(k) = C x(k) + v(k) [v] ( 0 Sigv ])
Inputs
sys system data structure
sigw
sigv intensities of independent Gaussian noise processes (as above)
q
r state, control weighting respectively. Control ARE is
in idx names or indices of controlled inputs (see sysidx, listidx)
default: last dim(R) inputs are assumed to be controlled inputs, all others
are assumed to be noise inputs.
Outputs
Chapter 28: Control Theory 253
k system data structure format LQG optimal controller (Obtain A,B,C matrices
with sys2ss, sys2tf, or sys2zp as appropriate)
p1 Solution of control (state feedback) algebraic Riccati equation
q1 Solution of estimation algebraic Riccati equation
ee estimator poles
es controller poles
Function File[k, p, e] = lqr (a, b, q, r, z)
construct the linear quadratic regulator for the continuous time system
dx
dt
= Ax + Bu
to minimize the cost functional
J =
∞
0
xT
Qx + uT
Ru
z omitted or
J =
∞
0
xT
Qx + uT
Ru + 2xT
Zu
z included.
The following values are returned:
k The state feedback gain, (A − BK) is stable and minimizes the cost
functional
p The stabilizing solution of appropriate algebraic Riccati equation.
e The vector of the closed loop poles of (A − BK).
Reference Anderson and Moore, OPTIMAL CONTROL: LINEAR QUADRATIC
METHODS, Prentice-Hall, 1990, pp. 56-58
Function Filelsim (sys, u, t, x0)
Produce output for a linear simulation of a system
Produces a plot for the output of the system, sys.
U is an array that contains the system’s inputs. Each column in u corresponds to
a different time step. Each row in u corresponds to a different input. T is an array
that contains the time index of the system. T should be regularly spaced. If initial
conditions are required on the system, the x0 vector should be added to the argument
list.
When the lsim function is invoked with output parameters: [y,x] = lsim(sys,u,t,[x0])
a plot is not displayed, however, the data is returned in y = system output and x =
system states.
Function Fileplace (sys, p)
Computes the matrix K such that if the state is feedback with gain K, then the
eigenvalues of the closed loop system (i.e. A-BK) are those specified in the vector p.
Version: Beta (May-1997): If you have any comments, please let me know. (see the
file place.m for my address)
254 GNU Octave
28.10 Miscellaneous Functions (Not yet properly
filed/documented)
Function Fileaxis2dlim (axdata)
determine axis limits for 2-d data(column vectors); leaves a 10% margin around the
plots. puts in margins of +/- 0.1 if data is one dimensional (or a single point)
Inputs axdata nx2 matrix of data [x,y]
Outputs axvec vector of axis limits appropriate for call to axis() function
Function Filemoddemo (inputs)
Octave Controls toolbox demo: Model Manipulations demo
Function Fileprompt (inputs)
function prompt([str])
Prompt user to continue
str: input string. Default value: "\n —- Press a key to continue —"
Function Filerldemo (inputs)
Octave Controls toolbox demo: Root Locus demo
Function Filerlocus (inputs)
[rldata, k] = rlocus(sys[,increment,min k,max k])
Displays root locus plot of the specified SISO system.
—– — ——–
—>| + |—|k|—->| SISO |———–>
—– — ——– |
- ^ |
| |
inputs: sys = system data structure
min k, max k,increment: minimum, maximum values of k and
the increment used in computing gain values
Outputs: plots the root locus to the screen.
rldata: Data points plotted column 1: real values, column 2: imaginary
values)
k: gains for real axis break points.
Function Filesortcom (inputs)
[yy,idx] = sortcom(xx[,opt]): sort a complex vector
xx: complex vector
opt: sorting option:
"re": real part (default)
"mag": by magnitude
"im": by imaginary part
Chapter 28: Control Theory 255
if opt != "im" then complex conjugate pairs are grouped together,
a - jb followed by a + jb.
yy: sorted values
idx: permutation vector: yy = xx(idx)
Function Filess2tf (inputs)
[num,den] = ss2tf(a,b,c,d)
Conversion from tranfer function to state-space.
The state space system
.
x = Ax + Bu
y = Cx + Du
is converted to a transfer function
num(s)
G(s)=——-
den(s)
used internally in system data structure format manipulations
Function Filess2zp (inputs)
Converts a state space representation to a set of poles and zeros.
[pol,zer,k] = ss2zp(a,b,c,d) returns the poles and zeros of the state space
system (a,b,c,d). K is a gain associated with the zeros.
used internally in system data structure format manipulations
Function Filestarp (inputs)
sys = starp(P, K, ny, nu)
Redheffer star product or upper/lower LFT, respectively.
+——-+
———>| |———>
| P |
+—>| |—+ ny
| +——-+ |
+——————-+
| |
+—————-+ |
| |
| +——-+ |
256 GNU Octave
+—>| |——+ nu
| K |
———>| |———>
+——-+
If ny and nu "consume" all inputs and outputs of K then the result
is a lower fractional transformation. If ny and nu "consume" all
inputs and outputs of P then the result is an upper fractional
transformation.
ny and/or nu may be negative (= negative feedback)
Function Filetf2ss (inputs)
Conversion from tranfer function to state-space.
The state space system
.
x = Ax + Bu
y = Cx + Du
is obtained from a transfer function
num(s)
G(s)=——-
den(s)
via the function call [a,b,c,d] = tf2ss(num,den).
The vector ’den’ must contain only one row, whereas the vector ’num’
may contain as many rows as there are outputs of the system ’y’.
The state space system matrices obtained from this function will be
in controllable canonical form as described in "Modern Control Theory",
[Brogan, 1991].
Function Filetf2zp (inputs)
Converts transfer functions to poles / zeros.
[zer,pol,k] = tf2zp(num,den) returns the zeros and poles of the SISO system defined
by num/den. K is a gain associated with the system zeros.
Function File[a, b, c, d] = zp2ss (zer, pol, k)
Conversion from zero / pole to state space. Inputs
zer
pol vectors of (possibly) complex poles and zeros of a transfer function. Complex
values must come in conjugate pairs (i.e., x+jy in zer means that x-jy
is also in zer)
k real scalar (leading coefficient)
Chapter 28: Control Theory 257
Outputs a, b, c, d The state space system
.
x = Ax + Bu
y = Cx + Du
is obtained from a vector of zeros and a vector of poles via the function call [a,b,c,d]
= zp2ss(zer,pol,k). The vectors ‘zer’ and ‘pol’ may either be row or column
vectors. Each zero and pole that has an imaginary part must have a conjugate in the
list. The number of zeros must not exceed the number of poles. ‘k’ is zp-form leading
coefficient.
Function File[num, den] = zp2tf (zer, pol, k)
Converts zeros / poles to a transfer function. Inputs
zer
pol vectors of (possibly complex) poles and zeros of a transfer function. Complex
values should appear in conjugate pairs
k real scalar (leading coefficient)
[num,den] = zp2tf(zer,pol,k) forms the transfer function num/den from the vectors
of poles and zeros.
258 GNU Octave
Chapter 29: Signal Processing 259
29 Signal Processing
I hope that someday Octave will include more signal processing functions. If you would
like to help improve Octave in this area, please contact bug-octave@bevo.che.wisc.edu.
Function Filedetrend (x, p)
If x is a vector, detrend (x, p) removes the best fit of a polynomial of order p from
the data x.
If x is a matrix, detrend (x, p) does the same for each column in x.
The second argument is optional. If it is not specified, a value of 1 is assumed. This
corresponds to removing a linear trend.
Loadable Functionfft (a, n)
Compute the FFT of a using subroutines from Fftpack. If a is a matrix, fft
computes the FFT for each column of a.
If called with two arguments, n is expected to be an integer specifying the number of
elements of a to use. If a is a matrix, n specifies the number of rows of a to use. If n
is larger than the size of a, a is resized and padded with zeros.
Loadable Functionifft (a, n)
Compute the inverse FFT of a using subroutines from Fftpack. If a is a matrix, fft
computes the inverse FFT for each column of a.
If called with two arguments, n is expected to be an integer specifying the number of
elements of a to use. If a is a matrix, n specifies the number of rows of a to use. If n
is larger than the size of a, a is resized and padded with zeros.
Loadable Functionfft2 (a, n, m)
Compute the two dimensional FFT of a.
The optional arguments n and m may be used specify the number of rows and columns
of a to use. If either of these is larger than the size of a, a is resized and padded with
zeros.
Loadable Functionifft2 (a, n, m)
Compute the two dimensional inverse FFT of a.
The optional arguments n and m may be used specify the number of rows and columns
of a to use. If either of these is larger than the size of a, a is resized and padded with
zeros.
Function Filefftconv (a, b, n)
Return the convolution of the vectors a and b, as a vector with length equal to the
length (a) + length (b) - 1. If a and b are the coefficient vectors of two polynomials,
the returned value is the coefficient vector of the product polynomial.
The computation uses the FFT by calling the function fftfilt. If the optional
argument n is specified, an N-point FFT is used.
260 GNU Octave
Function Filefftfilt (b, x, n)
With two arguments, fftfilt filters x with the FIR filter b using the FFT.
Given the optional third argument, n, fftfilt uses the overlap-add method to filter
x with b using an N-point FFT.
Loadable Functiony = filter (b, a, x)
Loadable Function[y, sf ] = filter (b, a, x, si)
Return the solution to the following linear, time-invariant difference equation:
N
k=0
ak+1yn−k =
M
k=0
bk+1xn−k, 1 ≤ n ≤ P
where a ∈ N−1
, b ∈ M−1
, and x ∈ P
. An equivalent form of this equation is:
yn = −
N
k=1
ck+1yn−k +
M
k=0
dk+1xn−k, 1 ≤ n ≤ P
where c = a/a1 and d = b/a1.
If the fourth argument si is provided, it is taken as the initial state of the system and
the final state is returned as sf. The state vector is a column vector whose length is
equal to the length of the longest coefficient vector minus one. If si is not supplied,
the initial state vector is set to all zeros.
In terms of the z-transform, y is the result of passing the discrete- time signal x
through a system characterized by the following rational system function:
H(z) =
M
k=0
dk+1z−k
1 +
N
k+1
ck+1z−k
Function File[h, w] = freqz (b, a, n, "whole")
Return the complex frequency response h of the rational IIR filter whose numerator
and denominator coefficients are b and a, respectively. The response is evaluated at
n angular frequencies between 0 and 2π.
The output value w is a vector of the frequencies.
If the fourth argument is omitted, the response is evaluated at frequencies between 0
and π.
If n is omitted, a value of 512 is assumed.
If a is omitted, the denominator is assumed to be 1 (this corresponds to a simple FIR
filter).
For fastest computation, n should factor into a small number of small primes.
Chapter 29: Signal Processing 261
Function Filesinc (x)
Return sin(πx)/(πx).
Function File[a, b] = arch fit (y, x, p, iter, gamma, a0, b0)
Fit an ARCH regression model to the time series y using the scoring algorithm in
Engle’s original ARCH paper. The model is
y(t) = b(1) * x(t,1) + ... + b(k) * x(t,k) + e(t),
h(t) = a(1) + a(2) * e(t-1)^2 + ... + a(p+1) * e(t-p)^2
in which e(t) is N(0, h(t)), given a time-series vector y up to time t − 1 and a matrix
of (ordinary) regressors x up to t. The order of the regression of the residual variance
is specified by p.
If invoked as arch_fit (y, k, p) with a positive integer k, fit an ARCH(k, p) process,
i.e., do the above with the t-th row of x given by
[1, y(t-1), ..., y(t-k)]
Optionally, one can specify the number of iterations iter, the updating factor gamma,
and initial values a0 and b0 for the scoring algorithm.
Function Filearch rnd (a, b, t)
Simulate an ARCH sequence of length t with AR coefficients b and CH coefficients
a. I.e., the result y(t) follows the model
y(t) = b(1) + b(2) * y(t-1) + ... + b(lb) * y(t-lb+1) + e(t),
where e(t), given y up to time t − 1, is N(0, h(t)), with
h(t) = a(1) + a(2) * e(t-1)^2 + ... + a(la) * e(t-la+1)^2
Function File[pval, lm] = arch_test (y, x, p)
For a linear regression model
y = x * b + e
perform a Lagrange Multiplier (LM) test of the null hypothesis of no conditional
heteroscedascity against the alternative of CH(p).
I.e., the model is
y(t) = b(1) * x(t,1) + ... + b(k) * x(t,k) + e(t),
given y up to t − 1 and x up to t, e(t) is N(0, h(t)) with
h(t) = v + a(1) * e(t-1)^2 + ... + a(p) * e(t-p)^2,
and the null is a(1) == . . . == a(p) == 0.
If the second argument is a scalar integer, k, perform the same test in a linear autoregression
model of order k, i.e., with
[1, y(t-1), ..., y(t-k)]
as the t-th row of x.
Under the null, LM approximately has a chisquare distribution with p degrees of
freedom and pval is the p-value (1 minus the CDF of this distribution at LM) of the
test.
If no output argument is given, the p-value is displayed.
262 GNU Octave
Function Filearma rnd (a, b, v, t, n)
Return a simulation of the ARMA model
x(n) = a(1) * x(n-1) + ... + a(k) * x(n-k)
+ e(n) + b(1) * e(n-1) + ... + b(l) * e(n-l)
in which k is the length of vector a, l is the length of vector b and e is gaussian white
noise with variance v. The function returns a vector of length t.
The optional parameter n gives the number of dummy x(i) used for initialization, i.e.,
a sequence of length t+n is generated and x(n+1:t+n) is returned. If n is omitted, n
= 100 is used.
Function Fileautocor (x, h)
Return the autocorrelations from lag 0 to h of vector x. If h is omitted, all autocorrelations
are computed. If x is a matrix, the autocorrelations of each column are
computed.
Function Fileautocov (x, h)
Return the autocovariances from lag 0 to h of vector x. If h is omitted, all autocovariances
are computed. If x is a matrix, the autocovariances of each column are
computed.
Function Fileautoreg matrix (y, k)
Given a time series (vector) y, return a matrix with ones in the first column and
the first k lagged values of y in the other columns. I.e., for t > k, [1, y(t-1), ...,
y(t-k)] is the t-th row of the result. The resulting matrix may be used as a regressor
matrix in autoregressions.
Function Filebartlett (m)
Return the filter coefficients of a Bartlett (triangular) window of length m.
For a definition of the Bartlett window, see e.g. A. V. Oppenheim & R. W. Schafer,
"Discrete-Time Signal Processing".
Function Fileblackman (m)
Return the filter coefficients of a Blackman window of length m.
For a definition of the Blackman window, see e.g. A. V. Oppenheim & R. W. Schafer,
"Discrete-Time Signal Processing".
Function File[d, dd] = diffpara (x, a, b)
Return the estimator d for the differencing parameter of an integrated time series.
The frequencies from [2 ∗ pi ∗ a/t, 2 ∗ pi ∗ b/T] are used for the estimation. If b is
omitted, the interval [2 ∗ pi/T, 2 ∗ pi ∗ a/T] is used. If both b and a are omitted then
a = 0.5 ∗ sqrt(T) and b = 1.5 ∗ sqrt(T) is used, where T is the sample size. If x is a
matrix, the differencing parameter of each column is estimated.
Chapter 29: Signal Processing 263
The estimators for all frequencies in the intervals described above is returned in dd.
The value of d is simply the mean of dd.
Reference: Brockwell, Peter J. & Davis, Richard A. Time Series: Theory and Methods
Springer 1987.
Function Filedurbinlevinson (c, oldphi, oldv)
Perform one step of the Durbin-Levinson algorithm.
The vector c specifies the autocovariances [gamma_0, ..., gamma_t] from lag 0 to t,
oldphi specifies the coefficients based on c(t-1) and oldv specifies the corresponding
error.
If oldphi and oldv are omitted, all steps from 1 to t of the algorithm are performed.
Function Filefftshift (v)
Perform a shift of the vector v, for use with the fft and ifft functions, in order the
move the frequency 0 to the center of the vector or matrix.
If v is a vector of E elements corresponding to E time samples spaced of Dt each,
then fftshift (fft (v)) corresponds to frequencies
f = linspace (-E/(4*Dt), (E/2-1)/(2*Dt), E)
If v is a matrix, the same holds for rows and columns.
Function Filefractdiff (x, d)
Compute the fractional differences (1 − L)ˆdx where L denotes the lag-operator and
d is greater than -1.
Function Filehamming (m)
Return the filter coefficients of a Hamming window of length m.
For a definition of the Hamming window, see e.g. A. V. Oppenheim & R. W. Schafer,
"Discrete-Time Signal Processing".
Function Filehanning (m)
Return the filter coefficients of a Hanning window of length m.
For a definition of this window type, see e.g. A. V. Oppenheim & R. W. Schafer,
"Discrete-Time Signal Processing".
Function Filehurst (x)
Estimate the Hurst parameter of sample x via the rescaled range statistic. If x is a
matrix, the parameter is estimated for every single column.
Function Fileperiodogram (x)
For a data matrix x from a sample of size n, return the periodogram.
264 GNU Octave
Function Filerectangle lw (n, b)
Rectangular lag window. Subfunction used for spectral density estimation.
Function Filerectangle sw (n, b)
Rectangular spectral window. Subfunction used for spectral density estimation.
Function Filesinetone (freq, rate, sec, ampl)
Return a sinetone of frequency freq with length of sec seconds at sampling rate rate
and with amplitude ampl. The arguments freq and ampl may be vectors of common
size.
Defaults are rate = 8000, sec = 1 and ampl = 64.
Function Filesinewave (m, n, d)
Return an m-element vector with i-th element given by sin (2 * pi * (i+d-1) / n).
The default value for d is 0.
Function Filespectral adf (c, win, b)
Return the spectral density estimator given a vector of autocovariances c, window
name win, and bandwidth, b.
The window name, e.g., "triangle" or "rectangle" is used to search for a function
called win_sw.
If win is omitted, the triangle window is used. If b is omitted, 1 / sqrt (length
(x)) is used.
Function Filespectral xdf (x, win, b)
Return the spectral density estimator given a data vector x, window name win, and
bandwidth, b.
The window name, e.g., "triangle" or "rectangle" is used to search for a function
called win_sw.
If win is omitted, the triangle window is used. If b is omitted, 1 / sqrt (length
(x)) is used.
Function Filespencer (x)
Return Spencer’s 15 point moving average of every single column of x.
Function File[y, c] = stft (x, win size, inc, num coef, w type)
Compute the short-term Fourier transform of the vector x with num coef coefficients
by applying a window of win size data points and an increment of inc points.
Before computing the Fourier transform, one of the following windows is applied:
hanning w type = 1
hamming w type = 2
Chapter 29: Signal Processing 265
rectangle w type = 3
The window names can be passed as strings or by the w type number.
If not all arguments are specified, the following defaults are used: win size = 80, inc
= 24, num coef = 64, and w type = 1.
y = stft (x, ...) returns the absolute values of the Fourier coefficients according to
the num coef positive frequencies.
[y, c] = stft (x, ...) returns the entire STFT-matrix y and a 3-element vector
c containing the window size, increment, and window type, which is needed by the
synthesis function.
Function Filesynthesis (y, c)
Compute a signal from its short-time Fourier transform y and a 3-element vector c
specifying window size, increment, and window type.
The values y and c can be derived by
[y, c] = stft (x , ...)
Function Filetriangle lw (n, b)
Triangular lag window. Subfunction used for spectral density estimation.
Function Filetriangle sw (n, b)
Triangular spectral window. Subfunction used for spectral density estimation.
Function File[a, v] = yulewalker (c)
Fit an AR (p)-model with Yule-Walker estimates given a vector c of autocovariances
[gamma_0, ..., gamma_p].
Returns the AR coefficients, a, and the variance of white noise, v.
266 GNU Octave
Chapter 30: Image Processing 267
30 Image Processing
Octave can display images with the X Window System using the xloadimage program.
You do not need to be running X in order to manipulate images, however, so some of these
functions may be useful even if you are not able to view the results.
Loading images only works with Octave’s image format (a file with a matrix containing
the image data, and a matrix containing the colormap). Contributions of robust, wellwritten
functions to read other image formats are welcome. If you can provide them, or
would like to improve Octave’s image processing capabilities in other ways, please contact
bug-octave@bevo.che.wisc.edu.
Function Filecolormap (map)
Function Filecolormap ("default")
Set the current colormap.
colormap (map) sets the current colormap to map. The color map should be an
n row by 3 column matrix. The columns contain red, green, and blue intensities
respectively. All entries should be between 0 and 1 inclusive. The new colormap is
returned.
colormap ("default") restores the default colormap (a gray scale colormap with 64
entries). The default colormap is returned.
With no arguments, colormap returns the current color map.
Function Filegray (n)
Return a gray colormap with n entries corresponding to values from 0 to n-1. The
argument n should be a scalar. If it is omitted, 64 is assumed.
Function File[img, map] = gray2ind ()
Convert a gray scale intensity image to an Octave indexed image.
Function Fileimage (x, zoom)
Function Fileimage (x, y, A, zoom)
Display a matrix as a color image. The elements of x are indices into the current
colormap and should have values between 1 and the length of the colormap. If zoom
is omitted, the image will be scaled to fit within 600x350 (to a max of 4).
The axis values corresponding to the matrix elements are specified in x and y. At
present they are ignored.
Function Fileimagesc (A, zoom)
Function Fileimagesc (x, y, A, zoom)
Display a scaled version of the matrix A as a color image. The matrix is scaled so
that its entries are indices into the current colormap. The scaled matrix is returned.
If zoom is omitted, a comfortable size is chosen.
The axis values corresponding to the matrix elements are specified in x and y. At
present they are ignored.
268 GNU Octave
Function Fileimshow (x, map)
Function Fileimshow (x, n)
Function Fileimshow (i, n)
Function Fileimshow (r, g, b)
Display images.
imshow (x) displays an indexed image using the current colormap.
imshow (x, map) displays an indexed image using the specified colormap.
imshow (i, n) displays a gray scale intensity image.
imshow (r, g, b) displays an RGB image.
Function Fileind2gray (x, map)
Convert an Octave indexed image to a gray scale intensity image. If map is omitted,
the current colormap is used to determine the intensities.
Function File[r, g, b] = ind2rgb (x, map)
Convert an indexed image to red, green, and blue color components. If map is omitted,
the current colormap is used for the conversion.
Function File[x, map] = loadimage (file)
Load an image file and it’s associated color map from the specified file. The image
must be stored in Octave’s image format.
Function Filergb2ntsc (rgb)
Image format conversion.
Function Filentsc2rgb (yiq)
Image format conversion.
Function Fileocean (n)
Create color colormap. The argument n should be a scalar. If it is omitted, 64 is
assumed.
Function File[x, map] = rgb2ind (r, g, b)
Convert and RGB image to an Octave indexed image.
Function Filesaveimage (file, x, fmt, map)
Save the matrix x to file in image format fmt. Valid values for fmt are
"img" Octave’s image format. The current colormap is also saved in the file.
"ppm" Portable pixmap format.
"ps" PostScript format. Note that images saved in PostScript format can not
be read back into Octave with loadimage.
Chapter 30: Image Processing 269
If the fourth argument is supplied, the specified colormap will also be saved along
with the image.
Note: if the colormap contains only two entries and these entries are black and white,
the bitmap ppm and PostScript formats are used. If the image is a gray scale image
(the entries within each row of the colormap are equal) the gray scale ppm and
PostScript image formats are used, otherwise the full color formats are used.
Built-in VariableIMAGEPATH
A colon separated list of directories in which to search for image files.
270 GNU Octave
Chapter 31: Audio Processing 271
31 Audio Processing
Octave provides a few functions for dealing with audio data. An audio ‘sample’ is a
single output value from an A/D converter, i.e., a small integer number (usually 8 or 16
bits), and audio data is just a series of such samples. It can be characterized by three
parameters: the sampling rate (measured in samples per second or Hz, e.g. 8000 or 44100),
the number of bits per sample (e.g. 8 or 16), and the number of channels (1 for mono, 2
for stereo, etc.).
There are many different formats for representing such data. Currently, only the two
most popular, linear encoding and mu-law encoding, are supported by Octave. There is an
excellent FAQ on audio formats by Guido van Rossum <guido@cwi.nl> which can be found at
any FAQ ftp site, in particular in the directory ‘/pub/usenet/news.answers/audio-fmts’
of the archive site rtfm.mit.edu.
Octave simply treats audio data as vectors of samples (non-mono data are not supported
yet). It is assumed that audio files using linear encoding have one of the extensions ‘lin’
or ‘raw’, and that files holding data in mu-law encoding end in ‘au’, ‘mu’, or ‘snd’.
Function Filelin2mu (x)
If the vector x represents mono audio data in 8- or 16-bit linear encoding, lin2mu
(x) is the corresponding mu-law encoding.
Function Filemu2lin (x, bps)
If the vector x represents mono audio data in mu-law encoding, mu2lin converts it
to linear encoding. The optional argument bps specifies whether the input data uses
8 bit per sample (default) or 16 bit.
Function Fileloadaudio (name, ext, bps)
Loads audio data from the file ‘name.ext’ into the vector x.
The extension ext determines how the data in the audio file is interpreted; the extensions
‘lin’ (default) and ‘raw’ correspond to linear, the extensions ‘au’, ‘mu’, or ‘snd’
to mu-law encoding.
The argument bps can be either 8 (default) or 16, and specifies the number of bits
per sample used in the audio file.
Function Filesaveaudio (name, x, ext, bps)
Saves a vector x of audio data to the file ‘name.ext’. The optional parameters ext
and bps determine the encoding and the number of bits per sample used in the audio
file (see loadaudio); defaults are ‘lin’ and 8, respectively.
The following functions for audio I/O require special A/D hardware and operating system
support. It is assumed that audio data in linear encoding can be played and recorded by
reading from and writing to ‘/dev/dsp’, and that similarly ‘/dev/audio’ is used for mu-law
encoding. These file names are system-dependent. Improvements so that these functions
will work without modification on a wide variety of hardware are welcome.
272 GNU Octave
Function Fileplayaudio (name, ext)
Function Fileplayaudio (x)
Plays the audio file ‘name.ext’ or the audio data stored in the vector x.
Function Filerecord (sec, sampling rate)
Records sec seconds of audio input into the vector x. The default value for sampling
rate is 8000 samples per second, or 8kHz. The program waits until the user
types RET and then immediately starts to record.
Function Filesetaudio ([w type [, value]])
executes the shell command ‘mixer [w type [, value]]’
Chapter 32: Quaternions 273
32 Quaternions
Quaternions are hypercomplex numbers used to represent spatial rotations in three dimensions.
This set of routines provides a useful basis for working with quaternions in
Octave. A tutorial is in the Octave source, scripts/quaternion/quaternion.ps.
These functions were written by A. S. Hodel, Associate Professor, Auburn University.
Function File[a, b, c, d] = quaternion (w)
Function File[vv, theta] = quaternion (w)
Function Filew = quaternion (a, b, c, d)
Function Filew = quaternion (vv, theta)
Construct or extract a quaternion
w = a*i + b*j + c*k + d
from given data.
Function Fileqconj (q)
Conjugate of a quaternion.
q = [w, x, y, z] = w*i + x*j + y*k + z
qconj (q) = -w*i -x*j -y*k + z
Function Fileqderiv (omega)
Derivative of a quaternion.
Let Q be a quaternion to transform a vector from a fixed frame to a rotating frame.
If the rotating frame is rotating about the [x, y, z] axes at angular rates [wx, wy, wz],
then the derivative of Q is given by
Q’ = qderivmat (omega) * Q
If the passive convention is used (rotate the frame, not the vector), then
Q’ = -qderivmat (omega) * Q
Function Fileqderivmat (omega)
Derivative of a quaternion.
Let Q be a quaternion to transform a vector from a fixed frame to a rotating frame.
If the rotating frame is rotating about the [x, y, z] axes at angular rates [wx, wy, wz],
then the derivative of Q is given by
Q’ = qderivmat (omega) * Q
If the passive convention is used (rotate the frame, not the vector), then
Q’ = -qderivmat (omega) * Q.
Function Fileqinv (q)
Return the inverse of a quaternion.
q = [w, x, y, z] = w*i + x*j + y*k + z
qmult (q, qinv (q)) = 1 = [0 0 0 1]
274 GNU Octave
Function Fileqmult (a, b)
Multiply two quaternions.
[w, x, y, z] = w*i + x*j + y*k + z
identities:
i^2 = j^2 = k^2 = -1
ij = k jk = i
ki = j kj = -i
ji = -k ik = -j
Function Fileqtrans (v, q)
Transform the unit quaternion v by the unit quaternion q. Returns v = q*v/q.
Function Fileqtransv (v, q)
Transform the 3-D vector v by the unit quaternion q. Return a column vector.
vi = (2*real(q)^2 - 1)*vb + 2*imag(q)*(imag(q)’*vb)
+ 2*real(q)*cross(imag(q),vb)
Where imag(q) is a column vector of length 3.
Function Fileqtransvmat (qib)
Construct a 3x3 transformation matrix from quaternion qib that is equivalent to
rotation of th radians about axis vv, where [vv, th] = quaternion (qib).
Function Fileqcoordinate plot (qf, qb, qv)
Plot in the current figure a set of coordinate axes as viewed from the orientation
specified by quaternion qv. Inertial axes are also plotted:
qf Quaternion from reference (x,y,z) to inertial.
qb Quaternion from reference to body.
qv Quaternion from reference to view angle.
Chapter 33: System Utilities 275
33 System Utilities
This chapter describes the functions that are available to allow you to get information
about what is happening outside of Octave, while it is still running, and use this information
in your program. For example, you can get information about environment variables, the
current time, and even start other programs from the Octave prompt.
33.1 Timing Utilities
Octave’s core set of functions for manipulating time values are patterned after the corresponding
functions from the standard C library. Several of these functions use a data
structure for time that includes the following elements:
usec Microseconds after the second (0-999999).
sec Seconds after the minute (0-61). This number can be 61 to account for leap
seconds.
min Minutes after the hour (0-59).
hour Hours since midnight (0-23).
mday Day of the month (1-31).
mon Months since January (0-11).
year Years since 1900.
wday Days since Sunday (0-6).
yday Days since January 1 (0-365).
isdst Daylight Savings Time flag.
zone Time zone.
In the descriptions of the following functions, this structure is referred to as a tm struct.
Loadable Functiontime ()
Return the current time as the number of seconds since the epoch. The epoch is
referenced to 00:00:00 CUT (Coordinated Universal Time) 1 Jan 1970. For example,
on Monday February 17, 1997 at 07:15:06 CUT, the value returned by time was
856163706.
Function Filectime (t)
Convert a value returned from time (or any other nonnegative integer), to the local
time and return a string of the same form as asctime. The function ctime (time)
is equivalent to asctime (localtime (time)). For example,
ctime (time ())
⇒ "Mon Feb 17 01:15:06 1997"
276 GNU Octave
Loadable Functiongmtime (t)
Given a value returned from time (or any nonnegative integer), return a time structure
corresponding to CUT. For example,
gmtime (time ())
⇒ {
usec = 0
year = 97
mon = 1
mday = 17
sec = 6
zone = CST
min = 15
wday = 1
hour = 7
isdst = 0
yday = 47
}
Loadable Functionlocaltime (t)
Given a value returned from time (or any nonnegative integer), return a time structure
corresponding to the local time zone.
localtime (time ())
⇒ {
usec = 0
year = 97
mon = 1
mday = 17
sec = 6
zone = CST
min = 15
wday = 1
hour = 1
isdst = 0
yday = 47
}
Loadable Functionmktime (tm struct)
Convert a time structure corresponding to the local time to the number of seconds
since the epoch. For example,
mktime (localtime (time ())
⇒ 856163706
Function Fileasctime (tm struct)
Convert a time structure to a string using the following five-field format: Thu Mar
28 08:40:14 1996. For example,
Chapter 33: System Utilities 277
asctime (localtime (time ())
⇒ "Mon Feb 17 01:15:06 1997\n"
This is equivalent to ctime (time ()).
Loadable Functionstrftime (tm struct)
Format a time structure in a flexible way using ‘%’ substitutions similar to those in
printf. Except where noted, substituted fields have a fixed size; numeric fields are
padded if necessary. Padding is with zeros by default; for fields that display a single
number, padding can be changed or inhibited by following the ‘%’ with one of the
modifiers described below. Unknown field specifiers are copied as normal characters.
All other characters are copied to the output without change. For example,
strftime ("%r (%Z) %A %e %B %Y", localtime (time ())
⇒ "01:15:06 AM (CST) Monday 17 February 1997"
Octave’s strftime function supports a superset of the ANSI C field specifiers.
Literal character fields:
% % character.
n Newline character.
t Tab character.
Numeric modifiers (a nonstandard extension):
- (dash) Do not pad the field.
_ (underscore)
Pad the field with spaces.
Time fields:
%H Hour (00-23).
%I Hour (01-12).
%k Hour (0-23).
%l Hour (1-12).
%M Minute (00-59).
%p Locale’s AM or PM.
%r Time, 12-hour (hh:mm:ss [AP]M).
%R Time, 24-hour (hh:mm).
%s Time in seconds since 00:00:00, Jan 1, 1970 (a nonstandard extension).
%S Second (00-61).
%T Time, 24-hour (hh:mm:ss).
%X Locale’s time representation (%H:%M:%S).
%Z Time zone (EDT), or nothing if no time zone is determinable.
278 GNU Octave
Date fields:
%a Locale’s abbreviated weekday name (Sun-Sat).
%A Locale’s full weekday name, variable length (Sunday-Saturday).
%b Locale’s abbreviated month name (Jan-Dec).
%B Locale’s full month name, variable length (January-December).
%c Locale’s date and time (Sat Nov 04 12:02:33 EST 1989).
%C Century (00-99).
%d Day of month (01-31).
%e Day of month ( 1-31).
%D Date (mm/dd/yy).
%h Same as %b.
%j Day of year (001-366).
%m Month (01-12).
%U Week number of year with Sunday as first day of week (00-53).
%w Day of week (0-6).
%W Week number of year with Monday as first day of week (00-53).
%x Locale’s date representation (mm/dd/yy).
%y Last two digits of year (00-99).
%Y Year (1970-).
Most of the remaining functions described in this section are not patterned after the
standard C library. Some are available for compatiblity with Matlab and others are
provided because they are useful.
Function Fileclock ()
Return a vector containing the current year, month (1-12), day (1-31), hour (0-23),
minute (0-59) and second (0-61). For example,
clock ()
⇒ [ 1993, 8, 20, 4, 56, 1 ]
The function clock is more accurate on systems that have the gettimeofday function.
Function Filedate ()
Return the date as a character string in the form DD-MMM-YY. For example,
date ()
⇒ "20-Aug-93"
Chapter 33: System Utilities 279
Function Fileetime (t1, t2)
Return the difference (in seconds) between two time values returned from clock. For
example:
t0 = clock ();
many computations later...
elapsed_time = etime (clock (), t0);
will set the variable elapsed_time to the number of seconds since the variable t0
was set.
Function File[total, user, system] = cputime ();
Return the CPU time used by your Octave session. The first output is the total time
spent executing your process and is equal to the sum of second and third outputs,
which are the number of CPU seconds spent executing in user mode and the number
of CPU seconds spent executing in system mode, respectively. If your system does
not have a way to report CPU time usage, cputime returns 0 for each of its output
values. Note that because Octave used some CPU time to start, it is reasonable to
check to see if cputime works by checking to see if the total CPU time used is nonzero.
Function Fileis leap year (year)
Return 1 if the given year is a leap year and 0 otherwise. If no arguments are provided,
is_leap_year will use the current year. For example,
is_leap_year (2000)
⇒ 1
Function Filetic ()
Function Filetoc ()
These functions set and check a wall-clock timer. For example,
tic ();
many computations later...
elapsed_time = toc ();
will set the variable elapsed_time to the number of seconds since the most recent
call to the function tic.
If you are more interested in the CPU time that your process used, you should use
the cputime function instead. The tic and toc functions report the actual wall clock
time that elapsed between the calls. This may include time spent processing other
jobs or doing nothing at all. For example,
tic (); sleep (5); toc ()
⇒ 5
t = cputime (); sleep (5); cputime () - t
⇒ 0
(This example also illustrates that the CPU timer may have a fairly coarse resolution.)
280 GNU Octave
Built-in Functionpause (seconds)
Suspend the execution of the program. If invoked without any arguments, Octave
waits until you type a character. With a numeric argument, it pauses for the given
number of seconds. For example, the following statement prints a message and then
waits 5 seconds before clearing the screen.
fprintf (stderr, "wait please...
");
pause (5);
clc;
Built-in Functionsleep (seconds)
Suspend the execution of the program for the given number of seconds.
Built-in Functionusleep (microseconds)
Suspend the execution of the program for the given number of microseconds. On
systems where it is not possible to sleep for periods of time less than one second,
usleep will pause the execution for round (microseconds / 1e6) seconds.
33.2 Filesystem Utilities
Octave includes the following functions for renaming and deleting files, creating, deleting,
and reading directories, and for getting information about the status of files.
Built-in Function[err, msg] = rename (old, new)
Change the name of file old to new.
If successful, err is 0 and msg is an empty string. Otherwise, err is nonzero and msg
contains a system-dependent error message.
Built-in Function[err, msg] = unlink (file)
Delete the file named file.
If successful, err is 0 and msg is an empty string. Otherwise, err is nonzero and msg
contains a system-dependent error message.
Built-in Function[files, err, msg] = readdir (dir)
Return names of the files in the directory dir as an array of strings. If an error occurs,
return an empty matrix in files.
If successful, err is 0 and msg is an empty string. Otherwise, err is nonzero and msg
contains a system-dependent error message.
Built-in Function[err, msg] = mkdir (dir)\nCreate a directory named dir.
If successful, err is 0 and msg is an empty string. Otherwise, err is nonzero and msg
contains a system-dependent error message.
Chapter 33: System Utilities 281
Built-in Function[err, msg] = rmdir (dir)
Remove the directory named dir.
If successful, err is 0 and msg is an empty string. Otherwise, err is nonzero and msg
contains a system-dependent error message.
Built-in Function[err, msg] = mkfifo (name)
Create a fifo special file named name with file mode mode \n If successful, err is 0
and msg is an empty string. Otherwise, err is nonzero and msg contains a systemdependent
error message.
Built-in Functionumask (mask)
Set the permission mask for file creation. The parameter mask is an integer, interpreted
as an octal number. If successful, returns the previous value of the mask (as an
integer to be interpreted as an octal number); otherwise an error message is printed.
Built-in Function[info, err, msg] = stat (file)
Built-in Function[info, err, msg] = lstat (file)
Return a structure s containing the following information about file.
dev ID of device containing a directory entry for this file.
ino File number of the file.
modestr File mode, as a string of ten letters or dashes as would be returned by ls
-l.
nlink Number of links.
uid User ID of file’s owner.
gid Group ID of file’s group.
rdev ID of device for block or character special files.
size Size in bytes.
atime Time of last access in the same form as time values returned from time.
See Section 33.1 [Timing Utilities], page 275.
mtime Time of last modification in the same form as time values returned from
time. See Section 33.1 [Timing Utilities], page 275.
ctime Time of last file status change in the same form as time values returned
from time. See Section 33.1 [Timing Utilities], page 275.
blksize Size of blocks in the file.
blocks Number of blocks allocated for file.
If the call is successful err is 0 and msg is an empty string. If the file does not exist,
or some other error occurs, s is an empty matrix, err is −1, and msg contains the
corresponding system error message.
282 GNU Octave
If file is a symbolic link, stat will return information about the actual file the is
referenced by the link. Use lstat if you want information about the symbolic link
itself.
For example,
[s, err, msg] = stat ("/vmlinuz")
⇒ s =
{
atime = 855399756
rdev = 0
ctime = 847219094
uid = 0
size = 389218
blksize = 4096
mtime = 847219094
gid = 6
nlink = 1
blocks = 768
modestr = -rw-r--r--
ino = 9316
dev = 2049
}
⇒ err = 0
⇒ msg =
Built-in Functionglob (pattern)
Given an array of strings in pattern, return the list of file names that match any of
them, or an empty string if no patterns match. Tilde expansion is performed on each
of the patterns before looking for matching file names. For example,
glob ("/vm*")
⇒ "/vmlinuz"
Note that multiple values are returned in a string matrix with the fill character set
to ASCII NUL.
Built-in Functionfnmatch (pattern, string)
Return 1 or zero for each element of string that matches any of the elements of the
string array pattern, using the rules of filename pattern matching. For example,
fnmatch ("a*b", ["ab"; "axyzb"; "xyzab"])
⇒ [ 1; 1; 0 ]
Built-in Functionfile in path (path, file)
Return the absolute name name of file if it can be found in path. The value of path
should be a colon-separated list of directories in the format described for the built-in
variable LOADPATH.
If the file cannot be found in the path, an empty matrix is returned. For example,
file_in_path (LOADPATH, "nargchk.m")
⇒ "/usr/local/share/octave/2.0/m/general/nargchk.m"
Chapter 33: System Utilities 283
Built-in Functiontilde expand (string)
Performs tilde expansion on string. If string begins with a tilde character, (‘~’), all
of the characters preceding the first slash (or all characters, if there is no slash) are
treated as a possible user name, and the tilde and the following characters up to the
slash are replaced by the home directory of the named user. If the tilde is followed
immediately by a slash, the tilde is replaced by the home directory of the user running
Octave. For example,
tilde_expand ("~joeuser/bin")
⇒ "/home/joeuser/bin"
tilde_expand ("~/bin")
⇒ "/home/jwe/bin"
33.3 Controlling Subprocesses
Octave includes some high-level commands like system and popen for starting subprocesses.
If you want to run another program to perform some task and then look at its
output, you will probably want to use these functions.
Octave also provides several very low-level Unix-like functions which can also be used
for starting subprocesses, but you should probably only use them if you can’t find any way
to do what you need with the higher-level functions.
Built-in Functionsystem (string, return output, type)
Execute a shell command specified by string. The second argument is optional. If
type is "async", the process is started in the background and the process id of the
child process is returned immediately. Otherwise, the process is started, and Octave
waits until it exits. If type argument is omitted, a value of "sync" is assumed.
If two input arguments are given (the actual value of return output is irrelevant) and
the subprocess is started synchronously, or if system is called with one input argument
and one or more output arguments, the output from the command is returned. Otherwise,
if the subprocess is executed synchronously, it’s output is sent to the standard
output. To send the output of a command executed with system through the pager,
use a command like
disp (system (cmd, 1));
or
printf ("%s
", system (cmd, 1));
The system function can return two values. The first is any output from the command
that was written to the standard output stream, and the second is the output status
of the command. For example,
[output, status] = system ("echo foo; exit 2");
will set the variable output to the string ‘foo’, and the variable status to the integer
‘2’.
284 GNU Octave
Built-in Functionfid = popen (command, mode)
Start a process and create a pipe. The name of the command to run is given by
command. The file identifier corresponding to the input or output stream of the
process is returned in fid. The argument mode may be
"r" The pipe will be connected to the standard output of the process, and
open for reading.
"w" The pipe will be connected to the standard input of the process, and open
for writing.
For example,
fid = popen ("ls -ltr / | tail -3", "r");
while (isstr (s = fgets (fid)))
fputs (stdout, s);
endwhile
drwxr-xr-x 33 root root 3072 Feb 15 13:28 etc
drwxr-xr-x 3 root root 1024 Feb 15 13:28 lib
drwxrwxrwt 15 root root 2048 Feb 17 14:53 tmp
Built-in Functionpclose (fid)
Close a file identifier that was opened by popen. You may also use fclose for the
same purpose.
Function File[in, out, pid] = popen2 (command, args)
Start a subprocess with two-way communication. The name of the process is given
by command, and args is an array of strings containing options for the command.
The file identifiers for the input and output streams of the subprocess are returned
in in and out. If execution of the command is successful, pid contains the process ID
of the subprocess. Otherwise, pid is −1.
For example,
[in, out, pid] = popen2 ("sort", "-nr");
fputs (in, "these\nare\nsome\nstrings\n");
fclose (in);
while (isstr (s = fgets (out)))
fputs (stdout, s);
endwhile
fclose (out);
are
some
strings
these
Built-in VariableEXEC PATH
The variable EXEC_PATH is a colon separated list of directories to search when executing
subprograms. Its initial value is taken from the environment variable OCTAVE_
EXEC_PATH (if it exists) or PATH, but that value can be overridden by the command
Chapter 33: System Utilities 285
line argument --exec-path PATH, or by setting the value of EXEC_PATH in a startup
script. If the value of EXEC_PATH begins (ends) with a colon, the directories
octave-home/libexec/octave/site/exec/arch
octave-home/libexec/octave/version/exec/arch
are prepended (appended) to EXEC_PATH, where octave-home is the top-level directory
where all of Octave is installed (the default value is ‘/usr/local’). If you don’t specify
a value for EXEC_PATH explicitly, these special directories are prepended to your shell
path.
In most cases, the following functions simply decode their arguments and make the
corresponding Unix system calls. For a complete example of how they can be used, look at
the definition of the function popen2.
Built-in Function[pid, msg] = fork ()
Create a copy of the current process.
Fork can return one of the following values:
> 0 You are in the parent process. The value returned from fork is the
process id of the child process. You should probably arrange to wait for
any child processes to exit.
0 You are in the child process. You can call exec to start another process.
If that fails, you should probably call exit.
< 0 The call to fork failed for some reason. You must take evasive action. A
system dependent error message will be waiting in msg.
Built-in Function[err, msg] = exec (file, args)
Replace current process with a new process. Calling exec without first calling fork
will terminate your current Octave process and replace it with the program named
by file. For example,
exec ("ls" "-l")
will run ls and return you to your shell prompt.
If successful, exec does not return. If exec does return, err will be nonzero, and msg
will contain a system-dependent error message.
Built-in Function[file ids, err, msg] = pipe ()
Create a pipe and return the vector file ids, which corresponding to the reading and
writing ends of the pipe.
If successful, err is 0 and msg is an empty string. Otherwise, err is nonzero and msg
contains a system-dependent error message.
Built-in Function[fid, msg] = dup2 (old, new)
Duplicate a file descriptor.
If successful, fid is greater than zero and contains the new file ID. Otherwise, fid is
negative and msg contains a system-dependent error message.
286 GNU Octave
Built-in Function[pid, msg] = waitpid (pid, options)
Wait for process pid to terminate. The pid argument can be:
−1 Wait for any child process.
0 Wait for any child process whose process group ID is equal to that of the
Octave interpreter process.
> 0 Wait for termination of the child process with ID pid.
The options argument can be:
0 Wait until signal is received or a child process exits (this is the default if
the options argument is missing).
1 Do not hang if status is not immediately available.
2 Report the status of any child processes that are stopped, and whose
status has not yet been reported since they stopped.
3 Implies both 1 and 2.
If the returned value of pid is greater than 0, it is the process ID of the child process
that exited. If an error occurs, pid will be less than zero and msg will contain a
system-dependent error message.
Built-in Function[err, msg] = fcntl (fid, request, arg)
Change the properties of the open file fid. The following values may be passed as
request:
F_DUPFD Return a duplicate file descriptor.
F_GETFD Return the file descriptor flags for fid.
F_SETFD Set the file descriptor flags for fid.
F_GETFL Return the file status flags for fid. The following codes may be returned
(some of the flags may be undefined on some systems).
O_RDONLY Open for reading only.
O_WRONLY Open for writing only.
O_RDWR Open for reading and writing.
O_APPEND Append on each write.
O_NONBLOCK
Nonblocking mode.
O_SYNC Wait for writes to complete.
O_ASYNC Asynchronous I/O.
F_SETFL Set the file status flags for fid to the value specified by arg. The only
flags that can be changed are O_APPEND and O_NONBLOCK.
If successful, err is 0 and msg is an empty string. Otherwise, err is nonzero and msg
contains a system-dependent error message.
Chapter 33: System Utilities 287
33.4 Process, Group, and User IDs
Built-in Functionpgid = getpgrp ()
Return the process group id of the current process.
Built-in Functionpid = getpid ()
Return the process id of the current process.
Built-in Functionpid = getppid ()
Return the process id of the parent process.
Built-in Functioneuid = geteuid ()
Return the effective user id of the current process.
Built-in Functionuid = getuid ()
Return the real user id of the current process.
Built-in Functionegid = getegid ()
Return the effective group id of the current process.
Built-in Functiongid = getgid ()
Return the real group id of the current process.
33.5 Environment Variables
Built-in Functiongetenv (var)
Return the value of the environment variable var. For example,
getenv ("PATH")
returns a string containing the value of your path.
Built-in Functionputenv (var, value)
Set the value of the environment variable var to value.
288 GNU Octave
33.6 Current Working Directory
Commandcd dir
Commandchdir dir
Change the current working directory to dir. If dir is omitted, the current directory
is changed to the users home directory. For example,
cd ~/octave
Changes the current working directory to ‘~/octave’. If the directory does not exist,
an error message is printed and the working directory is not changed.
Commandls options
Commanddir options
List directory contents. For example,
ls -l
total 12
-rw-r--r-- 1 jwe users 4488 Aug 19 04:02 foo.m
-rw-r--r-- 1 jwe users 1315 Aug 17 23:14 bar.m
The dir and ls commands are implemented by calling your system’s directory listing
command, so the available options may vary from system to system.
Built-in Functionpwd ()
Return the current working directory.
33.7 Password Database Functions
Octave’s password database functions return information in a structure with the following
fields.
name The user name.
passwd The encrypted password, if available.
uid The numeric user id.
gid The numeric group id.
gecos The GECOS field.
dir The home directory.
shell The initial shell.
In the descriptions of the following functions, this data structure is referred to as a
pw struct.
Loadable Functionpw struct = getpwent ()
Return a structure containing an entry from the password database, opening it if
necessary. Once the end of the data has been reached, getpwent returns 0.
Chapter 33: System Utilities 289
Loadable Functionpw struct = getpwuid (uid).
Return a structure containing the first entry from the password database with the
user ID uid. If the user ID does not exist in the database, getpwuid returns 0.
Loadable Functionpw struct = getpwnam (name)
Return a structure containing the first entry from the password database with the
user name name. If the user name does not exist in the database, getpwname returns
0.
Loadable Functionsetpwent ()
Return the internal pointer to the beginning of the password database.
Loadable Functionendpwent ()
Close the password database.
33.8 Group Database Functions
Octave’s group database functions return information in a structure with the following
fields.
name The user name.
passwd The encrypted password, if available.
gid The numeric group id.
mem The members of the group.
In the descriptions of the following functions, this data structure is referred to as a
grp struct.
Loadable Functiongrp struct = getgrent ()
Return an entry from the group database, opening it if necessary. Once the end of
the data has been reached, getgrent returns 0.
Loadable Functiongrp struct = getgrgid (gid).
Return the first entry from the group database with the group ID gid. If the group
ID does not exist in the database, getgrgid returns 0.
Loadable Functiongrp struct = getgrnam (name)
Return the first entry from the group database with the group name name. If the
group name does not exist in the database, getgrname returns 0.
Loadable Functionsetgrent ()
Return the internal pointer to the beginning of the group database.
Loadable Functionendgrent ()
Close the group database.
290 GNU Octave
33.9 System Information
Built-in Functioncomputer ()
Print or return a string of the form cpu-vendor-os that identifies the kind of computer
Octave is running on. If invoked with an output argument, the value is returned
instead of printed. For example,
computer ()
i586-pc-linux-gnu
x = computer ()
⇒ x = "i586-pc-linux-gnu"
Built-in Functionisieee ()
Return 1 if your computer claims to conform to the IEEE standard for floating point
calculations.
Built-in VariableOCTAVE VERSION
The version number of Octave, as a string.
Built-in Functionoctave config info (option)
Return a structure containing configuration and installation information for Octave.
if option is a string, return the configuration information for the specified option.
Loadable Functiongetrusage ()
Return a structure containing a number of statistics about the current Octave process.
Not all fields are available on all systems. If it is not possible to get CPU time
statistics, the CPU time slots are set to zero. Other missing data are replaced by
NaN. Here is a list of all the possible fields that can be present in the structure
returned by getrusage:
idrss Unshared data size.
inblock Number of block input operations.
isrss Unshared stack size.
ixrss Shared memory size.
majflt Number of major page faults.
maxrss Maximum data size.
minflt Number of minor page faults.
msgrcv Number of messages received.
msgsnd Number of messages sent.
nivcsw Number of involuntary context switches.
Chapter 33: System Utilities 291
nsignals Number of signals received.
nswap Number of swaps.
nvcsw Number of voluntary context switches.
oublock Number of block output operations.
stime A structure containing the system CPU time used. The structure has the
elements sec (seconds) usec (microseconds).
utime A structure containing the user CPU time used. The structure has the
elements sec (seconds) usec (microseconds).
292 GNU Octave
Appendix A: Tips and Standards 293
Appendix A Tips and Standards
This chapter describes no additional features of Octave. Instead it gives advice on
making effective use of the features described in the previous chapters.
A.1 Writing Clean Octave Programs
Here are some tips for avoiding common errors in writing Octave code intended for
widespread use:
• Since all global variables share the same name space, and all functions share another
name space, you should choose a short word to distinguish your program from other
Octave programs. Then take care to begin the names of all global variables, constants,
and functions with the chosen prefix. This helps avoid name conflicts.
If you write a function that you think ought to be added to Octave under a certain name,
such as fiddle_matrix, don’t call it by that name in your program. Call it mylib_
fiddle_matrix in your program, and send mail to bug-octave@bevo.che.wisc.edu
suggesting that it be added to Octave. If and when it is, the name can be changed
easily enough.
If one prefix is insufficient, your package may use two or three alternative common
prefixes, so long as they make sense.
Separate the prefix from the rest of the symbol name with an underscore ‘_’. This will
be consistent with Octave itself and with most Octave programs.
• When you encounter an error condition, call the function error (or usage). The error
and usage functions do not return. See Section 2.5 [Errors], page 25.
• Please put a copyright notice on the file if you give copies to anyone. Use the same
lines that appear at the top of the function files distributed with Octave. If you have
not signed papers to assign the copyright to anyone else, then place your name in the
copyright notice.
A.2 Tips for Making Code Run Faster.
Here are some ways of improving the execution speed of Octave programs.
• Avoid looping wherever possible.
• Use iteration rather than recursion whenever possible. Function calls are slow in Oc-
tave.
• Avoid resizing matrices unnecessarily. When building a single result matrix from a
series of calculations, set the size of the result matrix first, then insert values into it.
Write
result = zeros (big_n, big_m)
for i = over:and_over
r1 = ...
r2 = ...
result (r1, r2) = new_value ();
endfor
instead of
294 GNU Octave
result = [];
for i = ever:and_ever
result = [ result, new_value() ];
endfor
• Avoid calling eval or feval whenever possible, because they require Octave to parse
input or look up the name of a function in the symbol table.
If you are using eval as an exception handling mechanism and not because you need
to execute some arbitrary text, use the try statement instead. See Section 12.9 [The
try Statement], page 88.
• If you are calling lots of functions but none of them will need to change during your
run, set the variable ignore_function_time_stamp to "all" so that Octave doesn’t
waste a lot of time checking to see if you have updated your function files.
A.3 Tips for Documentation Strings
Here are some tips for the writing of documentation strings.
• Every command, function, or variable intended for users to know about should have a
documentation string.
• An internal variable or subroutine of an Octave program might as well have a documentation
string.
• The first line of the documentation string should consist of one or two complete sentences
that stand on their own as a summary.
The documentation string can have additional lines that expand on the details of how
to use the function or variable. The additional lines should also be made up of complete
sentences.
• For consistency, phrase the verb in the first sentence of a documentation string as
an infinitive with “to” omitted. For instance, use “Return the frob of A and B.” in
preference to “Returns the frob of A and B.” Usually it looks good to do likewise for
the rest of the first paragraph. Subsequent paragraphs usually look better if they have
proper subjects.
• Write documentation strings in the active voice, not the passive, and in the present
tense, not the future. For instance, use “Return a list containing A and B.” instead of
“A list containing A and B will be returned.”
• Avoid using the word “cause” (or its equivalents) unnecessarily. Instead of, “Cause
Octave to display text in boldface,” write just “Display text in boldface.”
• Do not start or end a documentation string with whitespace.
• Format the documentation string so that it fits in an Emacs window on an 80-column
screen. It is a good idea for most lines to be no wider than 60 characters.
However, rather than simply filling the entire documentation string, you can make it
much more readable by choosing line breaks with care. Use blank lines between topics
if the documentation string is long.
• Do not indent subsequent lines of a documentation string so that the text is lined up
in the source code with the text of the first line. This looks nice in the source code,
but looks bizarre when users view the documentation. Remember that the indentation
before the starting double-quote is not part of the string!
Appendix A: Tips and Standards 295
• The documentation string for a variable that is a yes-or-no flag should start with words
such as “Nonzero means. . .”, to make it clear that all nonzero values are equivalent
and indicate explicitly what zero and nonzero mean.
• When a function’s documentation string mentions the value of an argument of the
function, use the argument name in capital letters as if it were a name for that value.
Thus, the documentation string of the operator / refers to its second argument as
‘DIVISOR’, because the actual argument name is divisor.
Also use all caps for meta-syntactic variables, such as when you show the decomposition
of a list or vector into subunits, some of which may vary.
A.4 Tips on Writing Comments
Here are the conventions to follow when writing comments.
‘#’ Comments that start with a single sharp-sign, ‘#’, should all be aligned to the
same column on the right of the source code. Such comments usually explain
how the code on the same line does its job. In the Emacs mode for Octave, the
M-; (indent-for-comment) command automatically inserts such a ‘#’ in the
right place, or aligns such a comment if it is already present.
‘##’ Comments that start with two semicolons, ‘##’, should be aligned to the same
level of indentation as the code. Such comments usually describe the purpose
of the following lines or the state of the program at that point.
The indentation commands of the Octave mode in Emacs, such as M-; (indent-forcomment)
and TAB (octave-indent-line) automatically indent comments according to
these conventions, depending on the number of semicolons. See section “Manipulating
Comments” in The GNU Emacs Manual.
A.5 Conventional Headers for Octave Functions
Octave has conventions for using special comments in function files to give information
such as who wrote them. This section explains these conventions.
The top of the file should contain a copyright notice, followed by a block of comments
that can be used as the help text for the function. Here is an example:
## Copyright (C) 1996, 1997 John W. Eaton
##
## This file is part of Octave.
##
## Octave is free software; you can redistribute it and/or
## modify it under the terms of the GNU General Public
## License as published by the Free Software Foundation;
## either version 2, or (at your option) any later version.
##
## Octave is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied
## warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
## PURPOSE. See the GNU General Public License for more
296 GNU Octave
## details.
##
## You should have received a copy of the GNU General Public
## License along with Octave; see the file COPYING. If not,
## write to the Free Software Foundation, 59 Temple Place ##
Suite 330, Boston, MA 02111-1307, USA.
## usage: [IN, OUT, PID] = popen2 (COMMAND, ARGS)
##
## Start a subprocess with two-way communication. COMMAND
## specifies the name of the command to start. ARGS is an
## array of strings containing options for COMMAND. IN and
## OUT are the file ids of the input and streams for the
## subprocess, and PID is the process id of the subprocess,
## or -1 if COMMAND could not be executed.
##
## Example:
##
## [in, out, pid] = popen2 ("sort", "-nr");
## fputs (in, "these\nare\nsome\nstrings\n");
## fclose (in);
## while (isstr (s = fgets (out)))
## fputs (stdout, s);
## endwhile
## fclose (out);
Octave uses the first block of comments in a function file that do not appear to be a
copyright notice as the help text for the file. For Octave to recognize the first comment
block as a copyright notice, it must match the regular expression
^ Copyright (C).*\n\n This file is part of Octave.
or
^ Copyright (C).*\n\n This program is free softwar
(after stripping the leading comment characters). This is a fairly strict requirement, and
may be relaxed somewhat in the future.
After the copyright notice and help text come several header comment lines, each beginning
with ‘## header-name:’. For example,
## Author: jwe
## Keywords: subprocesses input-output
## Maintainer: jwe
Here is a table of the conventional possibilities for header-name:
‘Author’ This line states the name and net address of at least the principal author of the
library.
## Author: John W. Eaton <jwe@bevo.che.wisc.edu>
‘Maintainer’
This line should contain a single name/address as in the Author line, or an
address only, or the string ‘jwe’. If there is no maintainer line, the person(s)
Appendix A: Tips and Standards 297
in the Author field are presumed to be the maintainers. The example above is
mildly bogus because the maintainer line is redundant.
The idea behind the ‘Author’ and ‘Maintainer’ lines is to make possible a
function to “send mail to the maintainer” without having to mine the name
out by hand.
Be sure to surround the network address with ‘<...>’ if you include the person’s
full name as well as the network address.
‘Created’ This optional line gives the original creation date of the file. For historical
interest only.
‘Version’ If you wish to record version numbers for the individual Octave program, put
them in this line.
‘Adapted-By’
In this header line, place the name of the person who adapted the library for
installation (to make it fit the style conventions, for example).
‘Keywords’
This line lists keywords. Eventually, it will be used by an apropos command
to allow people will find your package when they’re looking for things by topic
area. To separate the keywords, you can use spaces, commas, or both.
Just about every Octave function ought to have the ‘Author’ and ‘Keywords’ header
comment lines. Use the others if they are appropriate. You can also put in header lines
with other header names—they have no standard meanings, so they can’t do any harm.
298 GNU Octave
Appendix B: Known Causes of Trouble 299
Appendix B Known Causes of Trouble
This section describes known problems that affect users of Octave. Most of these are
not Octave bugs per se—if they were, we would fix them. But the result for a user may be
like the result of a bug.
Some of these problems are due to bugs in other software, some are missing features that
are too much work to add, and some are places where people’s opinions differ as to what is
best.
B.1 Actual Bugs We Haven’t Fixed Yet
• Output that comes directly from Fortran functions is not sent through the pager and
may appear out of sequence with other output that is sent through the pager. One way
to avoid this is to force pending output to be flushed before calling a function that will
produce output from within Fortran functions. To do this, use the command
fflush (stdout)
Another possible workaround is to use the command
page_screen_output = "false"
to turn the pager off.
• If you get messages like
Input line too long
when trying to plot many lines on one graph, you have probably generated a plot
command that is too large for gnuplot’s fixed-length buffer for commands. Splitting
up the plot command doesn’t help because replot is implemented in gnuplot by simply
appending the new plotting commands to the old command line and then evaluating
it again.
You can demonstrate this ‘feature’ by running gnuplot and doing something like
plot sin (x), sin (x), sin (x), ... lots more ..., sin (x)
and then
replot sin (x), sin (x), sin (x), ... lots more ..., sin (x)
after repeating the replot command a few times, gnuplot will give you an error.
Also, it doesn’t help to use backslashes to enter a plot command over several lines,
because the limit is on the overall command line length, once the backslashed lines are
all pasted together.
Because of this, Octave tries to use as little of the command-line length as possible
by using the shortest possible abbreviations for all the plot commands and options.
Unfortunately, the length of the temporary file names is probably what is taking up
the most space on the command line.
You can buy a little bit of command line space by setting the environment variable
TMPDIR to be "." before starting Octave, or you can increase the maximum command
line length in gnuplot by changing the following limits in the file plot.h in the gnuplot
distribution and recompiling gnuplot.
300 GNU Octave
#define MAX_LINE_LEN 32768 /* originally 1024 */
#define MAX_TOKENS 8192 /* originally 400 */
Of course, this doesn’t really fix the problem, but it does make it much less likely that
you will run into trouble unless you are putting a very large number of lines on a given
plot.
A list of ideas for future enhancements is distributed with Octave. See the file ‘PROJECTS’
in the top level directory in the source distribution.
B.2 Reporting Bugs
Your bug reports play an essential role in making Octave reliable.
When you encounter a problem, the first thing to do is to see if it is already known. See
Appendix B [Trouble], page 299. If it isn’t known, then you should report the problem.
Reporting a bug may help you by bringing a solution to your problem, or it may not.
In any case, the principal function of a bug report is to help the entire community by
making the next version of Octave work better. Bug reports are your contribution to the
maintenance of Octave.
In order for a bug report to serve its purpose, you must include the information that
makes it possible to fix the bug.
If you have Octave working at all, the easiest way to prepare a complete bug report
is to use the Octave function bug_report. When you execute this function, Octave will
prompt you for a subject and then invoke the editor on a file that already contains all the
configuration information. When you exit the editor, Octave will mail the bug report for
you.
B.3 Have You Found a Bug?
If you are not sure whether you have found a bug, here are some guidelines:
• If Octave gets a fatal signal, for any input whatever, that is a bug. Reliable interpreters
never crash.
• If Octave produces incorrect results, for any input whatever, that is a bug.
• Some output may appear to be incorrect when it is in fact due to a program whose
behavior is undefined, which happened by chance to give the desired results on another
system. For example, the range operator may produce different results because of
differences in the way floating point arithmetic is handled on various systems.
• If Octave produces an error message for valid input, that is a bug.
• If Octave does not produce an error message for invalid input, that is a bug. However,
you should note that your idea of “invalid input” might be my idea of “an extension”
or “support for traditional practice”.
• If you are an experienced user of programs like Octave, your suggestions for improvement
are welcome in any case.
Appendix B: Known Causes of Trouble 301
B.4 Where to Report Bugs
If you have Octave working at all, the easiest way to prepare a complete bug report
is to use the Octave function bug_report. When you execute this function, Octave will
prompt you for a subject and then invoke the editor on a file that already contains all the
configuration information. When you exit the editor, Octave will mail the bug report for
you.
If for some reason you cannot use Octave’s bug_report function, send bug reports for
Octave to bug-octave@bevo.che.wisc.edu.
Do not send bug reports to ‘help-octave’. Most users of Octave do not want to receive
bug reports. Those that do have asked to be on the mailing list.
As a last resort, send bug reports on paper to:
Octave Bugs c/o John W. Eaton
University of Wisconsin-Madison
Department of Chemical Engineering
1415 Engineering Drive
Madison, Wisconsin 53706 USA
B.5 How to Report Bugs
Send bug reports for Octave to one of the addresses listed in Section B.4 [Bug Lists],
page 301.
The fundamental principle of reporting bugs usefully is this: report all the facts. If you
are not sure whether to state a fact or leave it out, state it!
Often people omit facts because they think they know what causes the problem and
they conclude that some details don’t matter. Thus, you might assume that the name of
the variable you use in an example does not matter. Well, probably it doesn’t, but one
cannot be sure. Perhaps the bug is a stray memory reference which happens to fetch from
the location where that name is stored in memory; perhaps, if the name were different, the
contents of that location would fool the interpreter into doing the right thing despite the
bug. Play it safe and give a specific, complete example.
Keep in mind that the purpose of a bug report is to enable someone to fix the bug if it
is not known. Always write your bug reports on the assumption that the bug is not known.
Sometimes people give a few sketchy facts and ask, “Does this ring a bell?” This cannot
help us fix a bug. It is better to send a complete bug report to begin with.
Try to make your bug report self-contained. If we have to ask you for more information, it
is best if you include all the previous information in your response, as well as the information
that was missing.
To enable someone to investigate the bug, you should include all these things:
• The version of Octave. You can get this by noting the version number that is printed
when Octave starts, or running it with the ‘-v’ option.
• A complete input file that will reproduce the bug.
A single statement may not be enough of an example—the bug might depend on other
details that are missing from the single statement where the error finally occurs.
302 GNU Octave
• The command arguments you gave Octave to execute that example and observe the
bug. To guarantee you won’t omit something important, list all the options.
If we were to try to guess the arguments, we would probably guess wrong and then we
would not encounter the bug.
• The type of machine you are using, and the operating system name and version number.
• The command-line arguments you gave to the configure command when you installed
the interpreter.
• A complete list of any modifications you have made to the interpreter source.
Be precise about these changes—show a context diff for them.
• Details of any other deviations from the standard procedure for installing Octave.
• A description of what behavior you observe that you believe is incorrect. For example,
"The interpreter gets a fatal signal," or, "The output produced at line 208 is incorrect."
Of course, if the bug is that the interpreter gets a fatal signal, then one can’t miss it.
But if the bug is incorrect output, we might not notice unless it is glaringly wrong.
Even if the problem you experience is a fatal signal, you should still say so explicitly.
Suppose something strange is going on, such as, your copy of the interpreter is out
of synch, or you have encountered a bug in the C library on your system. Your copy
might crash and the copy here would not. If you said to expect a crash, then when the
interpreter here fails to crash, we would know that the bug was not happening. If you
don’t say to expect a crash, then we would not know whether the bug was happening.
We would not be able to draw any conclusion from our observations.
Often the observed symptom is incorrect output when your program is run. Unfortunately,
this is not enough information unless the program is short and simple. It is very
helpful if you can include an explanation of the expected output, and why the actual
output is incorrect.
• If you wish to suggest changes to the Octave source, send them as context diffs. If you
even discuss something in the Octave source, refer to it by context, not by line number,
because the line numbers in the development sources probably won’t match those in
your sources.
Here are some things that are not necessary:
• A description of the envelope of the bug.
Often people who encounter a bug spend a lot of time investigating which changes to
the input file will make the bug go away and which changes will not affect it. Such
information is usually not necessary to enable us to fix bugs in Octave, but if you can
find a simpler example to report instead of the original one, that is a convenience.
Errors in the output will be easier to spot, running under the debugger will take less
time, etc. Most Octave bugs involve just one function, so the most straightforward way
to simplify an example is to delete all the function definitions except the one in which
the bug occurs.
However, simplification is not vital; if you don’t want to do this, report the bug anyway
and send the entire test case you used.
• A patch for the bug. Patches can be helpful, but if you find a bug, you should report
it, even if you cannot send a fix for the problem.
Appendix B: Known Causes of Trouble 303
B.6 Sending Patches for Octave
If you would like to write bug fixes or improvements for Octave, that is very helpful.
When you send your changes, please follow these guidelines to avoid causing extra work for
us in studying the patches.
If you don’t follow these guidelines, your information might still be useful, but using it
will take extra work. Maintaining Octave is a lot of work in the best of circumstances, and
we can’t keep up unless you do your best to help.
• Send an explanation with your changes of what problem they fix or what improvement
they bring about. For a bug fix, just include a copy of the bug report, and explain why
the change fixes the bug.
• Always include a proper bug report for the problem you think you have fixed. We need
to convince ourselves that the change is right before installing it. Even if it is right, we
might have trouble judging it if we don’t have a way to reproduce the problem.
• Include all the comments that are appropriate to help people reading the source in the
future understand why this change was needed.
• Don’t mix together changes made for different reasons. Send them individually.
If you make two changes for separate reasons, then we might not want to install them
both. We might want to install just one.
• Use ‘diff -c’ to make your diffs. Diffs without context are hard for us to install
reliably. More than that, they make it hard for us to study the diffs to decide whether
we want to install them. Unidiff format is better than contextless diffs, but not as easy
to read as ‘-c’ format.
If you have GNU diff, use ‘diff -cp’, which shows the name of the function that each
change occurs in.
• Write the change log entries for your changes.
Read the ‘ChangeLog’ file to see what sorts of information to put in, and to learn the
style that we use. The purpose of the change log is to show people where to find what
was changed. So you need to be specific about what functions you changed; in large
functions, it’s often helpful to indicate where within the function the change was made.
On the other hand, once you have shown people where to find the change, you need
not explain its purpose. Thus, if you add a new function, all you need to say about it
is that it is new. If you feel that the purpose needs explaining, it probably does—but
the explanation will be much more useful if you put it in comments in the code.
If you would like your name to appear in the header line for who made the change,
send us the header line.
B.7 How To Get Help with Octave
The mailing list help-octave@bevo.che.wisc.edu exists for the discussion of matters
related to using and installing Octave. If would like to join the discussion, please send a
short note to help-octave-request@bevo.che.wisc.edu.
Please do not send requests to be added or removed from the mailing list, or other
administrative trivia to the list itself.
304 GNU Octave
If you think you have found a bug in the installation procedure, however, you should send
a complete bug report for the problem to bug-octave@bevo.che.wisc.edu. See Section B.5
[Bug Reporting], page 301, for information that will help you to submit a useful report.
Appendix C: Installing Octave 305
Appendix C Installing Octave
Here is the procedure for installing Octave from scratch on a Unix system. For instructions
on how to install the binary distributions of Octave, see Section C.2 [Binary
Distributions], page 310.
• Run the shell script ‘configure’. This will determine the features your system has
(or doesn’t have) and create a file named ‘Makefile’ from each of the files named
‘Makefile.in’.
Here is a summary of the configure options that are most frequently used when building
Octave:
--prefix=prefix
Install Octave in subdirectories below prefix. The default value of prefix is
‘/usr/local’.
--srcdir=dir
Look for Octave sources in the directory dir.
--with-f2c
Use f2c even if a Fortran compiler is available.
--with-g77
Use g77 to compile Fortran code.
--enable-shared
Create shared libraries. If you are planning to use --enable-lite-kernel
or the dynamic loading features, you will probably want to use this option.
It will make your ‘.oct’ files much smaller and on some systems it may
be necessary to build shared libraries in order to use dynamically linked
functions.
You may also want to build a shared version of libstdc++, if your system
doesn’t already have one. Note that a patch is needed to build shared
versions of version 2.7.2 of libstdc++ on the HP-PA architecture. You
can find the patch at ftp://ftp.cygnus.com/pub/g++/libg++-2.7.2-
hppa-gcc-fix.
--enable-dl
Use dlopen and friends to make Octave capable of dynamically linking
externally compiled functions. This only works on systems that actually
have these functions. If you plan on using this feature, you should probably
also use --enable-shared to reduce the size of your ‘.oct’ files.
--enable-shl
Use shl_load and friends to make Octave capable of dynamically linking
externally compiled functions. This only works on systems that actually
have these functions (only HP-UX systems). If you plan on using this
feature, you should probably also use --enable-shared to reduce the size
of your ‘.oct’ files.
306 GNU Octave
--enable-lite-kernel
Compile smaller kernel. This currently requires the dynamic linking functions
dlopen or shl_load and friends so that Octave can load functions at
run time that are not loaded at compile time.
--without-fastblas
Compile and use the generic BLAS and LAPACK versions included with
Octave. By default, configure first looks for BLAS and LAPACK matrix
libraries on your system, including optimized BLAS implementations
such as the free ATLAS 3.0, as well as vendor-tuned libraries. (The use
of an optimized BLAS will generally result in several-times faster matrix
operations.) Only use this option if your system has BLAS/LAPACK
libraries that cause problems for some reason. You can also use --withfastblas=lib
to specify a particular BLAS library -llib that configure
doesn’t check for automatically.
--help Print a summary of the options recognized by the configure script.
See the file ‘INSTALL’ for more information about the command line options used by
configure. That file also contains instructions for compiling in a directory other than
where the source is located.
• Run make.
You will need a recent version of GNU Make. Modifying Octave’s makefiles to work
with other make programs is probably not worth your time. We recommend you get
and compile GNU Make instead.
For plotting, you will need to have gnuplot installed on your system. Gnuplot is a
command-driven interactive function plotting program. Gnuplot is copyrighted, but
freely distributable. The ‘gnu’ in gnuplot is a coincidence—it is not related to the
GNU project or the FSF in any but the most peripheral sense.
To compile Octave, you will need a recent version of GNU Make. You will also need
g++ 2.7.2 or later. Version 2.8.0 or egcs 1.0.x should work. Later versions may work,
but C++ is still evolving, so don’t be too surprised if you run into some trouble.
It is no longer necessary to have libg++, but you do need to have the GNU implementation
of libstdc++. If you are using g++ 2.7.2, libstdc++ is distributed along
with libg++, but for later versions, libstdc++ is distributed separately. For egcs,
libstdc++ is included with the compiler distribution.
If you plan to modify the parser you will also need GNU bison and flex. If you modify
the documentation, you will need GNU Texinfo, along with the patch for the makeinfo
program that is distributed with Octave.
GNU Make, gcc, and libstdc++, gnuplot, bison, flex, and Texinfo are all available
from many anonymous ftp archives. The primary site is ftp.gnu.org, but it is often
very busy. A list of sites that mirror the software on ftp.gnu.org is available by
anonymous ftp from ftp://ftp.gnu.org/pub/gnu/GNUinfo/FTP.
If you don’t have a Fortran compiler, or if your Fortran compiler doesn’t work like the
traditional Unix f77, you will need to have the Fortran to C translator f2c. You can
get f2c from any number of anonymous ftp archives. The most recent version of f2c
is always available from netlib.att.com.
Appendix C: Installing Octave 307
On an otherwise idle Pentium 133 running Linux, it will take somewhere between 1-
1/2 to 3 hours to compile everything, depending on whether you are building shared
libraries. You will need about 100 megabytes of disk storage to work with (considerably
less if you don’t compile with debugging symbols). To do that, use the command
make CFLAGS=-O CXXFLAGS=-O LDFLAGS=
instead of just ‘make’.
• If you encounter errors while compiling Octave, first check the list of known problems
below to see if there is a workaround or solution for your problem. If not, see
Appendix B [Trouble], page 299, for information about how to report bugs.
• Once you have successfully compiled Octave, run ‘make install’.
This will install a copy of octave, its libraries, and its documentation in the destination
directory. As distributed, Octave is installed in the following directories. In the table
below, prefix defaults to ‘/usr/local’, version stands for the current version number
of the interpreter, and arch is the type of computer on which Octave is installed (for
example, ‘i586-unknown-gnu’).
‘prefix/bin’
Octave and other binaries that people will want to run directly.
‘prefix/lib’
Libraries like libcruft.a and liboctave.a.
‘prefix/share’
Architecture-independent data files.
‘prefix/include/octave’
Include files distributed with Octave.
‘prefix/man/man1’
Unix-style man pages describing Octave.
‘prefix/info’
Info files describing Octave.
‘prefix/share/octave/version/m’
Function files distributed with Octave. This includes the Octave version,
so that multiple versions of Octave may be installed at the same time.
‘prefix/lib/octave/version/exec/arch’
Executables to be run by Octave rather than the user.
‘prefix/lib/octave/version/oct/arch’
Object files that will be dynamically loaded.
‘prefix/share/octave/version/imagelib’
Image files that are distributed with Octave.
C.1 Installation Problems
This section contains a list of problems (and some apparent problems that don’t really
mean anything is wrong) that may show up during installation of Octave.
308 GNU Octave
• On some SCO systems, info fails to compile if HAVE_TERMIOS_H is defined int
‘config.h’. Simply removing the definition from ‘info/config.h’ should allow it to
compile.
• If configure finds dlopen, dlsym, dlclose, and dlerror, but not the header file
‘dlfcn.h’, you need to find the source for the header file and install it in the directory
‘usr/include’. This is reportedly a problem with Slackware 3.1. For Linux/GNU
systems, the source for ‘dlfcn.h’ is in the ldso package.
• Building ‘.oct’ files doesn’t work.
You should probably have a shared version of libstdc++. A patch is needed to build
shared versions of version 2.7.2 of libstdc++ on the HP-PA architecture. You can find
the patch at ftp://ftp.cygnus.com/pub/g++/libg++-2.7.2-hppa-gcc-fix.
• On some alpha systems there may be a problem with the libdxml library, resulting in
floating point errors and/or segmentation faults in the linear algebra routines called by
Octave. If you encounter such problems, then you should modify the configure script
so that SPECIAL_MATH_LIB is not set to -ldxml.
• On FreeBSD systems Octave may hang while initializing some internal constants. The
fix appears to be to use
options GPL_MATH_EMULATE
rather than
options MATH_EMULATE
in the kernel configuration files (typically found in the directory ‘/sys/i386/conf’.
After making this change, you’ll need to rebuild the kernel, install it, and reboot.
• If you encounter errors like
passing ‘void (*)()’ as argument 2 of
‘octave_set_signal_handler(int, void (*)(int))’
or
warning: ANSI C++ prohibits conversion from ‘(int)’ to ‘(...)’
while compiling ‘sighandlers.cc’, you may need to edit some files in the gcc include
subdirectory to add proper prototypes for functions there. For example, Ultrix 4.2
needs proper declarations for the signal function and the SIG_IGN macro in the file
‘signal.h’.
On some systems the SIG_IGN macro is defined to be something like this:
#define SIG_IGN (void (*)())1
when it should really be something like:
#define SIG_IGN (void (*)(int))1
to match the prototype declaration for the signal function. This change should also
be made for the SIG_DFL and SIG_ERR symbols. It may be necessary to change the
definitions in ‘sys/signal.h’ as well.
The gcc fixincludes and fixproto scripts should probably fix these problems when
gcc installs its modified set of header files, but I don’t think that’s been done yet.
You should not change the files in ‘/usr/include’. You can find the gcc include
directory tree by running the command
Appendix C: Installing Octave 309
gcc -print-libgcc-file-name
The directory of gcc include files normally begins in the same directory that contains
the file ‘libgcc.a’.
• Some of the Fortran subroutines may fail to compile with older versions of the Sun
Fortran compiler. If you get errors like
zgemm.f:
zgemm:
warning: unexpected parent of complex expression subtree
zgemm.f, line 245: warning: unexpected parent of complex
expression subtree
warning: unexpected parent of complex expression subtree
zgemm.f, line 304: warning: unexpected parent of complex
expression subtree
warning: unexpected parent of complex expression subtree
zgemm.f, line 327: warning: unexpected parent of complex
expression subtree
pcc_binval: missing IR_CONV in complex op
make[2]: *** [zgemm.o] Error 1
when compiling the Fortran subroutines in the ‘libcruft’ subdirectory, you should
either upgrade your compiler or try compiling with optimization turned off.
• On NeXT systems, if you get errors like this:
/usr/tmp/cc007458.s:unknown:Undefined local symbol LBB7656
/usr/tmp/cc007458.s:unknown:Undefined local symbol LBE7656
when compiling ‘Array.cc’ and ‘Matrix.cc’, try recompiling these files without -g.
• Some people have reported that calls to shell cmd and the pager do not work on SunOS
systems. This is apparently due to having G_HAVE_SYS_WAIT defined to be 0 instead of
1 when compiling libg++.
• On NeXT systems, linking to ‘libsys_s.a’ may fail to resolve the following functions
_tcgetattr
_tcsetattr
_tcflow
which are part of ‘libposix.a’. Unfortunately, linking Octave with -posix results in
the following undefined symbols.
.destructors_used
.constructors_used
_objc_msgSend
_NXGetDefaultValue
_NXRegisterDefaults
.objc_class_name_NXStringTable
.objc_class_name_NXBundle
One kluge around this problem is to extract ‘termios.o’ from ‘libposix.a’, put it in
Octave’s ‘src’ directory, and add it to the list of files to link together in the makefile.
Suggestions for better ways to solve this problem are welcome!
• If Octave crashes immediately with a floating point exception, it is likely that it is
failing to initialize the IEEE floating point values for infinity and NaN.
310 GNU Octave
If your system actually does support IEEE arithmetic, you should be able to fix this
problem by modifying the function octave_ieee_init in the file ‘lo-ieee.cc’ to correctly
initialize Octave’s internal infinity and NaN variables.
If your system does not support IEEE arithmetic but Octave’s configure script incorrectly
determined that it does, you can work around the problem by editing the file
‘config.h’ to not define HAVE_ISINF, HAVE_FINITE, and HAVE_ISNAN.
In any case, please report this as a bug since it might be possible to modify Octave’s
configuration script to automatically determine the proper thing to do.
• After installing the binary distribution of Octave in an alternate directory, the Emacs
command run-octave doesn’t work. Emacs hangs in accept-process-output in
inferior-octave-startup.
This seems to be a problem with executing a shell script using the comint package. You
can avoid the problem by changing the way Octave is installed to eliminate the need for
the shell script. You can either compile and install Octave using the source distribution,
reinstall the binary distribution in the default directory, or copy the commands in the
octave shell script wrapper to your shell startup files (and the shell startup files for
anyone else who is using Octave) and then rename the file ‘octave.bin’ to be ‘octave’.
C.2 Binary Distributions
Although Octave is not very difficult to build from its sources, it is a relatively large
program that does require a significant amount of time and disk space to compile and install.
Because of this, many people want to be able to obtain binary distributions so they can
start using Octave immediately, without having to bother with the details of compiling it
first. This is understandable, so I try to maintain a current collection of binary distributions
at ftp://ftp.che.wisc.edu/pub/octave/BINARIES.
Please understand, however, that there is only a limited amount of time available to
devote to making binaries, so binaries may not be immediately available for some platforms.
(Please contact bug-octave@bevo.che.wisc.edu if you are interested in helping make a
binary distribution available for your system.)
C.2.1 Installing Octave from a Binary Distribution
To install Octave from a binary distribution, execute the command
sh ./install-octave
in the top level directory of the distribution.
Binary distributions are normally compiled assuming that Octave will be installed in the
following subdirectories of ‘/usr/local’.
‘bin’ Octave and other binaries that people will want to run directly.
‘lib’ Shared libraries that Octave needs in order to run. These files are not included
if you are installing a statically linked version of Octave.
‘man/man1’
Unix-style man pages describing Octave.
‘info’ Info files describing Octave.
Appendix C: Installing Octave 311
‘share/octave/version/m’
Function files distributed with Octave. This includes the Octave version, so
that multiple versions of Octave may be installed at the same time.
‘libexec/octave/version/exec/arch’
Executables to be run by Octave rather than the user.
‘libexec/octave/version/oct/arch’
Object files that will be dynamically loaded.
‘share/octave/version/imagelib’
Image files that are distributed with Octave.
where version stands for the current version number of the interpreter, and arch is the type
of computer on which Octave is installed (for example, ‘i586-pc-linux-gnu’).
If these directories don’t exist, the script install-octave will create them for you. The
installation script also creates the following subdirectories of ‘/usr/local’ that are intended
for locally installed functions:
‘share/octave/site/m’
Locally installed M-files.
‘libexec/octave/site/exec/arch’
Locally installed binaries intended to be run by Octave rather than by the user.
‘libexec/octave/site/octave/arch’
Local object files that will be dynamically linked.
If it is not possible for you to install Octave in ‘/usr/local’, or if you would prefer to
install it in a different directory, you can specify the name of the top level directory as an
argument to the ‘install-octave’ script. For example:
sh ./install-octave /some/other/directory
will install Octave in subdirectories of the directory ‘/some/other/directory’.
C.2.2 Creating a Binary Distribution
Here is how to build a binary distribution for others to use. If you want to make a
binary distribution for your system available along with the Octave sources and binaries
on ftp.che.wisc.edu, please follow this procedure. For directions explaining how to make
the binary available on the ftp site, please contact bug-octave@bevo.che.wisc.edu.
• Unpack the source distribution:
gunzip -c octave-2.1.x.tar.gz | tar xf •
Change your current directory to the top-level directory of the source distribution:
cd octave-2.1.x
• Make the binary distribution:
make binary-dist
This will create a compressed tar file ready for distribution. It will have a name like
‘octave-2.1.x-i586-pc-linux-gnu.tar.gz’
312 GNU Octave
Appendix D: Emacs Octave Support 313
Appendix D Emacs Octave Support
The development of Octave code can greatly be facilitated using Emacs with Octave
mode, a major mode for editing Octave files which can e.g. automatically indent the code,
do some of the typing (with Abbrev mode) and show keywords, comments, strings, etc. in
different faces (with Font-lock mode on devices that support it).
It is also possible to run Octave from within Emacs, either by directly entering commands
at the prompt in a buffer in Inferior Octave mode, or by interacting with Octave from within
a file with Octave code. This is useful in particular for debugging Octave code.
Finally, you can convince Octave to use the Emacs info reader for help -i.
All functionality is provided by the Emacs Lisp package EOS (for “Emacs Octave Support”).
This chapter describes how to set up and use this package.
Please contact <Kurt.Hornik@ci.tuwien.ac.at> if you have any questions or suggestions
on using EOS.
D.1 Installing EOS
The Emacs package EOS consists of the three files ‘octave-mod.el’, ‘octave-inf.el’,
and ‘octave-hlp.el’. These files, or better yet their byte-compiled versions, should be
somewhere in your Emacs load-path.
If you have GNU Emacs with a version number at least as high as 19.35, you are all set
up, because EOS is respectively will be part of GNU Emacs as of version 19.35.
Otherwise, copy the three files from the ‘emacs’ subdirectory of the Octave distribution
to a place where Emacs can find them (this depends on how your Emacs was installed).
Byte-compile them for speed if you want.
D.2 Using Octave Mode
If you are lucky, your sysadmins have already arranged everything so that Emacs automatically
goes into Octave mode whenever you visit an Octave code file as characterized by
its extension ‘.m’. If not, proceed as follows.
1. To begin using Octave mode for all ‘.m’ files you visit, add the following lines to a file
loaded by Emacs at startup time, typically your ‘~/.emacs’ file:
(autoload ’octave-mode "octave-mod" nil t)
(setq auto-mode-alist
(cons ’("\\.m$" . octave-mode) auto-mode-alist))
2. Finally, to turn on the abbrevs, auto-fill and font-lock features automatically, also add
the following lines to one of the Emacs startup files:
(add-hook ’octave-mode-hook
(lambda ()
(abbrev-mode 1)
(auto-fill-mode 1)
(if (eq window-system ’x)
(font-lock-mode 1))))
See the Emacs manual for more information about how to customize Font-lock mode.
314 GNU Octave
In Octave mode, the following special Emacs commands can be used in addition to the
standard Emacs commands.
C-h m Describe the features of Octave mode.
LFD Reindent the current Octave line, insert a newline and indent the new line
(octave-reindent-then-newline-and-indent). An abbrev before point is
expanded if abbrev-mode is non-nil.
TAB Indents current Octave line based on its contents and on previous lines (indent-
according-to-mode).
; Insert an “electric” semicolon (octave-electric-semi). If octave-autoindent
is non-nil, reindent the current line. If octave-auto-newline is
non-nil, automagically insert a newline and indent the new line.
‘ Start entering an abbreviation (octave-abbrev-start). If Abbrev mode is
turned on, typing ‘C-h or ‘? lists all abbrevs. Any other key combination is
executed normally. Note that all Octave abbrevs start with a grave accent.
M-LFD Break line at point and insert continuation marker and alignment (octave-
split-line).
M-TAB Perform completion on Octave symbol preceding point, comparing that symbol
against Octave’s reserved words and builtin variables (octave-complete-
symbol).
M-C-a Move backward to the beginning of a function (octave-beginning-of-defun).
With prefix argument N, do it that many times if N is positive; otherwise, move
forward to the N-th following beginning of a function.
M-C-e Move forward to the end of a function (octave-end-of-defun). With prefix
argument N, do it that many times if N is positive; otherwise, move back to
the N-th preceding end of a function.
M-C-h Puts point at beginning and mark at the end of the current Octave function,
i.e., the one containing point or following point (octave-mark-defun).
M-C-q Properly indents the Octave function which contains point (octave-indent-
defun).
M-; If there is no comment already on this line, create a code-level comment (started
by two comment characters) if the line is empty, or an in-line comment (started
by one comment character) otherwise (octave-indent-for-comment). Point
is left after the start of the comment which is properly aligned.
C-c ; Puts the comment character ‘#’ (more precisely, the string value of octavecomment-start)
at the beginning of every line in the region (octave-commentregion).
With just C-u prefix argument, uncomment each line in the region.
A numeric prefix argument N means use N comment characters.
C-c : Uncomments every line in the region (octave-uncomment-region).
C-c C-p Move one line of Octave code backward, skipping empty and comment lines
(octave-previous-code-line). With numeric prefix argument N, move that
many code lines backward (forward if N is negative).
Appendix D: Emacs Octave Support 315
C-c C-n Move one line of Octave code forward, skipping empty and comment lines
(octave-next-code-line). With numeric prefix argument N, move that many
code lines forward (backward if N is negative).
C-c C-a Move to the ‘real’ beginning of the current line (octave-beginning-of-line).
If point is in an empty or comment line, simply go to its beginning; otherwise,
move backwards to the beginning of the first code line which is not inside a
continuation statement, i.e., which does not follow a code line ending in ‘...’
or ‘\’, or is inside an open parenthesis list.
C-c C-e Move to the ‘real’ end of the current line (octave-end-of-line). If point is in
a code line, move forward to the end of the first Octave code line which does
not end in ‘...’ or ‘\’ or is inside an open parenthesis list. Otherwise, simply
go to the end of the current line.
C-c M-C-n Move forward across one balanced begin-end block of Octave code (octaveforward-block).
With numeric prefix argument N, move forward across n
such blocks (backward if N is negative).
C-c M-C-p Move back across one balanced begin-end block of Octave code (octavebackward-block).
With numeric prefix argument N, move backward across N
such blocks (forward if N is negative).
C-c M-C-d Move forward down one begin-end block level of Octave code (octave-downblock).
With numeric prefix argument, do it that many times; a negative
argument means move backward, but still go down one level.
C-c M-C-u Move backward out of one begin-end block level of Octave code (octavebackward-up-block).
With numeric prefix argument, do it that many times;
a negative argument means move forward, but still to a less deep spot.
C-c M-C-h Put point at the beginning of this block, mark at the end (octave-mark-block).
The block marked is the one that contains point or follows point.
C-c ] Close the current block on a separate line (octave-close-block). An error is
signaled if no block to close is found.
C-c f Insert a function skeleton, prompting for the function’s name, arguments and
return values which have to be entered without parens (octave-insert-defun).
C-c C-h Search the function, operator and variable indices of all info files with documentation
for Octave for entries (octave-help). If used interactively, the entry
is prompted for with completion. If multiple matches are found, one can cycle
through them using the standard ‘,’ (Info-index-next) command of the Info
reader.
The variable octave-help-files is a list of files to search through and defaults
to ’("octave"). If there is also an Octave Local Guide with corresponding info
file, say, ‘octave-LG’, you can have octave-help search both files by
(setq octave-help-files ’("octave" "octave-LG"))
in one of your Emacs startup files.
A common problem is that the RET key does not indent the line to where the new
text should go after inserting the newline. This is because the standard Emacs convention
316 GNU Octave
is that RET (aka C-m) just adds a newline, whereas LFD (aka C-j) adds a newline and
indents it. This is particularly inconvenient for users with keyboards which do not have a
special LFD key at all; in such cases, it is typically more convenient to use RET as the
LFD key (rather than typing C-j).
You can make RET do this by adding
(define-key octave-mode-map "\C-m"
’octave-reindent-then-newline-and-indent)
to one of your Emacs startup files. Another, more generally applicable solution is
(defun RET-behaves-as-LFD ()
(let ((x (key-binding "\C-j")))
(local-set-key "\C-m" x)))
(add-hook ’octave-mode-hook ’RET-behaves-as-LFD)
(this works for all modes by adding to the startup hooks, without having to know the
particular binding of RET in that mode!). Similar considerations apply for using M-RET
as M-LFD . As Barry A. Warsaw <bwarsaw@cnri.reston.va.us> says in the documentation
for his cc-mode, “This is a very common question. :-) If you want this to be the default
behavior, don’t lobby me, lobby RMS!”
The following variables can be used to customize Octave mode.
octave-auto-indent
Non-nil means auto-indent the current line after a semicolon or space. Default
is nil.
octave-auto-newline
Non-nil means auto-insert a newline and indent after semicolons are typed.
The default value is nil.
octave-blink-matching-block
Non-nil means show matching begin of block when inserting a space, newline
or ‘;’ after an else or end keyword. Default is t. This is an extremely useful
feature for automatically verifying that the keywords match—if they don’t, an
error message is displayed.
octave-block-offset
Extra indentation applied to statements in block structures. Default is 2.
octave-continuation-offset
Extra indentation applied to Octave continuation lines. Default is 4.
octave-continuation-string
String used for Octave continuation lines. Normally ‘\’.
octave-mode-startup-message
If t (default), a startup message is displayed when Octave mode is called.
If Font Lock mode is enabled, Octave mode will display
• strings in font-lock-string-face
• comments in font-lock-comment-face
• the Octave reserved words (such as all block keywords) and the text functions (such as
‘cd’ or ‘who’) which are also reserved using font-lock-keyword-face
Appendix D: Emacs Octave Support 317
• the builtin operators (‘&&’, ‘<>’, . . .) using font-lock-reference-face
• the builtin variables (such as ‘prefer_column_vectors’, ‘NaN’ or ‘LOADPATH’) in font-
lock-variable-name-face
• and the function names in function declarations in font-lock-function-name-face.
There is also rudimentary support for Imenu (currently, function names can be indexed).
You can generate TAGS files for Emacs from Octave ‘.m’ files using the shell script otags
that is installed alongside your copy of Octave.
Customization of Octave mode can be performed by modification of the variable octavemode-hook.
If the value of this variable is non-nil, turning on Octave mode calls its value.
If you discover a problem with Octave mode, you can conveniently send a bug report
using C-c C-b (octave-submit-bug-report). This automatically sets up a mail buffer
with version information already added. You just need to add a description of the problem,
including a reproducible test case and send the message.
D.3 Running Octave From Within Emacs
The package ‘octave’ provides commands for running an inferior Octave process in a
special Emacs buffer. Use
M-x run-octave
to directly start an inferior Octave process. If Emacs does not know about this command,
add the line
(autoload ’run-octave "octave-inf" nil t)
to your ‘.emacs’ file.
This will start Octave in a special buffer the name of which is specified by the variable
inferior-octave-buffer and defaults to "*Inferior Octave*". From within this buffer,
you can interact with the inferior Octave process ‘as usual’, i.e., by entering Octave commands
at the prompt. The buffer is in Inferior Octave mode, which is derived from the
standard Comint mode, a major mode for interacting with an inferior interpreter. See the
documentation for comint-mode for more details, and use C-h b to find out about available
special keybindings.
You can also communicate with an inferior Octave process from within files with Octave
code (i.e., buffers in Octave mode), using the following commands.
C-c i l Send the current line to the inferior Octave process (octave-send-line). With
positive prefix argument N, send that many lines. If octave-send-line-autoforward
is non-nil, go to the next unsent code line.
C-c i b Send the current block to the inferior Octave process (octave-send-block).
C-c i f Send the current function to the inferior Octave process (octave-send-defun).
C-c i r Send the region to the inferior Octave process (octave-send-region).
C-c i s Make sure that ‘inferior-octave-buffer’ is displayed (octave-show-process-
buffer).
C-c i h Delete all windows that display the inferior Octave buffer (octave-hide-
process-buffer).
318 GNU Octave
C-c i k Kill the inferior Octave process and its buffer (octave-kill-process).
The effect of the commands which send code to the Octave process can be customized
by the following variables.
octave-send-echo-input
Non-nil means echo input sent to the inferior Octave process. Default is t.
octave-send-show-buffer
Non-nil means display the buffer running the Octave process after sending a
command (but without selecting it). Default is t.
If you send code and there is no inferior Octave process yet, it will be started automat-
ically.
The startup of the inferior Octave process is highly customizable. The variable
inferior-octave-startup-args can be used for specifying command lines arguments
to be passed to Octave on startup as a list of strings. For example, to suppress the
startup message and use ‘traditional’ mode, set this to ’("-q" "--traditional"). You
can also specify a startup file of Octave commands to be loaded on startup; note that
these commands will not produce any visible output in the process buffer. Which file to
use is controlled by the variable inferior-octave-startup-file. If this is nil, the file
‘~/.emacs-octave’ is used if it exists.
And finally, inferior-octave-mode-hook is run after starting the process and putting
its buffer into Inferior Octave mode. Hence, if you like the up and down arrow keys to
behave in the interaction buffer as in the shell, and you want this buffer to use nice colors,
add
(add-hook ’inferior-octave-mode-hook
(lambda ()
(turn-on-font-lock)
(define-key inferior-octave-mode-map [up]
’comint-previous-input)
(define-key inferior-octave-mode-map [down]
’comint-next-input)))
to your ‘.emacs’ file. You could also swap the roles of C-a (beginning-of-line) and C-c
C-a (comint-bol) using this hook.
Note: If you set your Octave prompts to something different from the defaults,
make sure that inferior-octave-prompt matches them. Otherwise, nothing
will work, because Emacs will have no idea when Octave is waiting for input,
or done sending output.
D.4 Using the Emacs Info Reader for Octave
You can also set up the Emacs Info reader for dealing with the results of Octave’s
‘help -i’. For this, the package ‘gnuserv’ needs to be installed, which unfortunately
still does not come with GNU Emacs (it does with XEmacs). It can be retrieved
from any GNU Emacs Lisp Code Directory archive, e.g. ftp://ftp.cis.ohiostate.edu/pub/gnu/emacs/elisp-archive,
in the ‘packages’ subdirectory. A recent
version of gnuserv is available from http://www.meltin.net/hacks/emacs/src/gnuserv-
3.12.2.tar.gz.
Appendix D: Emacs Octave Support 319
If ‘gnuserv’ is installed, add the lines
(autoload ’octave-help "octave-hlp" nil t)
(require ’gnuserv)
(gnuserv-start)
to your ‘.emacs’ file.
You can use either ‘plain’ Emacs Info or the function octave-help as your Octave
info reader (for ‘help -i’). In the former case, set the Octave variable INFO_PROGRAM to
"info-emacs-info". The latter is perhaps more attractive because it allows to look up
keys in the indices of several info files related to Octave (provided that the Emacs variable
octave-help-files is set correctly). In this case, set INFO_PROGRAM to "info-emacs-
octave-help".
If you use Octave from within Emacs, these settings are best done in the
‘~/.emacs-octave’ startup file (or the file pointed to by the Emacs variable
inferior-octave-startup-file).
320 GNU Octave
Appendix E: Grammar 321
Appendix E Grammar
Someday I hope to expand this to include a semi-formal description of Octave’s language.
E.1 Keywords
The following identifiers are keywords, and may not be used as variable or function
names:
all_va_args endwhile
break for
case function
catch global
continue gplot
else gsplot
elseif if
end otherwise
end_try_catch return
end_unwind_protect switch
endfor try
endfunction unwind_protect
endif unwind_protect_cleanup
endswitch while
The following command-like functions are also speical. They may be used as simple
variable names, but not as formal parameters for functions, or as the names of structure
variables. Failed assignments leave them undefined (you can recover the orginal definition
as a function using clear).
casesen echo load show
cd edit_history ls type
chdir format more which
clear help run_history who
diary history save whos
dir hold set
322 GNU Octave
Appendix F: GNU GENERAL PUBLIC LICENSE 323
Appendix F GNU GENERAL PUBLIC LICENSE
Version 2, June 1991
Copyright c 1989, 1991 Free Software Foundation, Inc.
59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
F.1 Preamble
The licenses for most software are designed to take away your freedom to share and
change it. By contrast, the GNU General Public License is intended to guarantee your
freedom to share and change free software—to make sure the software is free for all its users.
This General Public License applies to most of the Free Software Foundation’s software
and to any other program whose authors commit to using it. (Some other Free Software
Foundation software is covered by the GNU Library General Public License instead.) You
can apply it to your programs, too.
When we speak of free software, we are referring to freedom, not price. Our General
Public Licenses are designed to make sure that you have the freedom to distribute copies
of free software (and charge for this service if you wish), that you receive source code or
can get it if you want it, that you can change the software or use pieces of it in new free
programs; and that you know you can do these things.
To protect your rights, we need to make restrictions that forbid anyone to deny you
these rights or to ask you to surrender the rights. These restrictions translate to certain
responsibilities for you if you distribute copies of the software, or if you modify it.
For example, if you distribute copies of such a program, whether gratis or for a fee, you
must give the recipients all the rights that you have. You must make sure that they, too,
receive or can get the source code. And you must show them these terms so they know
their rights.
We protect your rights with two steps: (1) copyright the software, and (2) offer you this
license which gives you legal permission to copy, distribute and/or modify the software.
Also, for each author’s protection and ours, we want to make certain that everyone
understands that there is no warranty for this free software. If the software is modified by
someone else and passed on, we want its recipients to know that what they have is not the
original, so that any problems introduced by others will not reflect on the original authors’
reputations.
Finally, any free program is threatened constantly by software patents. We wish to avoid
the danger that redistributors of a free program will individually obtain patent licenses, in
effect making the program proprietary. To prevent this, we have made it clear that any
patent must be licensed for everyone’s free use or not licensed at all.
The precise terms and conditions for copying, distribution and modification follow.
324 GNU Octave
F.2 TERMS AND CONDITIONS FOR COPYING,
DISTRIBUTION AND MODIFICATION
0. This License applies to any program or other work which contains a notice placed
by the copyright holder saying it may be distributed under the terms of this General
Public License. The “Program”, below, refers to any such program or work, and a
“work based on the Program” means either the Program or any derivative work under
copyright law: that is to say, a work containing the Program or a portion of it, either
verbatim or with modifications and/or translated into another language. (Hereinafter,
translation is included without limitation in the term “modification”.) Each licensee is
addressed as “you”.
Activities other than copying, distribution and modification are not covered by this
License; they are outside its scope. The act of running the Program is not restricted,
and the output from the Program is covered only if its contents constitute a work based
on the Program (independent of having been made by running the Program). Whether
that is true depends on what the Program does.
1. You may copy and distribute verbatim copies of the Program’s source code as you
receive it, in any medium, provided that you conspicuously and appropriately publish
on each copy an appropriate copyright notice and disclaimer of warranty; keep intact
all the notices that refer to this License and to the absence of any warranty; and give
any other recipients of the Program a copy of this License along with the Program.
You may charge a fee for the physical act of transferring a copy, and you may at your
option offer warranty protection in exchange for a fee.
2. You may modify your copy or copies of the Program or any portion of it, thus forming a
work based on the Program, and copy and distribute such modifications or work under
the terms of Section 1 above, provided that you also meet all of these conditions:
a. You must cause the modified files to carry prominent notices stating that you
changed the files and the date of any change.
b. You must cause any work that you distribute or publish, that in whole or in part
contains or is derived from the Program or any part thereof, to be licensed as a
whole at no charge to all third parties under the terms of this License.
c. If the modified program normally reads commands interactively when run, you
must cause it, when started running for such interactive use in the most ordinary
way, to print or display an announcement including an appropriate copyright notice
and a notice that there is no warranty (or else, saying that you provide a warranty)
and that users may redistribute the program under these conditions, and telling
the user how to view a copy of this License. (Exception: if the Program itself is
interactive but does not normally print such an announcement, your work based
on the Program is not required to print an announcement.)
These requirements apply to the modified work as a whole. If identifiable sections
of that work are not derived from the Program, and can be reasonably considered
independent and separate works in themselves, then this License, and its terms, do not
apply to those sections when you distribute them as separate works. But when you
distribute the same sections as part of a whole which is a work based on the Program,
the distribution of the whole must be on the terms of this License, whose permissions
Appendix F: GNU GENERAL PUBLIC LICENSE 325
for other licensees extend to the entire whole, and thus to each and every part regardless
of who wrote it.
Thus, it is not the intent of this section to claim rights or contest your rights to
work written entirely by you; rather, the intent is to exercise the right to control the
distribution of derivative or collective works based on the Program.
In addition, mere aggregation of another work not based on the Program with the
Program (or with a work based on the Program) on a volume of a storage or distribution
medium does not bring the other work under the scope of this License.
3. You may copy and distribute the Program (or a work based on it, under Section 2)
in object code or executable form under the terms of Sections 1 and 2 above provided
that you also do one of the following:
a. Accompany it with the complete corresponding machine-readable source code,
which must be distributed under the terms of Sections 1 and 2 above on a medium
customarily used for software interchange; or,
b. Accompany it with a written offer, valid for at least three years, to give any third
party, for a charge no more than your cost of physically performing source distribution,
a complete machine-readable copy of the corresponding source code, to be
distributed under the terms of Sections 1 and 2 above on a medium customarily
used for software interchange; or,
c. Accompany it with the information you received as to the offer to distribute corresponding
source code. (This alternative is allowed only for noncommercial distribution
and only if you received the program in object code or executable form
with such an offer, in accord with Subsection b above.)
The source code for a work means the preferred form of the work for making modifications
to it. For an executable work, complete source code means all the source code
for all modules it contains, plus any associated interface definition files, plus the scripts
used to control compilation and installation of the executable. However, as a special
exception, the source code distributed need not include anything that is normally
distributed (in either source or binary form) with the major components (compiler,
kernel, and so on) of the operating system on which the executable runs, unless that
component itself accompanies the executable.
If distribution of executable or object code is made by offering access to copy from
a designated place, then offering equivalent access to copy the source code from the
same place counts as distribution of the source code, even though third parties are not
compelled to copy the source along with the object code.
4. You may not copy, modify, sublicense, or distribute the Program except as expressly
provided under this License. Any attempt otherwise to copy, modify, sublicense or
distribute the Program is void, and will automatically terminate your rights under this
License. However, parties who have received copies, or rights, from you under this
License will not have their licenses terminated so long as such parties remain in full
compliance.
5. You are not required to accept this License, since you have not signed it. However,
nothing else grants you permission to modify or distribute the Program or its derivative
works. These actions are prohibited by law if you do not accept this License. Therefore,
by modifying or distributing the Program (or any work based on the Program), you
326 GNU Octave
indicate your acceptance of this License to do so, and all its terms and conditions for
copying, distributing or modifying the Program or works based on it.
6. Each time you redistribute the Program (or any work based on the Program), the
recipient automatically receives a license from the original licensor to copy, distribute
or modify the Program subject to these terms and conditions. You may not impose
any further restrictions on the recipients’ exercise of the rights granted herein. You are
not responsible for enforcing compliance by third parties to this License.
7. If, as a consequence of a court judgment or allegation of patent infringement or for any
other reason (not limited to patent issues), conditions are imposed on you (whether by
court order, agreement or otherwise) that contradict the conditions of this License, they
do not excuse you from the conditions of this License. If you cannot distribute so as
to satisfy simultaneously your obligations under this License and any other pertinent
obligations, then as a consequence you may not distribute the Program at all. For
example, if a patent license would not permit royalty-free redistribution of the Program
by all those who receive copies directly or indirectly through you, then the only way
you could satisfy both it and this License would be to refrain entirely from distribution
of the Program.
If any portion of this section is held invalid or unenforceable under any particular
circumstance, the balance of the section is intended to apply and the section as a
whole is intended to apply in other circumstances.
It is not the purpose of this section to induce you to infringe any patents or other
property right claims or to contest validity of any such claims; this section has the
sole purpose of protecting the integrity of the free software distribution system, which
is implemented by public license practices. Many people have made generous contributions
to the wide range of software distributed through that system in reliance on
consistent application of that system; it is up to the author/donor to decide if he or
she is willing to distribute software through any other system and a licensee cannot
impose that choice.
This section is intended to make thoroughly clear what is believed to be a consequence
of the rest of this License.
8. If the distribution and/or use of the Program is restricted in certain countries either
by patents or by copyrighted interfaces, the original copyright holder who places the
Program under this License may add an explicit geographical distribution limitation
excluding those countries, so that distribution is permitted only in or among countries
not thus excluded. In such case, this License incorporates the limitation as if written
in the body of this License.
9. The Free Software Foundation may publish revised and/or new versions of the General
Public License from time to time. Such new versions will be similar in spirit to the
present version, but may differ in detail to address new problems or concerns.
Each version is given a distinguishing version number. If the Program specifies a
version number of this License which applies to it and “any later version”, you have
the option of following the terms and conditions either of that version or of any later
version published by the Free Software Foundation. If the Program does not specify a
version number of this License, you may choose any version ever published by the Free
Software Foundation.
Appendix F: GNU GENERAL PUBLIC LICENSE 327
10. If you wish to incorporate parts of the Program into other free programs whose distribution
conditions are different, write to the author to ask for permission. For software
which is copyrighted by the Free Software Foundation, write to the Free Software Foundation;
we sometimes make exceptions for this. Our decision will be guided by the two
goals of preserving the free status of all derivatives of our free software and of promoting
the sharing and reuse of software generally.
NO WARRANTY
11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO
WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE
LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM “AS
IS” WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY
AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE
RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH
YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST
OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN
WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO
MAY MODIFY AND/OR REDISTRIBUTE THE PROGRAM AS PERMITTED
ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL,
SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF
THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT
LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR
LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE
PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH
HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
SUCH DAMAGES.
END OF TERMS AND CONDITIONS
328 GNU Octave
F.3 Appendix: How to Apply These Terms to Your New
Programs
If you develop a new program, and you want it to be of the greatest possible use to
the public, the best way to achieve this is to make it free software which everyone can
redistribute and change under these terms.
To do so, attach the following notices to the program. It is safest to attach them to the
start of each source file to most effectively convey the exclusion of warranty; and each file
should have at least the “copyright” line and a pointer to where the full notice is found.
one line to give the program’s name and a brief idea of what it does.
Copyright (C) 19yy name of author
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
02111-1307, USA.
Also add information on how to contact you by electronic and paper mail.
If the program is interactive, make it output a short notice like this when it starts in an
interactive mode:
Gnomovision version 69, Copyright (C) 19yy name of author
Gnomovision comes with ABSOLUTELY NO WARRANTY; for details
type ‘show w’. This is free software, and you are welcome
to redistribute it under certain conditions; type ‘show c’
for details.
The hypothetical commands ‘show w’ and ‘show c’ should show the appropriate parts of
the General Public License. Of course, the commands you use may be called something
other than ‘show w’ and ‘show c’; they could even be mouse-clicks or menu items—whatever
suits your program.
You should also get your employer (if you work as a programmer) or your school, if any,
to sign a “copyright disclaimer” for the program, if necessary. Here is a sample; alter the
names:
Yoyodyne, Inc., hereby disclaims all copyright interest in the program
‘Gnomovision’ (which makes passes at compilers) written by James Hacker.
signature of Ty Coon, 1 April 1989
Ty Coon, President of Vice
This General Public License does not permit incorporating your program into proprietary
programs. If your program is a subroutine library, you may consider it more useful to permit
Appendix F: GNU GENERAL PUBLIC LICENSE 329
linking proprietary applications with the library. If this is what you want to do, use the
GNU Library General Public License instead of this License.
330 GNU Octave
Concept Index 331
Concept Index
#
‘#’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
‘#!’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
%
‘%’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
--braindead
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
--debug. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
--echo-commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
--exec-path path . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
--help. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
--info-file filename . . . . . . . . . . . . . . . . . . . . . . . . 13
--info-program program. . . . . . . . . . . . . . . . . . . . . 13
--interactive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
--no-init-file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
--no-line-editing . . . . . . . . . . . . . . . . . . . . . . . . . . 14
--no-site-file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
--norc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
--path path. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
--quiet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
--silent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
--traditional . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
--verbose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
--version . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
-? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
-d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
-f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
-h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
-i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
-p path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
-q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
-v . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
-V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
-x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
.
.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95, 96
... continuation marker. . . . . . . . . . . . . . . . . . . . . . 88
.octaverc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
~
~/.octaverc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
\
\ continuation marker. . . . . . . . . . . . . . . . . . . . . . . . 88
A
acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
addition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
and operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
answers, incorrect . . . . . . . . . . . . . . . . . . . . . . 300, 302
any key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
arguments in function call . . . . . . . . . . . . . . . . . . . . 65
arithmetic operators . . . . . . . . . . . . . . . . . . . . . . . . . 67
assignment expressions . . . . . . . . . . . . . . . . . . . . . . . 72
assignment operators. . . . . . . . . . . . . . . . . . . . . . . . . 72
B
body of a loop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
boolean expressions . . . . . . . . . . . . . . . . . . . . . . . . . . 70
boolean operators. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
break statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
bug criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
bug report mailing lists . . . . . . . . . . . . . . . . . . . . . 301
bugs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
bugs, investigating . . . . . . . . . . . . . . . . . . . . . . . . . . 302
bugs, known. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
bugs, reporting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
built-in data types . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
built-in function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
C
case statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
catch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
cell arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
character strings . . . . . . . . . . . . . . . . . . . . . . . . . 29, 37
Cholesky factorization . . . . . . . . . . . . . . . . . . . . . . 167
clearing the screen . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
coding standards . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
command and ouput logs . . . . . . . . . . . . . . . . . . . . . 24
command completion . . . . . . . . . . . . . . . . . . . . . . . . 20
command descriptions. . . . . . . . . . . . . . . . . . . . . . . . 10
command echoing. . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
command history . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
command options . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
command-line editing . . . . . . . . . . . . . . . . . . . . . . . . 18
comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
comparison expressions. . . . . . . . . . . . . . . . . . . . . . . 69
complex-conjugate transpose. . . . . . . . . . . . . . . . . . 67
compounding, value of . . . . . . . . . . . . . . . . . . . . . . 203
containers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
continuation lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
continue statement. . . . . . . . . . . . . . . . . . . . . . . . . . 86
contributing to Octave . . . . . . . . . . . . . . . . . . . . . . . . 3
contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
332 GNU Octave
conversion specifications (printf) . . . . . . . . . . . . 118
conversion specifications (scanf) . . . . . . . . . . . . . 124
copyright . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
core dump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
customizing the prompt . . . . . . . . . . . . . . . . . . . . . . 23
D
DAE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
data structures. . . . . . . . . . . . . . . . . . . . . . . . . . . 29, 45
data types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
data types, built-in . . . . . . . . . . . . . . . . . . . . . . . . . . 29
data types, user-defined . . . . . . . . . . . . . . . . . . . . . . 30
decrement operator . . . . . . . . . . . . . . . . . . . . . . . . . . 73
defining functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
description format . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
diary of commands and output. . . . . . . . . . . . . . . . 24
Differential Equations . . . . . . . . . . . . . . . . . . . . . . . 177
diffs, submitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
distribution of Octave . . . . . . . . . . . . . . . . . . . . . . . . . 3
division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
do-until statement. . . . . . . . . . . . . . . . . . . . . . . . . . 83
documentation notation . . . . . . . . . . . . . . . . . . . . . . . 8
documenting Octave programs . . . . . . . . . . . . . . . . 26
dynamic linking . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
E
echoing executing commands . . . . . . . . . . . . . . . . . 24
editing the command line. . . . . . . . . . . . . . . . . . . . . 18
element-by-element evaluation . . . . . . . . . . . . . . . . 70
else statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
elseif statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Emacs TAGS files . . . . . . . . . . . . . . . . . . . . . . . . . . 317
end statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
end_try_catch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
end_unwind_protect. . . . . . . . . . . . . . . . . . . . . . . . . 87
endfor statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
endfunction statement . . . . . . . . . . . . . . . . . . . . . . 91
endif statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
endswitch statement. . . . . . . . . . . . . . . . . . . . . . . . . 81
endwhile statement. . . . . . . . . . . . . . . . . . . . . . . . . . 82
equality operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
equality, tests for . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
equations, nonlinear . . . . . . . . . . . . . . . . . . . . . . . . 173
erroneous messages . . . . . . . . . . . . . . . . . . . . . . . . . 300
erroneous results . . . . . . . . . . . . . . . . . . . . . . . 300, 302
error message notation . . . . . . . . . . . . . . . . . . . . . . . . 9
error messages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
error messages, incorrect . . . . . . . . . . . . . . . . . . . . 300
escape sequence notation . . . . . . . . . . . . . . . . . . . . . 37
evaluation notation . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
executable scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
execution speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
exiting octave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5, 16
exponentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
expression, range . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
expressions, assignment . . . . . . . . . . . . . . . . . . . . . . 72
expressions, boolean . . . . . . . . . . . . . . . . . . . . . . . . . 70
expressions, comparison . . . . . . . . . . . . . . . . . . . . . . 69
expressions, logical. . . . . . . . . . . . . . . . . . . . . . . . . . . 70
F
factorial function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
fatal signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
financial functions . . . . . . . . . . . . . . . . . . . . . . . . . . 203
flag character (printf) . . . . . . . . . . . . . . . . . . . . . . 120
flag character (scanf) . . . . . . . . . . . . . . . . . . . . . . . 124
flying high and fast . . . . . . . . . . . . . . . . . . . . . . . . . . 53
fonts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
for statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Fordyce, A. P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Frobenius norm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
function descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . 9
function file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10, 98
function statement. . . . . . . . . . . . . . . . . . . . . . . . . . 91
functions, user-defined . . . . . . . . . . . . . . . . . . . . . . . 91
funding Octave development . . . . . . . . . . . . . . . . . . . 3
G
getting a good job . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
global statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
global variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
grammar rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
greater than operator . . . . . . . . . . . . . . . . . . . . . . . . 69
H
header comments . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
help, on-line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
help, where to find. . . . . . . . . . . . . . . . . . . . . . . . . . 303
Hermitian operator . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Hessenberg decomposition . . . . . . . . . . . . . . . . . . . 167
history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
history of commands . . . . . . . . . . . . . . . . . . . . . . . . . 20
Concept Index 333
I
if statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
improving Octave . . . . . . . . . . . . . . . . . . . . . . 300, 303
incorrect error messages . . . . . . . . . . . . . . . . . . . . . 300
incorrect output. . . . . . . . . . . . . . . . . . . . . . . . 300, 302
incorrect results . . . . . . . . . . . . . . . . . . . . . . . . 300, 302
increment operator. . . . . . . . . . . . . . . . . . . . . . . . . . . 73
infinity norm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
initialization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
input conversions, for scanf . . . . . . . . . . . . . . . . . 125
input history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
installation trouble . . . . . . . . . . . . . . . . . . . . . . . . . 299
installing Octave. . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
invalid input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
J
job hunting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
K
keywords. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
known causes of trouble . . . . . . . . . . . . . . . . . . . . . 299
L
language definition. . . . . . . . . . . . . . . . . . . . . . . . . . 321
less than operator. . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
lists. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
loadable function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
logging commands and output . . . . . . . . . . . . . . . . 24
logical expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
logical operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
looping over structure elements . . . . . . . . . . . . . . . 84
LP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
LU decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . 168
lvalue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
M
mapping function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
matching failure, in scanf . . . . . . . . . . . . . . . . . . . 124
matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
matrix multiplication . . . . . . . . . . . . . . . . . . . . . . . . 67
maximum field width (scanf). . . . . . . . . . . . . . . . 125
messages, error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
minimum field width (printf) . . . . . . . . . . . . . . . 120
money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
N
negation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
NLP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
nonlinear equations . . . . . . . . . . . . . . . . . . . . . . . . . 173
nonlinear programming . . . . . . . . . . . . . . . . . . . . . 179
not operator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
numeric constant . . . . . . . . . . . . . . . . . . . . . . . . . 29, 31
numeric value . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29, 31
O
Octave command options. . . . . . . . . . . . . . . . . . . . . 13
ODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
on-line help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
operator precedence. . . . . . . . . . . . . . . . . . . . . . . . . . 74
operators, arithmetic. . . . . . . . . . . . . . . . . . . . . . . . . 67
operators, assignment . . . . . . . . . . . . . . . . . . . . . . . . 72
operators, boolean . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
operators, decrement . . . . . . . . . . . . . . . . . . . . . . . . . 73
operators, increment . . . . . . . . . . . . . . . . . . . . . . . . . 73
operators, logical . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
operators, relational. . . . . . . . . . . . . . . . . . . . . . . . . . 69
optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
options, Octave command . . . . . . . . . . . . . . . . . . . . 13
or operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
oregonator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
otags. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
otherwise statement. . . . . . . . . . . . . . . . . . . . . . . . . 81
output conversions, for printf. . . . . . . . . . . . . . . 120
P
partial fraction expansion . . . . . . . . . . . . . . . . . . . 208
patches, submitting . . . . . . . . . . . . . . . . . . . . . . . . . 303
plotting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
precision (printf) . . . . . . . . . . . . . . . . . . . . . . . . . . 120
printing notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
program, self contained. . . . . . . . . . . . . . . . . . . . . . . 26
programs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
prompt customization . . . . . . . . . . . . . . . . . . . . . . . . 23
Q
QP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
QR factorization. . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
quadratic programming . . . . . . . . . . . . . . . . . . . . . 179
quitting octave . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5, 16
quotient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
334 GNU Octave
R
range expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
relational operators . . . . . . . . . . . . . . . . . . . . . . . . . . 69
reporting bugs . . . . . . . . . . . . . . . . . . . . . . . . . 300, 301
results, incorrect . . . . . . . . . . . . . . . . . . . . . . . 300, 302
S
Schur decomposition . . . . . . . . . . . . . . . . . . . . . . . . 170
script files. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
self contained programs . . . . . . . . . . . . . . . . . . . . . . 26
short-circuit evaluation. . . . . . . . . . . . . . . . . . . . . . . 71
side effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
singular value decomposition . . . . . . . . . . . . . . . . 170
speedups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
standards of coding style . . . . . . . . . . . . . . . . . . . . 293
startup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
startup files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
strings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29, 37
structure elements, looping over. . . . . . . . . . . . . . . 84
structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29, 45
submitting diffs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
submitting patches. . . . . . . . . . . . . . . . . . . . . . . . . . 303
subtraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
suggestions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
switch statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
T
TAGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
tests for equality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
tips. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
transpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
transpose, complex-conjugate . . . . . . . . . . . . . . . . . 67
troubleshooting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
try statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
U
unary minus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
undefined behavior. . . . . . . . . . . . . . . . . . . . . . . . . . 300
undefined function value . . . . . . . . . . . . . . . . . . . . 300
unwind_protect statement . . . . . . . . . . . . . . . . . . . 87
unwind_protect_cleanup . . . . . . . . . . . . . . . . . . . . 87
use of comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
user-defined data types. . . . . . . . . . . . . . . . . . . . . . . 30
user-defined functions . . . . . . . . . . . . . . . . . . . . . . . . 91
user-defined variables . . . . . . . . . . . . . . . . . . . . . . . . 53
V
variable descriptions . . . . . . . . . . . . . . . . . . . . . . . . . 11
Variable-length argument lists . . . . . . . . . . . . . . . . 95
Variable-length return lists . . . . . . . . . . . . . . . . . . . 96
variables, global . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
variables, user-defined . . . . . . . . . . . . . . . . . . . . . . . . 53
W
warranty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
while statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
wrong answers . . . . . . . . . . . . . . . . . . . . . . . . . 300, 302
Variable Index 335
Variable Index
A
all_va_args . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
ans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
argv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
automatic_replot . . . . . . . . . . . . . . . . . . . . . . 57, 132
B
beep_on_error. . . . . . . . . . . . . . . . . . . . . . . . . . 57, 108
C
completion_append_char . . . . . . . . . . . . . . . . . 20, 57
crash_dumps_octave_core . . . . . . . . . . . . . . . 58, 114
D
default_eval_print_flag . . . . . . . . . . . . . . . . 57, 77
default_global_variable_value . . . . . . . . . . . . . 54
DEFAULT_LOADPATH . . . . . . . . . . . . . . . . . . . . . . . 56, 99
default_return_value . . . . . . . . . . . . . . . . . . . 57, 95
default_save_format . . . . . . . . . . . . . . . . . . . 58, 114
define_all_return_values . . . . . . . . . . . . . . . 58, 95
do_fortran_indexing . . . . . . . . . . . . . . . . . . . . 58, 63
do_what_i_mean_not_what_i_say . . . . . . . . . . . . . 11
E
e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
echo_executing_commands . . . . . . . . . . . . . . . . . . . 24
EDITOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22, 56, 61
empty_list_elements_ok . . . . . . . . . . . . . . . . . 35, 58
eps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
error_text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
EXEC_PATH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57, 284
F
F_DUPFD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
F_GETFD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
F_GETFL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
F_SETFD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
F_SETFL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
false . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
fixed_point_format . . . . . . . . . . . . . . . . . . . . . 34, 58
G
gnuplot_binary. . . . . . . . . . . . . . . . . . . . . . . . . 58, 141
gnuplot_command_axes. . . . . . . . . . . . . . . . . . . . . . 142
gnuplot_command_end. . . . . . . . . . . . . . . . . . . . . . . 142
gnuplot_command_plot. . . . . . . . . . . . . . . . . . . . . . 142
gnuplot_command_replot . . . . . . . . . . . . . . . . . . . 142
gnuplot_command_splot . . . . . . . . . . . . . . . . . . . . 142
gnuplot_command_title . . . . . . . . . . . . . . . . . . . . 142
gnuplot_command_using . . . . . . . . . . . . . . . . . . . . 142
gnuplot_command_with. . . . . . . . . . . . . . . . . . . . . . 142
gnuplot_has_frames. . . . . . . . . . . . . . . . . . . . . . . . 141
gnuplot_has_multiplot . . . . . . . . . . . . . . . . . . . . 142
H
history_file . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22, 58
history_size . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22, 58
I
i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
If . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54, 73, 104
ignore_function_time_stamp. . . . . . . . . . . . . 58, 99
IMAGEPATH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
implicit_num_to_str_ok . . . . . . . . . . . . . . . . . 42, 58
implicit_str_to_num_ok . . . . . . . . . . . . . . . . . 42, 58
inf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
Inf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
INFO_FILE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17, 57
INFO_PROGRAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17, 57
J
j . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
J . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
L
LOADPATH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57, 99
M
MAKEINFO_PROGRAM . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
max_recursion_depth . . . . . . . . . . . . . . . . . . . . 59, 67
336 GNU Octave
N
nan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
NaN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
nargin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
nargout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
O
O_APPEND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
O_ASYNC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
O_NONBLOCK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
O_RDONLY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
O_RDWR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
O_SYNC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
O_WRONLY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
OCTAVE_EXEC_PATH . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
OCTAVE_HISTFILE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
OCTAVE_HISTSIZE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
OCTAVE_HOME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
OCTAVE_INFO_FILE . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
OCTAVE_INFO_PROGRAM. . . . . . . . . . . . . . . . . . . . . . . . 61
OCTAVE_PATH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
OCTAVE_VERSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
ok_to_lose_imaginary_part. . . . . . . . . . . . . 59, 150
output_max_field_width . . . . . . . . . . . . . . . . . 33, 59
output_precision . . . . . . . . . . . . . . . . . . . . . . . 33, 59
P
page_output_immediately . . . . . . . . . . . . . . . . . . 109
page_screen_output . . . . . . . . . . . . . . . . . . . . 59, 109
PAGER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57, 109
pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
prefer_column_vectors . . . . . . . . . . . . . . . . . . 59, 64
prefer_zero_one_indexing . . . . . . . . . . . . . . . . . . 64
print_answer_id_name . . . . . . . . . . . . . . . . . . 59, 112
print_empty_dimensions . . . . . . . . . . . . . . . . . 34, 59
program_invocation_name . . . . . . . . . . . . . . . . . . . 15
program_name . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
propagate_empty_matrices . . . . . . . . . . . . . . . . . . 35
PS1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23, 57
PS2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23, 57
PS4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23, 57
R
realmax. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
realmin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
resize_on_range_error . . . . . . . . . . . . . . . . . . 59, 65
return. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
return_last_computed_value. . . . . . . . . . . . . 59, 98
S
save_precision. . . . . . . . . . . . . . . . . . . . . . . . . 59, 115
saving_history. . . . . . . . . . . . . . . . . . . . . . . . . . 22, 59
SEEK_CUR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
SEEK_END . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
SEEK_SET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
silent_functions . . . . . . . . . . . . . . . . . . . . . . . 60, 93
split_long_rows. . . . . . . . . . . . . . . . . . . . . . . . . 33, 60
stderr. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
stdin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
stdout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
string_fill_char . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
struct_levels_to_print . . . . . . . . . . . . . . . . . 46, 60
suppress_verbose_help_message . . . . . . . . . 18, 60
T
treat_neg_dim_as_zero . . . . . . . . . . . . . . . . . 60, 150
true . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
W
warn_assign_as_truth_value. . . . . . . . . . . . . 60, 81
warn_comma_in_global_decl . . . . . . . . . . . . . . . . . 60
warn_divide_by_zero . . . . . . . . . . . . . . . . . . . . 60, 69
warn_function_name_clash . . . . . . . . . . . . . . 60, 100
warn_future_time_stamp . . . . . . . . . . . . . . . . . . . 100
warn_missing_semicolon . . . . . . . . . . . . . . . . . . . . 93
warn_reload_forces_clear . . . . . . . . . . . . . . 60, 103
warn_separator_insert . . . . . . . . . . . . . . . . . . . . . 32
warn_single_quote_string . . . . . . . . . . . . . . . . . . 42
warn_variable_switch_label. . . . . . . . . . . . . 60, 82
whitespace_in_literal_matrix. . . . . . . . . . . 32, 60
Function Index 337
Function Index
(
([w type. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
(c, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
(x). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
=
=. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262, 264
[
[pval, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
A
abcddim. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
abs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
acos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
acosh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
acot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
acsc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
acsch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
airy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
all . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
analdemo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
anova. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
any . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
append. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
arch_fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
arch_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
are . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
arg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
arma_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
asctime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
asec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
asech. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
asin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
asinh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
atan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
atan2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
atanh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
atexit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
autocor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
autocov. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
autoreg_matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
axis2dlim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
B
balance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
bar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
bartlett . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
bartlett_test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
bddemo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
besselh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
besseli. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
besselj. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
besselk. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
bessely. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
beta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
beta_cdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
beta_inv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
beta_pdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
beta_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
betainc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
bin2dec. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
bincoeff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
binomial_cdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
binomial_inv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
binomial_pdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
binomial_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
blackman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
blanks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
bode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
bode_bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
bottom_title. . . . . . . . . . . . . . . . . . . . . . . . . . 139, 141
bug_report . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300, 301
buildssic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
C
c2d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
cauchy_cdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
cauchy_inv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
cauchy_pdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
cauchy_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
cd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10, 288
ceil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
center. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
chdir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10, 288
chisquare_cdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
chisquare_inv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
chisquare_pdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
chisquare_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
chisquare_test_homogeneity . . . . . . . . . . . . . . . 186
chisquare_test_independence . . . . . . . . . . . . . . 186
chol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
clc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
clear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
338 GNU Octave
clearplot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
clg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
clock. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
cloglog. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
closeplot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
colloc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
colormap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
columns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
com2str. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
common_size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
commutation_matrix. . . . . . . . . . . . . . . . . . . . . . . . 161
compan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
complement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
completion_matches. . . . . . . . . . . . . . . . . . . . . . . . . 20
computer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
cond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
conj . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
contour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
conv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
cor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
cor_test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
corrcoef . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
cos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
cosh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
cot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
coth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
cov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
cputime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
create_set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
cross. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
csc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
csch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
ctime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
ctrb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
cumprod. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
cumsum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
D
d2c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
damp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
dare . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
dassl. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
dassl_options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
dcgain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
deblank. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
dec2bin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
dec2hex. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
deconv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
DEMOcontrol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
det . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
detrend. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
dgkfdemo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
dgram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
diag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
diary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
diff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
dir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
discrete_cdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
discrete_inv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
discrete_pdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
discrete_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
disp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
dkalman. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
dlqe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
dlqr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
dlyap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
dmr2d. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
dmult. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
do_string_escapes . . . . . . . . . . . . . . . . . . . . . . . . . . 41
document. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
dot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
dre . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
dup2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
duplication_matrix. . . . . . . . . . . . . . . . . . . . . . . . 161
durbinlevinson . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
E
echo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
edit_history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
eig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
empirical_cdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
empirical_inv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
empirical_pdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
empirical_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
endgrent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
endpwent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
erf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
erfc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
erfinv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
etime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
eval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
exec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
exist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
exit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
exp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
expm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
exponential_cdf . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
exponential_inv . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
exponential_pdf . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
Function Index 339
exponential_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
F
f_cdf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
f_inv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
f_pdf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
f_rnd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
f_test_regression. . . . . . . . . . . . . . . . . . . . . . . . . 187
fclose. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
fcntl. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
fdisp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
feof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
ferror. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
feval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
fflush. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
fft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
fft2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
fftconv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
fftfilt. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
fftshift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
fgetl. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
fgets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
figure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
file_in_loadpath . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
file_in_path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
filter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
find . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
findstr. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
finite. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
fir2sys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
fix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
fliplr. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
flipud. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
floor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
fnmatch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
foo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
fopen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
fork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
format. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
fprintf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
fputs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
fractdiff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
frdemo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
fread. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
freport. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
freqchkw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
freqz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
frewind. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
fscanf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
fseek. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
fsolve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
fsolve_options . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
ftell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
fv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
fvl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
fwrite. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
G
gain, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
gamma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
gamma_cdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
gamma_inv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
gamma_pdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
gamma_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
gammainc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
gammaln. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
gcd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
geometric_cdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
geometric_inv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
geometric_pdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
geometric_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
getegid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
getenv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
geteuid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
getgid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
getgrent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
getgrgid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
getgrnam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
getpgrp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
getpid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
getppid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
getpwent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
getpwnam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
getpwuid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
getrusage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
getuid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
givens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
glob . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
gls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
gmtime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
gplot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
gram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
graw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
gray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
gray2ind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
gset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
gshow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
gsplot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
340 GNU Octave
H
h2norm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
hamming. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
hankel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
hanning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
hess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
hex2dec. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
hilb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
hinf_ctr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
hinfdemo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
hinfnorm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
hinfsyn. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
hinfsyn_chk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
hinfsyn_ric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
hist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
history. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
hold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
home . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
hotelling_test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
hotelling_test_2 . . . . . . . . . . . . . . . . . . . . . . . . . . 187
housh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
hurst. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
hypergeometric_cdf. . . . . . . . . . . . . . . . . . . . . . . . 197
hypergeometric_inv. . . . . . . . . . . . . . . . . . . . . . . . 197
hypergeometric_pdf. . . . . . . . . . . . . . . . . . . . . . . . 197
hypergeometric_rnd. . . . . . . . . . . . . . . . . . . . . . . . 197
I
ifft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
ifft2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
imag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
imagesc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
impulse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
imshow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
ind2gray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
ind2rgb. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
input. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
int2str. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
intersection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
inv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
inverse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
invhilb. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
iqr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
irr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
is_abcd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
is_bool. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
is_complex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
is_controllable . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
is_detectable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
is_dgkf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
is_digital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
is_duplicate_entry. . . . . . . . . . . . . . . . . . . . . . . . 143
is_global . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
is_leap_year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
is_list. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
is_matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
is_observable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
is_sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
is_scalar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
is_signal_list . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
is_siso. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
is_square . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
is_stabilizable . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
is_stable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
is_stream . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
is_struct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
is_symmetric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
is_vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
isalnum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
isalpha. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
isascii. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
iscell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
iscntrl. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
isdigit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
isempty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
isgraph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
ishold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
isieee. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
isinf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
islower. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
isnan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
isnumeric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
isprint. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
ispunct. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
isreal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
isspace. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
isstr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
isupper. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
isxdigit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
J
jet707. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
Function Index 341
K
kbhit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
kendall. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
keyboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
kolmogorov_smirnov_cdf . . . . . . . . . . . . . . . . . . . 198
kolmogorov_smirnov_test . . . . . . . . . . . . . . . . . . 187
kolmogorov_smirnov_test_2 . . . . . . . . . . . . . . . . 188
kron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
kruskal_wallis_test. . . . . . . . . . . . . . . . . . . . . . . 188
krylov. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
kurtosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
L
laplace_cdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
laplace_inv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
laplace_pdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
laplace_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
lcm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
lgamma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
lin2mu. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
linspace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
loadaudio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
loadimage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
localtime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
log . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
log10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
log2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
logistic_cdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
logistic_inv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
logistic_pdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
logistic_regression. . . . . . . . . . . . . . . . . . . . . . . 192
logistic_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
logit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
loglog. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
logm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
lognormal_cdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
lognormal_inv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
lognormal_pdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
lognormal_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
logspace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
lqe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
lqg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
lqr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
ls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
lsim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
lsode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
lsode_options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
lstat. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
ltifr. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
lu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
lyap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
M
mahalanobis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
manova. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
mcnemar_test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
meansq. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
median. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
meshdom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
meshgrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
mkdir. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
mkfifo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
mktime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
moddemo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
moment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
more . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
mplot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
mu2lin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
multiplot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
N
nargchk. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
newtroot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
nextpow2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
norm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
normal_cdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
normal_inv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
normal_pdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
normal_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
nper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
npv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
nth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
ntsc2rgb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
null . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
num2str. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
nyquist. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
O
obsv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
ocean. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
octave_config_info. . . . . . . . . . . . . . . . . . . . . . . . 290
ols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
oneplot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
ones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
342 GNU Octave
ord2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
orth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
P
parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
pascal_cdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
pascal_inv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
pascal_pdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
pascal_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
pause. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
pclose. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
periodogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
perror. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
pinv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
place. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
playaudio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
plot_border . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
pmt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
poisson_cdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
poisson_inv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
poisson_pdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
poisson_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
polar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
poly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
polyderiv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
polyfit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
polyinteg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
polyreduce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
polyval. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
polyvalm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
popen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
popen2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
postpad. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
pow2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
ppplot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
prepad. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
printf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
probit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
prod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
prompt. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
prop_test_2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
purge_tmp_files . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
putenv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
puts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
pv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
pvl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
pwd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
pzmap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
Q
qconj. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
qcoordinate_plot . . . . . . . . . . . . . . . . . . . . . . . . . . 274
qderiv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
qderivmat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
qinv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
qmult. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
qqplot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
qr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
qtrans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
qtransv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
qtransvmat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
quad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
quad_options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
quaternion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
quit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
qz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
qzhess. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
qzval. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
R
rand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
randn. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
randperm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
rank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
ranks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
read_readline_init_file . . . . . . . . . . . . . . . . . . . 22
readdir. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
real . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
record. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
rectangle_lw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
rectangle_sw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
rehash. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
rem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
rename. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
replot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
reshape. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
residue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
reverse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
rgb2ind. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
rgb2ntsc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
rindex. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
rldemo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
rlocus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
rmdir. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
roots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
rot90. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
round. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
rows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Function Index 343
run_count . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
run_history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
run_test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
S
save . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
saveaudio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
saveimage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
schur. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
sec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
sech . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
semilogx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
semilogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
setgrent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
setpwent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
setstr. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
shg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132, 135
shift. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
show . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
sign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
sign_test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
sin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
sinc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
sinetone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
sinewave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
sinh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
skewness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
sleep. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
sort . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
sortcom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
spearman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
spectral_adf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
spectral_xdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
spencer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
splice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
split . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
sprintf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
sqrt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
sqrtm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
ss2sys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
ss2tf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
ss2zp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
sscanf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
stairs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
starp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
stat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
std . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
stdnormal_cdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
stdnormal_inv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
stdnormal_pdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
stdnormal_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
str2mat. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
str2num. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
strcat. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
strcmp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
strerror . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
strftime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
strrep. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
struct_contains . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
struct_elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
studentize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
subplot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
substr. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
subwindow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
sum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
sumsq. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
svd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
syl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
sylvester_matrix . . . . . . . . . . . . . . . . . . . . . . . . . . 151
synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
sys2fir. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
sys2ss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
sys2tf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
sys2zp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
sysadd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
sysappend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
syschnames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
syschtsam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
sysconnect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
syscont. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
sysdimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
sysdisc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
sysdup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
sysgetsignals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
sysgettsam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
sysgettype . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
sysgroup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
sysmin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
sysmult. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
sysout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
sysprune . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
sysreorder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
sysrepdemo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
sysscale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
syssetsignals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
syssub. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
sysupdate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
344 GNU Octave
T
t_cdf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
t_inv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
t_pdf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
t_rnd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
t_test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
t_test_2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
t_test_regression. . . . . . . . . . . . . . . . . . . . . . . . . 190
table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
tan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
tanh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
tf2ss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
tf2sys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
tf2zp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
tfout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
tic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
tilde_expand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
title. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
tmpnam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
toascii. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
toc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
toeplitz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
tolower. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
top_title . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
toupper. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
trace. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
triangle_lw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
triangle_sw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
tril . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
triu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
typeinfo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
tzero. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
tzero2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
U
u_test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
ugain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
umask. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
undo_string_escapes. . . . . . . . . . . . . . . . . . . . . . . . 41
uniform_cdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
uniform_inv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
uniform_pdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
uniform_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
union. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
unlink. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
usage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
usleep. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
V
va_arg. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
va_start. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
vander. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
var . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
var_test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
vec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
vech . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
vol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
vr_val. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
W
waitpid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
warning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
weibull_cdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
weibull_inv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
weibull_pdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
weibull_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
welch_test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
wgt1o. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
which . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
who . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
whos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
wiener_rnd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
wilcoxon_test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
X
xlabel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
xor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Y
ylabel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
yulewalker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
Z
z_test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
z_test_2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
zeros. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
zgfmul. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
zgfslv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
zginit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
zgreduce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
zgrownorm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
zgscal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
zgsgiv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
zgshsr. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
zlabel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
zp2ss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
zp2sys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
zp2tf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
zpout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Operator Index 345
Operator Index
!
!. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
!= . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
&
&. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
&& . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
’
’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29, 37, 68
(
( . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
)
) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
*
* . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
** . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
,
,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
-
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
-- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
.
.’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
.*. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
.** . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
./. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
.+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
.^. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
.\. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
/
/ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
:
:. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
;
;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
=
=. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
== . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
[
[. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
]
]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
|
| . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
|| . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
~
~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
~= . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
"
". . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29, 37
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
++ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
>
> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
>= . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
^
^ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
\
\ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
346 GNU Octave
<
< . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
<= . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
<> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69