General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Bi7740: Scientific computing
Matlab remider
Vlad Popovici
popovici@iba.muni.cz
Institute of Biostatistics and Analyses
Masaryk University, Brno
March 11, 2014
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Outline
1 General purpose commands
2 Arrays
3 Mathematical operations
4 Programming with Matlab
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Help and paths
doc, help, helpdesk, helpwin, lookfor: different ways of
obtaining help
docopt: (on UNIX) path where the help files reside
addpath, path, pathtool, rmpath: manage search paths
for functions
lasterr, lastwarn: last error and warning
type, what, which: list a file, list a directory, locate functions
and files
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Creating arrays
var = [val1 val2 ...] row vector from values
var = [val1; val2; ...] column vector from values;
equivalent to var = [val1 val2 ...]' (' is the
transposition operator)
equally spaced data: <low>:<step>:<high>; is <step> is 1,
omit :<step>. Example: 1:2:10, 1:10, 1.5:0.1:2.1. last
value might not be in the generated sequence
decreasing sequences: as above, with negative <step>:
20:−5:0
equally spacing of an interval:
linspace(<first>,<last>,<number_of_values>)
<first> and <last> values will be in the sequence
logarithmically equally space points: logspace
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Creating 2D arrays - matrices
var = [a11, a12,...; a21, a22,...; ...] from
values
you can use vector generators, as before, for the rows of the
matrix
zeros(m,n), ones(m,n), eye(m): all-zeros, all-ones, or
identity matrix with m rows and n columns
transpose of X: X'
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Arrays dimension
size(a), size(b), size(b,2)
length(a): for vectors
numel(b): total number of elements
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Addressing the elements of an array
by index: a = 1:3:10; a(1) and
b = [1:4;5:8]; b(1,2)
by index vectors: a(1:2), b(1,:), b(2,2:end): end gives
the last index in the corresponding dimension of an array
all elements as a row vector: a(:), b(:): column-by-column
ordering of matrix elements (column-major)
you can use single index for n-dimensional arrays too! Pay
attention to ordering of elements: b(1:5)
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Extending/reducing arrays
arrays are dynamical structures, you can add a new value
beyond the dimension of the array: b(3,3)= 13: Matlab adds
0s to fill-in to the required new dimension
this operation is expensive: better pre-allocate the array!
concatenation: [a a], [a;a]: the arrays must be consistent
general concatenation: cat(...)
delete elements: replace them by empty arrays:
c = b; c(3,:)= []. You have to keep the shape of the
array!
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
(Re-)shaping the array
reshape(b, <new_extent_specification>). The total
number of elements must not change!
reshape(b, [1,2,2,3])
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Strings
s = 'ab cd ef'
s = char('aaa', 'bb', 'c') rows are the strings given
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Basic operators
The arrays must have conforming shapes/sizes, depending on the
operation.
+,−,*,^ classical matrix operators (addition, subtraction,
multiplication, power)
/: matrix division, related to the inverse (we discussed)
.*,.^,./ element-wise operations
scalars are multicast: [1 2 3; 4 5 6] * 2 and operation is
kept element-wise
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Some basic built-in functions for arrays
Usually, the summaries are column-wise - see the help for details
min(b), min(b, 4), [m,n] = min(b) max(...)
mean(...), median(...), std(...)
sum(...), prod(...)
dot(...,..): dot(a,a) is the same as a*a'
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Random arrays
rand(m,n): random uniformly distributed numbers between 0
and 1, in the form of a matrix (or vector, or scalar, depending
on m and n)
randperm(n): random permutation of 1:n vector
randperm(n,k) random selection of k elements out of 1:n
randi(imax, m, n): random uniformly distributed integers
between 1 and imax, in the form of a matrix (or vector, or
scalar)
randn(...): normally distributed random numbers: try
hist(randn(1000, 1))
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Relational operators
Check help precedence for precedence of operators!
relational operators: <, >, =<, ≥, ==, ∼=
the result is either logical 1 (true) or logical 0 (false) and has
the shape of the operands (after bringing them to compatible
shapes)
example: mod(1:10,5)< 3
logical results can be used to address elements of arrays:
a = randn(4); a(a < 0.5) what happend?
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Logical operators and functions
AND: x & y, and(x, y)
OR: x | y, or(x, y)
NOT: ∼x, not(x)
XOR: xor(x,y)
all(x), any(x), find(x)
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Conditional branching
1 if <conditional statement 1>
2 <block 1>
3 [elseif <conditional statement 2>
4 <block 2>]
5 ..........
6 [else
7 <block 3>]
8 end
One-liner: if <cond> instruction; end
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
1 switch <expression>
2 case value1
3 <block 1>
4 case {value2, value3,...}
5 <block 2>
6 ..........
7 otherwise
8 <block n>
9 end
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Loops
1 for iterator = sequence
2 <block>
3 end
4
5 while <condition_is_true>
6 <block>
7 end
continue skips the rest of the block and jumps to the next
iteration (if any)
break: breaks out of the loop; if it is outside a loop, it
terminates the script/function
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Functions
One visible function per <function_name>.m file.
1 function [<output>] = <name>(<parameters>)
2 % document your function here
3
4 % process arguments
5 if nargin < ...
6 ...
7 end
8
9 <block>
10
11 % prepare the return values
12 if nargout...
13 ...
14 end
15 end % or return: not mandatory, but a good practice
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
usually, the variables created in the functions are local
use global <variable> to declare that a variable is from
the global environment (put globals at the top of the file)
the file with the function must be in the search path of Matlab
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Anonymous functions
1 <function_name> = @(arguments) <expression>
2
3 cube = @(x) x.^3
<expression> must be a single valid Matlab expression
you can use also variables from the context in which the
anonymous function is defined
anonymous functions can be used as parameters for other
functions
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Inline functions
1 <function_name> = inline('mathematical expression ...
as a string')
2
3 square = inline('x .^ 2')
4 square(1:5)
5 quad = inline('x .^ 2 + y .^ 2 + dot(x,y)', 'x', 'y')
if you do not provide explicit parameters, they are deduced
from the expression and ordered alphabetically in the
argument list
you cannot use i and j as variables
the inline functions can be used as arguments for other
functions
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Functions as arguments
@function_name gives you a function handle, that can be used
for calling the function itself.
1 function y = funplot(F, x0, x1)
2 x = linspace(x0, x1, 100);
3 y = F(x);
4 plot(x, y);
5 return
6
7 funplot(@cos, 0, 2*pi)
8 funplot(square, −3, 3)
9 funplot(@(x) x .^ 3, 0, 5)
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Subfunctions
In a file "main_function.m":
1 function ...= main_function(...)
2 end
3
4 function ...= subfunction_1(...)
5 ...
6 end
7
8 function ...= subfunction_2(...)
9 ...
10 end
Vlad Bi7740: Scientific computing
General purpose commands
Arrays
Mathematical operations
Programming with Matlab
Nested functions
1 function ...= A(...)
2 function ...= B(...)
3 ...
4 end
5 ...
6 function ...= C(...)
7 ...
8 end
9 ...
10 end
Vlad Bi7740: Scientific computing