# prirazeni hodnoty (value assignment)
x <- -7
x = -7

x = 10

x == 0
x != 0
x == 10
x != 10
x>0
x<0
x>=0
x>=10
x<=10
-x>=10


### Matematicke funkce (mathematic function)

# absolutni hodnota (absolute value)
abs(x)


# nasobeni a deleni (multiplication and division)
3*3
x*3
9/3
x/3
(x-3)/(x/3)


1/0
log(0)
Inf*Inf
Inf/Inf
0/0

# celociselne deleni (intager division)
13%/%2
library(numbers)
div(13,2)  
# zbytek po deleni (reminder after division)
13%%2
mod(13,2) 

library(numbers) # Determine whether p is the power of an integer.
isIntpower(144)
isIntpower(8)


library(schoolmath)

x <- c(1.002, 2, 3.14, 4, 5, 6.31, 7) 
schoolmath::is.decimal(x)
schoolmath::is.whole(x)

library(FRACTION)
FRACTION::is.wholenumber(x, tol = .Machine$double.eps^0.5)


x <- c(1, 2, 3, 4, 5, 6, 7) 
schoolmath::is.even(x)
schoolmath::is.odd(x)
x %% 2 == 0 
x %% 2 != 0
is.even <- function(x) x %% 2 == 0; is.even(x) 
is.odd <- function(x) x %% 2 != 0; is.odd(x) 


x <- c(-1, -2, 3.02, 4, -5.2, 6, -7) 
schoolmath::is.negative(x)
schoolmath::is.positive(x)
schoolmath::is.real.positive(x)

x <- c(1, 2, 3, 4, 5, 6, 7) 
schoolmath::is.prim(x)
library(DescTools)
DescTools::IsPrime(x)
library(numbers)
numbers::isPrime(x)
library(cmna)
cmna::isPrime(x)

is.integer(x)
library(ttutils)
isInteger(x)
isInteger(c("test", 1, 2, 2.1)) # vektor (vector)


### Rozklad na prvocísla (decomposition to primes) ###

library(schoolmath)
schoolmath::prime.factor(21) 
schoolmath::prime.factor(100)

library(DescTools)
DescTools::Factorize(47)
DescTools::Factorize(seq(101, 111, by=2))

library(numbers)
numbers::primeFactors(21) 


# Find All Primes Less Than n 
library(DescTools)
DescTools::Primes(100)
library(schoolmath)
schoolmath::primes(start = 12, end = 99)
library(numbers) 
numbers::Primes(99)
numbers::Primes(n1 = 12, n2 = 99)

library(numbers) # nejblizsi vyssi prvocislo (nearest higher prime)
numbers::nextPrime(12)
numbers::previousPrime(12)


### Prirozene cislo (intager)
library(litteR)
is_natural_number(12)
is_natural_number(1.2)

library(numbers)
numbers::isNatural(x)


### Prevod desetinných císel na zlomky (Convert decimal numbers to fractions) ###
library(MASS)
fractions(-0.1666667)
fractions(0.14)
fractions(0.4)

x = fractions(-0.1666667)
frsp = strsplit(as.character(x),"/")
as.numeric(frsp[[1]][1]) # citatel (numerator)
as.numeric(frsp[[1]][2]) # jmenovatel (denominator)

library(fractional)
fractional(-0.1666667, eps = 1e-06, maxConv = 20, sync = FALSE)

library(FRACTION)
fra(-0.1666667) # nefunguje (not function)
fra(0.14)
fra(0.4)


### zjednodusení zlomku (fractions simplification) ###
library(schoolmath)
cancel.fraction(42, 56)
cancel.fraction(-167, 100)

fra(-0.1666667) 
cancel.fraction(-1666667, 1e+07) # nefunguje
decimal2fraction(0.1,6)          # funguje


library(fractional)
fractional(-0.1666667, eps = 1e-06, maxConv = 20, sync = FALSE)
numerators(-0.1666667) # vypise citatele (numerator)
denominators(-0.1666667) # vypise jmenovatele (denominator)
numerical(fractional(-0.1666667, eps = 1e-06, maxConv = 20, sync = FALSE))
unfractional(fractional(-0.1666667, eps = 1e-06, maxConv = 20, sync = FALSE))



### Nejvetsí spolecný delitel (greatest common divisor) ###
x = 12
y = 8

library(schoolmath)
schoolmath::gcd(x, y)

library(FRACTION)
FRACTION::gcd(x, y)

library(DescTools)
DescTools::GCD(x, y, na.rm = FALSE)
DescTools::GCD(c(10,12,8), na.rm = FALSE)

library(numbers)
numbers::GCD(12, 10) 
numbers::GCD(46368, 75025)
numbers::mGCD(c(2, 3, 5, 7) * 11)
numbers::mGCD(c(2*3, 3*5, 5*7))

numbers::coprime(12, 10) # maji/nemaji prvociselneho delitele
numbers::coprime(46368, 75025) 




### Nejmensí spolecný násobek (smallest common multiple) ###
x = 12
y = 8

library(schoolmath)
schoolmath::scm(x, y)

library(DescTools)
DescTools::LCM(x, y)
DescTools::LCM(c(12,10,8), na.rm = FALSE)

library(numbers)
numbers::LCM(12, 10) 
numbers::LCM(46368, 75025) 
numbers::mLCM(c(2, 3, 5, 7) * 11) 
numbers::mLCM(c(2*3, 3*5, 5*7))



# odmocnina (root)
sqrt(x)
x^(1/2)
x^(-1/2)

# mocnina (power)
x**2
x^2
x^(-2)

# goniometricke a hyperbolicke funkce (geometric and hyperbolic function)
cos(x)
sin(x)
tan(x)
acos(x)
asin(x)
atan(x)
atan2(y, x)
cospi(x) # cos(pi*x)
sinpi(x) # sin(pi*x)
tanpi(x) # tan(pi*x)
cosh(x)
sinh(x)
tanh(x)
acosh(x)
asinh(x)
atanh(x)

# logaritmy (logarithm)
x = 10
log(x)  # base e
log(x, base = exp(1))  # base e
logb(x, base = exp(1)) # base e
log10(x) # base 10
log(x,base = 10)
log2(x)  # base 2
log(x,base = 2)
log1p(x) # computes log(1+x) 

# exponenty (exponents)
10^x # exponent
10**x # exponent
exp(x)   # e^x


### vektory (vectores) ########################################################################

1:6
c(2:12)
rev(c(2:12))
seq(from=1, to=20, by=2)
seq(5, -5, -1)
seq(from=5, by=-1, along.with = 1:20)
rep(1, len = 9)
rep(1:4, len = 9)
rep(1:4, 2)
rep(1:4, each = 2)       # not the same.
rep(1:4, c(2,2,2,2))     # same as second.
rep(1:4, c(2,1,2,1))
rep(1:4, each = 2, len = 4)    # first 4 only.
rep(1:4, each = 2, len = 10)   # 8 integers plus two recycled 1's.
rep(1:4, each = 2, times = 3)  

# prazdny vektor ()
xx = NULL
is.null(xx)
is.null(x)


# nahodna cisla
sample(12:99, 9, replace = FALSE) # bez opakovani
sort(sample(1:20, 9, replace = FALSE))
sample(12:99, 9, replace = TRUE) # s opakovanim
sort(sample(1:20, 9, replace = TRUE))

# rada prvocísel
library(DescTools)
DescTools::Primes(100)
library(schoolmath)
schoolmath::primes(start = 12, end = 99)
library(numbers) 
numbers::Primes(99)
numbers::Primes(n1 = 12, n2 = 99)

# rada Fibonacciho cisel (z daného rozmezi)
library(numbers)
fibonacci(50, sequence = TRUE) 

# rada náhodných císel z daného rozmezí
# set.seed(123)
runif(n=5, min=0, max=1) # rovnomerne rozdeleni
runif(6,-2,2)
sample(12:99, 9, replace = FALSE) # bez opakovani
sort(sample(1:20, 9, replace = FALSE))
sample(12:99, 9, replace = TRUE) # s opakovanim
sort(sample(1:20, 9, replace = TRUE))
library(gdata)
resample(1:20, 9, replace = FALSE, prob = NULL)
resample(1:20, 9, replace = TRUE, prob = NULL)  # normalni rozdeleni
rnorm(n=6, mean=0, sd=1)
rnorm(6,9,1.5)
rbinom(30,c(0,1),0.5) #mince
rbinom(30,c(1:6),(1/6)) #kostka (dice)


# indexy
set.seed(123)
x = sample(12:99,19, replace = FALSE)
is.vector(x)
x
x[1]
x[1:5]
x[c(1:5)]
x[length(x)]
x[(length(x)-1)]
x[-1]
x[-(1:5)]
x[-c(1:5)]
x[-length(x)]
x[length(x)-3:length(x)]#poslednich 6 hodnot
x[c(1,4,7)]#vybrane hodnoty
which.max(x)
which.min(x)
library(Rmpfr)
which.min(x)
which(x<=50)
x[which(x<=50)]
x[x<=50]
which(x>=50)
x[which(x>=50)]
which(x == max(x))#maximalni hodnota
which(x == 10)
which(x != 10)
x[x > 40]#hodnoty vyssi nez 400.
x[x < 40]#hodnoty mensi nez 100
which(x > 10)#hodnoty vyssi nez 10.
which(x < 10)#hodnoty mensi nez 10.
seq_along(x)

rank(x)  # vhodne pro vektory, nevhodne pro matice 
is.unsorted(x)
sort(x)
sort(x, decreasing = FALSE)
sort(x, decreasing = TRUE)
sort(x[which(x>=50)])
order(x)  # poradi (indexy) pro sort
x[order(x)]


# Vector Arithmetics
a = c(1, 3, 5, 7) 
b = c(1, 2, 4, 8) 
5 * a
a + b 
a - b 
a * b 
a / b

u = c(10, 20, 30) 
v = c(1, 2, 3, 4, 5, 6, 7, 8, 9) 
u + v 

max(x)
min(x)
range(x)
library(DescTools)
Range(x)
sum(x)
cumsum(x)
prod(x)
cumprod(x)
diff(x)
sign(x)


x = sample(12:99, 9, replace = TRUE)
x
unique(x)
table(x)
summary(as.factor(x))
# frekvence vyskytu daneho cisla
sum(x==57)
length(which(x==57))

numbers =c(4,23,4,23,5,43,54,56,657,67,67,435,453,435,7,65,34,435)
table(numbers)[2]==1
numbers[2]
sum(numbers==435)

duplicated(numbers) # identifying duplicated elements 
numbers[duplicated(numbers)]
unique(numbers) # extracting unique elements,

ifelse(x<50,0,1)
x[x<50] = 0
x[x>=50] = 1
x

set.seed(123)
x = sample(12:99,19)
x


### matice ###################################################################

x1 = sample(12:99,19, replace = FALSE)
x2 = sample(12:99,19, replace = TRUE)

x12 = rbind(x1,x2)
x12 = cbind(x1,x2)
is.matrix(x12)
nrow(x12)
ncol(x12)

x12[order(x1),]
x12[order(x2),]
x12[,1]
x12[,"x"]

colnames(x12)
colnames(x12)=c("X","Y")
rownames(x12)
rownames(x12) = LETTERS[1:length(x1)] 


### dataframes ##################################################################################

x1 = sample(12:99,19, replace = FALSE)
x2 = sample(12:99,19, replace = TRUE)
z = LETTERS[1:length(x1)] 

x12 = rbind(x1,x2,z)
x12 = cbind(x1,x2,z)
nrow(x12)
ncol(x12)
is.data.frame(x12)
is.matrix(x12)

as.data.frame(x12)
is.data.frame(x12)
colnames()
rownames()


### lists ###########################################################################################

x1 = sample(12:99,19, replace = FALSE)
x2 = sample(12:99,19, replace = TRUE)
x3 = sample(12:99,19, replace = TRUE)

x123 = list(x1,x2,x3)
is.list(x123)
names(x123) = c("x1","x2","x3") 

unlist(x123)
do.call(rbind,x123)
do.call(cbind,x123)

stack(x123)


##############################################################################################################
##############################################################################################################


#### Fyzikalni konstanty  ##########################################################################################################

### Ludolfovo cislo ####
pi
print(pi, digits=20)

### Eulerovo cislo ####
exp(1)
print(exp(1), digits=20) 

library(marelac)
data(Constants)
Constants

Constants$gasCt1
Constants$gasCt2
Constants$gasCt3
R = as.numeric(Constants$gasCt2[1]); R # hodnota
Constants$gasCt2[2] # jednotka


### Vylepseni
mm = "gas"
consts = do.call(rbind,Constants) # list to dataframe
MM = sapply(consts[,3], function(xxx) grepl(mm, xxx, fixed = TRUE))
SMM = consts[which(MM==TRUE),]
SMM
# zadat poradi polozky ve vystupu
SMM[2,] # pro 1 polozku SMM[1]
R = as.numeric(SMM[2,1]); R # hodnota
SMM[2,2] # jednotka


library(constants)
codata
lookup("planck", ignore.case=TRUE)
lookup("avogadro", ignore.case=TRUE)
lookup("faraday", ignore.case=TRUE)
lookup("molar", ignore.case=TRUE)
lookup("molar mass", ignore.case=TRUE)
lookup("light", ignore.case=TRUE)
lookup("boltzmann", ignore.case=TRUE)
lookup("mass", ignore.case=TRUE)
lookup("mass constant", ignore.case=TRUE)
lookup("proton mass", ignore.case=TRUE)
lookup("electron mass", ignore.case=TRUE)

# Univerzalni plynova konstanta
lookup("gas", ignore.case=TRUE)
codata[214,]
R = as.numeric(codata[214,3]) # hodnota
Ru = as.numeric(codata[214,5]) # nejistota
codata[214,4] # jednotka


#### Atomove a molekulove hmotnosti ###################################################################################################################################

library(periodicTable)
data(periodicTable)
periodicTable

library(CHNOSZ)
# atomova hmotnost
AW = mass("Ca"); AW
# molarni hmotnost
MW = mass("CaCO3"); MW
# pocet atomu prvku ve vzorci
ce = count.elements("CaCO3"); ce
as.chemical.formula(ce, drop.zero = TRUE)

library(NORRRM)# archiv
# atomova hmotnost
data(AtomWeight)
AtomWeight
AW = AtomWeight["Si","AWeight"]; AW
el = c("Ca","Si","Al")
AW = AtomWeight[el,'AWeight']; AW
names(AW) = el
AW

# prepocet na oxidy
data(OxiWeight)
OxiWeight
OxiWeight ['Si','OWeight']


library(IsoSpecR)
data(isotopicData)
isotopicData


#### Prevody jednotek ##########################################################################################################

library(scales) # %
percent(0.05)

library(pracma) # uhly vs radiany
deg2rad(120) 
rad2deg(3.14)


library(measurements)
conv_unit_options # pouzivane jednotky

# length
conv_unit(1, from="mm", to="m")
conv_unit(1, from="nm", to="angstrom")

# pressure
conv_unit(101, from="Pa", to="mmHg")
conv_unit(1, from="atm", to="Pa")

# temperature
conv_unit(100, from="C", to="K")

# energy
conv_unit(500, from="cal", to="J")
conv_unit(1, from="erg", to="J")

#volume
conv_unit(100, from="l", to="m3")

# mass
conv_unit(100, from="g", to="mg")
conv_unit(100, from="ug", to="g")

# speed
conv_unit(1, from="km_per_hr", to="m_per_sec")
conv_unit(1, from="light", to="km_per_hr")
conv_unit(1, from="light", to="m_per_sec")


### multiunits
conv_multiunit(x = 1, from="ug / l", to="g / m3")
conv_multiunit(x = 1, from="mg / l", to="kg / m3")
conv_multiunit(x = 1, from="cal / kg", to="J / g")


### Plynný systém mení svuj objem o 1200 ml za konstantního vnejsího tlaku 30 atm.Jakou práci vykoná plyn pri expanzi? Vyjádrete v ruzných energetických jednotkách.
# W = p . dV
dV = 1200 # [ml]
dV = conv_unit(dV, from="ml", to="m3"); dV
p = 30 # [atm] to [Pa]
p = conv_unit(p, from="atm", to="Pa"); p
W = p*dV; W # [J]
W1 = conv_unit(W, from="J", to="cal"); W1 # [cal]
W2 = conv_unit(W, from="J", to="Wsec"); W2 # [W.s]
W3 = conv_unit(W, from="J", to="erg"); W3 # [erg]


### Kolik tepla se uvolní pri pruchodu 26.43 coulombu elektrického proudu vodicem pri potenciálovém spádu 2.432 V.
# 64.33 J, 64.33e7 erg, 15.37 cal
# Q = U . I . t = U . q 
q = 26.43 # [C]
U = 2.432 # [V]
Q = U*q; Q # [J]
Q1 = conv_unit(Q, from="J", to="cal"); Q1 # [cal]
Q3 = conv_unit(Q, from="J", to="erg"); Q3 # [erg]


# Prevod casovych jednotek

library(datetime)
xx = as.minute(7658) # 7658 min
as.second(xx)
as.hour(xx)
as.day(xx)


### Pokus trval 7658 minut. Kolik je to dní, hodin a minut?
tt = 7658 # [min]

library(lubridate)
seconds_to_period(tt*60)
library(datetime)
seconds_to_period(as.second(as.minute(tt)))

# opacny vypocet
library(datetime)
dur <- duration(week = 0, day = 5, hours = 7, minutes = 38)
as.numeric(dur, "minutes")


#### nasobky jednotek SI
library(sitools)
f2si(10000)
f2si(0.023, unit="l")
f2si(3.5e-5, unit="mol")
numbers <- c(1e5, 3.5e-12, 0.004) 
f2si(numbers, unit="g")


##############################################################################################################


#### Nacitani externich dat ##########################################################################################################

pisky<- read.table("c:\\Users\\lubop\\Documents\\kurs\\DVpisky1.txt", header=T)
pisky<- read.csv("c:\\Users\\lubop\\Documents\\kurs\\DVpisky1.csv", header=T)

library(openxlsx)
shn = getSheetNames("c:\\Users\\lubop\\Documents\\kurs\\DVpisky1.xlsx")
shn
pisky <- read.xlsx("c:\\Users\\lubop\\Documents\\kurs\\DVpisky1.xlsx", sheet = "DVPisky", startRow = 1, colNames = TRUE, rowNames = TRUE,detectDates = FALSE, skipEmptyRows = TRUE,rows = NULL, cols = NULL,check.names = FALSE)
summary(pisky)
pisky = pisky[,-1]


#### NA and data imputation #####################################################################################################

### vektory

x = pisky[,"Sr"]
length(x)
x[4] = NA
any(is.na(x))
is.na(x)

library(jwutil) # rel. podil hodnot ve vektoru
propIsNa(x)

xx = na.omit(x)
length(xx)


### Matice a dataframes

x = pisky
x[5,5]<- NA
any(is.na(x))
is.na(x)

library(ryouready)
count_na(x, along = 1)
count_na(x, along = 2)
# along: 1 = rows, 2=columns

library(jwutil) # rel. podil hodnot ve sloupcich
propNaPerField(x)

library(agricolae)
delete.na(x, alternative="less")
delete.na(x, alternative="greater")
# "less"    = vynechava sloupce
# "greater" = vynechava radky


### Imputace

library(DescTools)
ZeroIfNA(x)
NAIfZero(x)
#
BlankIfNA(x, blank="")
BlankIfNA(x, blank="UDL")
NAIfBlank(x)

library(jwutil) # NA na 0
zero_na(x)
zero_na(x, na_ish = TRUE)


library(DescTools) # nahrazeni medianem sloupce
x5 = Impute(x[,5], FUN = function(x) median(x, na.rm = TRUE))
rbind(x[,5],x5,pisky[,5])
x[,5] = x5 # nahrazeni

library(compositions) # nahrazeni nasobkem DL
x0 = ZeroIfNA(x) # library(DescTools)
dl=rep(0.1,ncol(x)) # vektor DL
xdl = zeroreplace(x0[,5],d = 0.1,a = 1/2)
x[,5] = xdl # nahrazeni

library(na.tools)
all_na(x)
any_na(x)
is_na(x)
which_na(x[,5])
which_na(x[5,])

xdl = na.replace(x[,5], .na=0.05)
x[,5] = xdl # nahrazeni

na.constant(x[,5], 0.05)
na.max(x[,5])
na.min(x[,5])
na.mean(x[,5])
na.median(x[,5])
na.quantile(x[,5], prob=0.4 )
na.mode(x[,5])
na.most_freq(x[,5])
na.inf(x[,5])
na.neginf(x[,5])
na.true(x[,5])
na.false(x[,5])
na.zero(x[,5])

set.seed(123)
xb = na.bootstrap(x[,5])
xr = na.resample(x[,5])
rbind(x[,5],xb,xr,pisky[,5])



### ZAOKROUHLOVANI ##########################################################################################

# Zaokrouhlovani na dany pocet desetinnych mist #####
round(1234.567,2)
round(123.456,digits=2)

library(guf)
round_something(123.456, decimals = 2)
round_something("123.456", decimals = 2)

library(PKNCA)
roundString(3141.59265, digits = 3, sci_range = 0, sci_sep = "e")
roundString(3141.59265, digits = 3, sci_range = 0, sci_sep = "x10^")
roundString(3141.59265, digits = 3, sci_range = Inf, sci_sep = "e")

# Pocet desetinnych mist daneho cisla
decimalplaces <- function(x) { # error due to rounding double precision floating point numbers -- replacing the x %% 1
  if (abs(x - round(x)) > .Machine$double.eps^0.5) {
    nchar(strsplit(sub('0+$', '', as.character(x)), ".", fixed = TRUE)[[1]][[2]])
  } else { return(0) } }

decimalplaces(3.14) 
decimalplaces(3.1415) 
decimalplaces(3.14159265)


#### Zaokrouhlovani na dany pocet platnych cislic #########
signif(1234.567,4)
signif(123.456,digits=4)

library(PKNCA)
signifString(3141.59265, digits = 1, sci_range = 0, sci_sep = "e")
signifString(3141.59265, digits = 1, sci_range = 0,sci_sep = "x10^")
signifString(3141.59265, digits = 1, sci_range = Inf, sci_sep = "e")

# Urceni poctu platnych cislic daneho cisla
sigdig <- function(x) length(gregexpr("[[:digit:]]", as.character(x))[[1]]) 

sigdig(3.14) 
sigdig(3.1415) 
sigdig(3.14159265)


### Relativni chyba zaokrouhleneho cisla
X = 0.053450
n = 2 # zvoleny pocet platnych cislic
library(PKNCA)
# nacist funkci sigdig()
A = as.numeric(substring(signifString(X, digits = sigdig(X), sci_range = 0, sci_sep = "e"), 1, 1))
s = 1/(2*A*10^(n-1)); s
library(scales)
percent(s)
library(jwutil)
percentize(s)