Basic R commands – 2 – probability distributions

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Basic Commands and Statistics with R – 2 – probability distibutions. R Functions for the most common probability distibutions.

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
# Basic Commands and Statistics with R - 2 - probability distibutions 
# An overview of the most common probability distibutions 
# eg: # https://en.wikipedia.org/wiki/List_of_probability_distributions
# path: ~/ownCloud/STA_Statistics/Basic_Statistics/
# file_name: statistic_basics2.R
# files_used:

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
# Probability Plots

# Distribution                    Functions
#
# Normal                          pnorm       qnorm      dnorm      rnorm
# Beta                            pbeta       qbeta      dbeta      rbeta
# Binomial                        pbinom      qbinom     dbinom     rbinom
# Uniform                         punif       qunif      dunif      runif
# Cauchy                          pcauchy     qcauchy    dcauchy    rcauchy
# Chi-Square                      pchisq      qchisq     dchisq     rchisq
# Exponential                     pexp        qexp       dexp       rexp
# F                               pf          qf         df         rf
# Gamma                           pgamma      qgamma     dgamma     rgamma
# Geometric                       pgeom       qgeom      dgeom      rgeom
# Hypergeometric                  phyper      qhyper     dhyper     rhyper
# Logistic                        plogis      qlogis     dlogis     rlogis
# Log Normal                      plnorm      qlnorm     dlnorm     rlnorm
# Negative Binomial               pnbinom     qnbinom    dnbinom    rnbinom
# Poisson                         ppois       qpois      dpois      rpois
# Student t                       pt          qt         dt         rt
# Studentized Range               ptukey      qtukey     dtukey     rtukey
# Weibull                         pweibull    qweibull   dweibull   rweibull
# Wilcoxon Rank Sum Statistic     pwilcox     qwilcox    dwilcox    rwilcox
# Wilcoxon Signed Rank Statistic  psignrank   qsignrank  dsignrank  rsignrank
# ...

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
# Normal  pnorm, qnorm, dnorm, rnorm

# distribution function
# direct - P ( X < 23.5 )
pn <- pnorm( 23.5, mean = 50, sd = 20 )
str( pn ) 
# num 0.0926

pn <- pnorm( 1:100, mean = 50, sd = 20 )
str( pn )
# num [1:100] 0.0512 0.0548 0.0586 0.0626 0.0668 ...

par( mfrow = c( 1, 2 ) )

hist( pn, main = "normal mean = 50, sd = 20" )
plot( 1:100, pn, main = "normal mean = 50, sd = 20")
abline( h = 0.5, v = 50, col = "red" )

par( mfrow = c( 1, 1 ) )

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

# Basic Commands and Statistics with R - 2 - probability distibutions

# An overview of the most common probability distibutions

# eg: # https://en.wikipedia.org/wiki/List_of_probability_distributions

# path: ~/ownCloud/STA_Statistics/Basic_Statistics/

# file_name: statistic_basics2.R

# files_used:

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

# Probability Plots

# Distribution Functions

# Normal pnorm qnorm dnorm rnorm

# Beta pbeta qbeta dbeta rbeta

# Binomial pbinom qbinom dbinom rbinom

# Uniform punif qunif dunif runif

# Cauchy pcauchy qcauchy dcauchy rcauchy

# Chi-Square pchisq qchisq dchisq rchisq

# Exponential pexp qexp dexp rexp

# F pf qf df rf

# Gamma pgamma qgamma dgamma rgamma

# Geometric pgeom qgeom dgeom rgeom

# Hypergeometric phyper qhyper dhyper rhyper

# Logistic plogis qlogis dlogis rlogis

# Log Normal plnorm qlnorm dlnorm rlnorm

# Negative Binomial pnbinom qnbinom dnbinom rnbinom

# Poisson ppois qpois dpois rpois

# Student t pt qt dt rt

# Studentized Range ptukey qtukey dtukey rtukey

# Weibull pweibull qweibull dweibull rweibull

# Wilcoxon Rank Sum Statistic pwilcox qwilcox dwilcox rwilcox

# Wilcoxon Signed Rank Statistic psignrank qsignrank dsignrank rsignrank

# ...

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

# Normal pnorm, qnorm, dnorm, rnorm

# distribution function

# direct - P ( X < 23.5 )

pn <- pnorm( 23.5, mean = 50, sd = 20 )

str( pn )

# num 0.0926

pn <- pnorm( 1:100, mean = 50, sd = 20 )

str( pn )

# num [1:100] 0.0512 0.0548 0.0586 0.0626 0.0668 ...

par( mfrow = c( 1, 2 ) )

hist( pn, main = "normal mean = 50, sd = 20" )

plot( 1:100, pn, main = "normal mean = 50, sd = 20")

abline( h = 0.5, v = 50, col = "red" )

par( mfrow = c( 1, 1 ) )

# quantile function 
# Inverse - qnorm looks up the p-th quantile of the normal distribution

qn <- qnorm( 0.5, mean = 50, sd = 20 )
str( qn )
# num 50

qn <- qnorm( ( ( 1:100 ) / 100 ), mean = 50, sd = 20 )
str( qn ); qn;
# [1]  3.47  8.93 12.38 14.99 17.10 18.90 20.48 21.90 23.18 24.37 25.47 26.5
#hist(qn,breaks=150)

par( mfrow = c( 1, 2 ) )
hist( qn, main = "normal mean = 50, sd = 20" )
plot( ( ( 1:100 ) / 100 ), qn, main = "normal mean = 50, sd = 20" )
abline( v = 0.5, h = 50, col = "red" )

par( mfrow = c( 1, 1 ) )

# quantile function

# Inverse - qnorm looks up the p-th quantile of the normal distribution

qn <- qnorm( 0.5, mean = 50, sd = 20 )

str( qn )

# num 50

qn <- qnorm( ( ( 1:100 ) / 100 ), mean = 50, sd = 20 )

str( qn ); qn;

# [1] 3.47 8.93 12.38 14.99 17.10 18.90 20.48 21.90 23.18 24.37 25.47 26.5

#hist(qn,breaks=150)

par( mfrow = c( 1, 2 ) )

hist( qn, main = "normal mean = 50, sd = 20" )

plot( ( ( 1:100 ) / 100 ), qn, main = "normal mean = 50, sd = 20" )

abline( v = 0.5, h = 50, col = "red" )

par( mfrow = c( 1, 1 ) )

# invertet plot

par( mfrow = c( 1, 2 ) )

plot( ( ( 1:100 ) / 100 ), qn, main = "normal mean = 50, sd = 20")
abline( h = 150, col = "red" )
plot( qn, ( ( 1:100 ) / 100 ), main = "normal mean = 50, sd = 20")
abline( v = 150, col = "red" )

# invertet plot

par( mfrow = c( 1, 2 ) )

plot( ( ( 1:100 ) / 100 ), qn, main = "normal mean = 50, sd = 20")

abline( h = 150, col = "red" )

plot( qn, ( ( 1:100 ) / 100 ), main = "normal mean = 50, sd = 20")

abline( v = 150, col = "red" )

# Density function

dn <- dnorm( 1:100, mean = 50, sd = 20)
str( dn )
dn

# [1]  0.00099187 0.00111973 0.00126091 0.00141635 0.00158698 0.00177373 
#      0.00197750 0.00219918 0.00243960 0.00269955 0.00297974 0.00328079
# [13] 0.00360324 0.00394751 0.00431387 0.00470245 0.00511325 0.00554604 
#      0.00600045 0.00647588 0.00697153 0.00748637 0.00801917 0.00856843
# [25] 0.00913245 0.00970930 0.01029681 0.01089261 0.01149411 0.01209854 
#      0.01270295 0.01330426 0.01389924 0.01448458 0.01505687 0.01561270
# [37] 0.01614862 0.01666123 0.01714719 0.01760327 0.01802635 0.01841351 
#      0.01876202 0.01906939 0.01933341 0.01955213 0.01972397 0.01984763
# [49] 0.01992220 0.01994711 0.01992220 0.01984763 0.01972397 0.01955213 
#      0.01933341 0.01906939 0.01876202 0.01841351 0.01802635 0.01760327
# [61] 0.01714719 0.01666123 0.01614862 0.01561270 0.01505687 0.01448458 
#      0.01389924 0.01330426 0.01270295 0.01209854 0.01149411 0.01089261
# [73] 0.01029681 0.00970930 0.00913245 0.00856843 0.00801917 0.00748637 
#      0.00697153 0.00647588 0.00600045 0.00554604 0.00511325 0.00470245
# [85] 0.00431387 0.00394751 0.00360324 0.00328079 0.00297974 0.00269955 
#      0.00243960 0.00219918 0.00197750 0.00177373 0.00158698 0.00141635
# [97] 0.00126091 0.00111973 0.00099187 0.00087642

sum( dn )

# [1] 0.98756

par( mfrow = c( 1, 2 ) )
hist( dn, main = "normal mean = 50, sd = 20" )
plot( 1:100, dn, main = "normal mean = 50, sd = 20" )
par( mfrow = c( 1, 1 ) )

# Density function

dn <- dnorm( 1:100, mean = 50, sd = 20)

str( dn )

# [1] 0.00099187 0.00111973 0.00126091 0.00141635 0.00158698 0.00177373

# 0.00197750 0.00219918 0.00243960 0.00269955 0.00297974 0.00328079

# [13] 0.00360324 0.00394751 0.00431387 0.00470245 0.00511325 0.00554604

# 0.00600045 0.00647588 0.00697153 0.00748637 0.00801917 0.00856843

# [25] 0.00913245 0.00970930 0.01029681 0.01089261 0.01149411 0.01209854

# 0.01270295 0.01330426 0.01389924 0.01448458 0.01505687 0.01561270

# [37] 0.01614862 0.01666123 0.01714719 0.01760327 0.01802635 0.01841351

# 0.01876202 0.01906939 0.01933341 0.01955213 0.01972397 0.01984763

# [49] 0.01992220 0.01994711 0.01992220 0.01984763 0.01972397 0.01955213

# 0.01933341 0.01906939 0.01876202 0.01841351 0.01802635 0.01760327

# [61] 0.01714719 0.01666123 0.01614862 0.01561270 0.01505687 0.01448458

# 0.01389924 0.01330426 0.01270295 0.01209854 0.01149411 0.01089261

# [73] 0.01029681 0.00970930 0.00913245 0.00856843 0.00801917 0.00748637

# 0.00697153 0.00647588 0.00600045 0.00554604 0.00511325 0.00470245

# [85] 0.00431387 0.00394751 0.00360324 0.00328079 0.00297974 0.00269955

# 0.00243960 0.00219918 0.00197750 0.00177373 0.00158698 0.00141635

# [97] 0.00126091 0.00111973 0.00099187 0.00087642

sum( dn )

# [1] 0.98756

par( mfrow = c( 1, 2 ) )

hist( dn, main = "normal mean = 50, sd = 20" )

plot( 1:100, dn, main = "normal mean = 50, sd = 20" )

par( mfrow = c( 1, 1 ) )

cumsum(dn)

# [1]  0.00099187 0.00211159 0.00337251 0.00478886 0.00637584 0.00814957 
#      0.01012707 0.01232625 0.01476585 0.01746540 0.02044514 0.02372593
# [13] 0.02732917 0.03127668 0.03559054 0.04029300 0.04540624 0.05095229 
#      0.05695274 0.06342862 0.07040014 0.07788652 0.08590568 0.09447411
# [25] 0.10360657 0.11331587 0.12361268 0.13450529 0.14599940 0.15809794 
#      0.17080089 0.18410515 0.19800440 0.21248897 0.22754584 0.24315854
# [37] 0.25930716 0.27596839 0.29311558 0.31071885 0.32874520 0.34715870 
#      0.36592072 0.38499011 0.40432352 0.42387565 0.44359962 0.46344725
# [49] 0.48336944 0.50331656 0.52323875 0.54308638 0.56281035 0.58236248 
#      0.60169589 0.62076528 0.63952729 0.65794080 0.67596715 0.69357042
# [61] 0.71071761 0.72737884 0.74352746 0.75914015 0.77419702 0.78868160 
#      0.80258085 0.81588511 0.82858806 0.84068660 0.85218071 0.86307331
# [73] 0.87337013 0.88307943 0.89221188 0.90078031 0.90879948 0.91628585 
#      0.92325738 0.92973326 0.93573371 0.94127975 0.94639300 0.95109545
# [85] 0.95540932 0.95935683 0.96296007 0.96624086 0.96922060 0.97192015 
#      0.97435975 0.97655893 0.97853643 0.98031016 0.98189714 0.98331349
# [97] 0.98457440 0.98569413 0.98668600 0.98756241

par( mfrow = c( 1, 2 ) )
plot( 1:100, dn, main = "normal mean=50, sd=20" )
plot( 1:100, cumsum( dn ), main= "normal mean=50, sd=20" ) 

par( mfrow = c( 1,1 ) )

cumsum(dn)

# [1] 0.00099187 0.00211159 0.00337251 0.00478886 0.00637584 0.00814957

# 0.01012707 0.01232625 0.01476585 0.01746540 0.02044514 0.02372593

# [13] 0.02732917 0.03127668 0.03559054 0.04029300 0.04540624 0.05095229

# 0.05695274 0.06342862 0.07040014 0.07788652 0.08590568 0.09447411

# [25] 0.10360657 0.11331587 0.12361268 0.13450529 0.14599940 0.15809794

# 0.17080089 0.18410515 0.19800440 0.21248897 0.22754584 0.24315854

# [37] 0.25930716 0.27596839 0.29311558 0.31071885 0.32874520 0.34715870

# 0.36592072 0.38499011 0.40432352 0.42387565 0.44359962 0.46344725

# [49] 0.48336944 0.50331656 0.52323875 0.54308638 0.56281035 0.58236248

# 0.60169589 0.62076528 0.63952729 0.65794080 0.67596715 0.69357042

# [61] 0.71071761 0.72737884 0.74352746 0.75914015 0.77419702 0.78868160

# 0.80258085 0.81588511 0.82858806 0.84068660 0.85218071 0.86307331

# [73] 0.87337013 0.88307943 0.89221188 0.90078031 0.90879948 0.91628585

# 0.92325738 0.92973326 0.93573371 0.94127975 0.94639300 0.95109545

# [85] 0.95540932 0.95935683 0.96296007 0.96624086 0.96922060 0.97192015

# 0.97435975 0.97655893 0.97853643 0.98031016 0.98189714 0.98331349

# [97] 0.98457440 0.98569413 0.98668600 0.98756241

par( mfrow = c( 1, 2 ) )

plot( 1:100, dn, main = "normal mean=50, sd=20" )

plot( 1:100, cumsum( dn ), main= "normal mean=50, sd=20" )

par( mfrow = c( 1,1 ) )

# Random generations - with specified normal distribution
# random generation for the normal distribution

rn <- rnorm( 100, mean = 50, sd = 20 )
par( mfrow=c( 1, 2 ) )
hist( rn, probability = FALSE, main = "normal mean = 50, sd = 20" )
hist( rn, probability = TRUE, main="normal mean = 50, sd = 20" )
#points( rn, dnorm( rn, mean = 50, sd = 20), col = "red" )
lines( sort( rn ), dnorm( sort( rn ), mean = 50, sd = 20 ), col= "red" )

par ( mfrow = c( 1, 1 ) )

# Random generations - with specified normal distribution

# random generation for the normal distribution

rn <- rnorm( 100, mean = 50, sd = 20 )

par( mfrow=c( 1, 2 ) )

hist( rn, probability = FALSE, main = "normal mean = 50, sd = 20" )

hist( rn, probability = TRUE, main="normal mean = 50, sd = 20" )

#points( rn, dnorm( rn, mean = 50, sd = 20), col = "red" )

lines( sort( rn ), dnorm( sort( rn ), mean = 50, sd = 20 ), col= "red" )

par ( mfrow = c( 1, 1 ) )

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
# distributions for the mtcars data dnorm densities
# https://stat.ethz.ch/R-manual/R-patched/library/datasets/html/mtcars.html

attach( mtcars )

hist(mtcars$mpg, probability = TRUE)
lines( sort( mtcars$mpg ), 
       dnorm( sort( mtcars$mpg ) , 
              mean = mean(mtcars$mpg) ,sd = sd(mtcars$mpg) ), col= "red" )

par( mfrow = c( 3, 4 ) )
for( i in 1:length( mtcars[1,] ) ){ 
  hist( mtcars[,i], probability = TRUE, 
        main = paste( "Data: MTcars", colnames( mtcars )[i] ),
        xlab = paste( colnames( mtcars )[i] ) )
  lines( sort( mtcars[,i] ), 
         dnorm( sort( mtcars[,i] ) , 
                mean = mean( mtcars[,i] ) ,sd = sd( mtcars[,i] ) ), col= "red" )
}

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

# distributions for the mtcars data dnorm densities

# https://stat.ethz.ch/R-manual/R-patched/library/datasets/html/mtcars.html

attach( mtcars )

hist(mtcars$mpg, probability = TRUE)

lines( sort( mtcars$mpg ),

dnorm( sort( mtcars$mpg ) ,

mean = mean(mtcars$mpg) ,sd = sd(mtcars$mpg) ), col= "red" )

par( mfrow = c( 3, 4 ) )

for( i in 1:length( mtcars[1,] ) ){

hist( mtcars[,i], probability = TRUE,

main = paste( "Data: MTcars", colnames( mtcars )[i] ),

xlab = paste( colnames( mtcars )[i] ) )

lines( sort( mtcars[,i] ),

dnorm( sort( mtcars[,i] ) ,

mean = mean( mtcars[,i] ) ,sd = sd( mtcars[,i] ) ), col= "red" )

}

# Martin Stoppacher                                                             #
# office@martinstoppacher.com                                                   #
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
#################################################################################

# Martin Stoppacher #

# office@martinstoppacher.com #

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

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

Basic R commands – 1.2 – permutations and matrix functions

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# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
# Basic Commands and Statistics with R - 1.2 - permutations
# path: ~/ownCloud/STA_Statistics/Basic_Statistics/
# file_name: statistic_basics3.R
# files_used:

#install.packages( 'gtools' )
library( gtools )
#install.packages( "combinat" )
library( combinat )

#install.packages( "magrittr" )
library( "magrittr" )

# - - - - - - - - - - - - - - - - 
#

x <- 6

factorial( x )
# [1] 720

for( i in 1:x ) print( factorial( i ) )
# [1] 1
# [1] 2
# [1] 6
# [1] 24
# [1] 120
# [1] 720

# - - - - - - - - - - - - - - - - 
#

x <- c( "a", "b", "c" )

combinat::permn( x )

# [[1]]
# [1] "a" "b" "c"
# [[2]]
# [1] "a" "c" "b"
# [[3]]
# [1] "c" "a" "b"
# [[4]]
# [1] "c" "b" "a"
# [[5]]
# [1] "b" "c" "a"
# [[6]]
# [1] "b" "a" "c"

# - - - - - - - - - - - - - - - - 
# string conversion using combinat::

x <- "ABCDEFG"
x <- strsplit( x, "" )[[1]]
y <- combinat::permn( x )
y

x <- LETTERS[1:5]
y <- combinat::permn( x )

paste( y[[1]], collapse = "" )
for( i in 1:length( y ) ) print( paste( y[[i]], collapse = "" ) )

# - - - - - - - - - - - - - - - - 
# using gtools:: for permutations

gtools::permutations( 5, 5, x )
# [,1] [,2] [,3] [,4] [,5]
# [1,] "A"  "C"  "I"  "M"  "P" 
# [2,] "A"  "C"  "I"  "P"  "M" 
# [3,] "A"  "C"  "M"  "I"  "P" 
# [4,] "A"  "C"  "M"  "P"  "I" 
# [5,] "A"  "C"  "P"  "I"  "M"
# ...

gtools::permutations( 5, 5, x, repeats.allowed = TRUE )
# [,1] [,2] [,3] [,4] [,5]
# [1,] "A"  "A"  "A"  "A"  "A" 
# [2,] "A"  "A"  "A"  "A"  "C" 
# [3,] "A"  "A"  "A"  "A"  "I" 
# [4,] "A"  "A"  "A"  "A"  "M" 
# [5,] "A"  "A"  "A"  "A"  "P" 
# [6,] "A"  "A"  "A"  "C"  "A" 
# [7,] "A"  "A"  "A"  "C"  "C" 
# [8,] "A"  "A"  "A"  "C"  "I" 
# [9,] "A"  "A"  "A"  "C"  "M" 
# [10,] "A"  "A"  "A"  "C"  "P" 
# ...

# - - - - - - - - - - - - - - - - 
# using gtools:: for combinations

gtools::combinations( 4, 2, x ) 

gtools::combinations( 5, 2, x )

gtools::combinations( 5, 3, x )

gtools::combinations( 4, 2, x, repeats.allowed = TRUE )

gtools::combinations( 2, 5, x, repeats.allowed = TRUE )

# Martin Stoppacher                                                             #
# office@martinstoppacher.com                                                   #
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
#################################################################################

100

101

102

103

104

105

106

107

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

# Basic Commands and Statistics with R - 1.2 - permutations

# path: ~/ownCloud/STA_Statistics/Basic_Statistics/

# file_name: statistic_basics3.R

# files_used:

#install.packages( 'gtools' )

library( gtools )

#install.packages( "combinat" )

library( combinat )

#install.packages( "magrittr" )

library( "magrittr" )

# - - - - - - - - - - - - - - - -

x <- 6

factorial( x )

# [1] 720

for( i in 1:x ) print( factorial( i ) )

# [1] 1

# [1] 2

# [1] 6

# [1] 24

# [1] 120

# [1] 720

# - - - - - - - - - - - - - - - -

x <- c( "a", "b", "c" )

combinat::permn( x )

# [[1]]

# [1] "a" "b" "c"

# [[2]]

# [1] "a" "c" "b"

# [[3]]

# [1] "c" "a" "b"

# [[4]]

# [1] "c" "b" "a"

# [[5]]

# [1] "b" "c" "a"

# [[6]]

# [1] "b" "a" "c"

# - - - - - - - - - - - - - - - -

# string conversion using combinat::

x <- "ABCDEFG"

x <- strsplit( x, "" )[[1]]

y <- combinat::permn( x )

x <- LETTERS[1:5]

y <- combinat::permn( x )

paste( y[[1]], collapse = "" )

for( i in 1:length( y ) ) print( paste( y[[i]], collapse = "" ) )

# - - - - - - - - - - - - - - - -

# using gtools:: for permutations

gtools::permutations( 5, 5, x )

# [,1] [,2] [,3] [,4] [,5]

# [1,] "A" "C" "I" "M" "P"

# [2,] "A" "C" "I" "P" "M"

# [3,] "A" "C" "M" "I" "P"

# [4,] "A" "C" "M" "P" "I"

# [5,] "A" "C" "P" "I" "M"

# ...

gtools::permutations( 5, 5, x, repeats.allowed = TRUE )

# [,1] [,2] [,3] [,4] [,5]

# [1,] "A" "A" "A" "A" "A"

# [2,] "A" "A" "A" "A" "C"

# [3,] "A" "A" "A" "A" "I"

# [4,] "A" "A" "A" "A" "M"

# [5,] "A" "A" "A" "A" "P"

# [6,] "A" "A" "A" "C" "A"

# [7,] "A" "A" "A" "C" "C"

# [8,] "A" "A" "A" "C" "I"

# [9,] "A" "A" "A" "C" "M"

# [10,] "A" "A" "A" "C" "P"

# ...

# - - - - - - - - - - - - - - - -

# using gtools:: for combinations

gtools::combinations( 4, 2, x )

gtools::combinations( 5, 2, x )

gtools::combinations( 5, 3, x )

gtools::combinations( 4, 2, x, repeats.allowed = TRUE )

gtools::combinations( 2, 5, x, repeats.allowed = TRUE )

# Martin Stoppacher #

# office@martinstoppacher.com #

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

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

# matrix algebra

m1 <- matrix( c( 1, 2, 3, 4, 5, 6, 7, 8, 9 ) , 3, 3 )
m1

m2 <- matrix( rep( 2, 9 ), 3, 3 )
m2

#       [,1] [,2] [,3]
# [1,]    1    4    7
# [2,]    2    5    8
# [3,]    3    6    9

m1 * m1  # element multipliction

#       [,1] [,2] [,3]
# [1,]    1   16   49
# [2,]    4   25   64
# [3,]    9   36   81

m1 * m2

#       [,1] [,2] [,3]
# [1,]    2    8   14
# [2,]    4   10   16
# [3,]    6   12   18


# Matrix Multiplication
m1 %*% m1

#       [,1] [,2] [,3]
# [1,]   30   66  102
# [2,]   36   81  126
# [3,]   42   96  150

# Transpose
t( m1 )

#       [,1] [,2] [,3]
# [1,]    1    2    3
# [2,]    4    5    6
# [3,]    7    8    9

# Outer Product

m1[ 1 , ]
m1[ , 1 ] 
m1[ 1 , ] %o%  m1[ , 1 ] 

m1 %o% m1

# , , 1, 1
# 
#       [,1] [,2] [,3]
# [1,]    1    4    7
# [2,]    2    5    8
# [3,]    3    6    9
# 
# , , 2, 1
# 
#       [,1] [,2] [,3]
# [1,]    2    8   14
# [2,]    4   10   16
# [3,]    6   12   18
# 
# , , 3, 1
# 
#       [,1] [,2] [,3]
# [1,]    3   12   21
# [2,]    6   15   24
# [3,]    9   18   27
# 
# , , 1, 2
# 
#       [,1] [,2] [,3]
# [1,]    4   16   28
# [2,]    8   20   32
# [3,]   12   24   36
# 
# , , 2, 2
# 
#       [,1] [,2] [,3]
# [1,]    5   20   35
# [2,]   10   25   40
# [3,]   15   30   45
# 
# , , 3, 2
# 
#       [,1] [,2] [,3]
# [1,]    6   24   42
# [2,]   12   30   48
# [3,]   18   36   54
# 
# , , 1, 3
# 
#       [,1] [,2] [,3]
# [1,]    7   28   49
# [2,]   14   35   56
# [3,]   21   42   63
# 
# , , 2, 3
# 
#       [,1] [,2] [,3]
# [1,]    8   32   56
# [2,]   16   40   64
# [3,]   24   48   72
# 
# , , 3, 3
# 
#       [,1] [,2] [,3]
# [1,]    9   36   63
# [2,]   18   45   72
# [3,]   27   54   81

# kroenecker product

m1 %x% m1

#       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
# [1,]    1    4    7    4   16   28    7   28   49
# [2,]    2    5    8    8   20   32   14   35   56
# [3,]    3    6    9   12   24   36   21   42   63
# [4,]    2    8   14    5   20   35    8   32   56
# [5,]    4   10   16   10   25   40   16   40   64
# [6,]    6   12   18   15   30   45   24   48   72
# [7,]    3   12   21    6   24   42    9   36   63
# [8,]    6   15   24   12   30   48   18   45   72
# [9,]    9   18   27   18   36   54   27   54   81

m1 %x% m2

#       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
# [1,]    2    2    2    8    8    8   14   14   14
# [2,]    2    2    2    8    8    8   14   14   14
# [3,]    2    2    2    8    8    8   14   14   14
# [4,]    4    4    4   10   10   10   16   16   16
# [5,]    4    4    4   10   10   10   16   16   16
# [6,]    4    4    4   10   10   10   16   16   16
# [7,]    6    6    6   12   12   12   18   18   18
# [8,]    6    6    6   12   12   12   18   18   18
# [9,]    6    6    6   12   12   12   18   18   18

# cross Product 

m1[ , 1 ]
m1[ , 2 ] 

crossprod( m1, m2[ , 1 ]  )

#       [,1]
# [1,]   32
# [2,]   77
# [3,]  122

crossprod( m1 )

#      [,1] [,2] [,3]
# [1,]   14   32   50
# [2,]   32   77  122
# [3,]   50  122  194

crossprod( m1, m2 )

#       [,1] [,2] [,3]
# [1,]   12   12   12
# [2,]   30   30   30
# [3,]   48   48   48

# Diagonal Matrix with elements of x in the diagonal

diag( nrow = 3 )

# [,1] [,2] [,3]
# [1,]    1    0    0
# [2,]    0    1    0
# [3,]    0    0    1

diag( 3,  nrow = 3 )

# [,1] [,2] [,3]
# [1,]    3    0    0
# [2,]    0    3    0
# [3,]    0    0    3

# returns a vector of the principal diagonal elements
m1
diag( m1 )

# [,1] [,2] [,3]
# [1,]    1    0    0
# [2,]    0    2    0
# [3,]    0    0    3

# k * k identity matrix for m1[ , 1 ]
diag( m1[ , 1 ] )

# [,1] [,2] [,3]
# [1,]    1    0    0
# [2,]    0    2    0
# [3,]    0    0   

# simple combinations

cbind( m1, m2 )
rbind( m1, m2 )

# means and sums

rowMeans( m1 )
rowSums( m1 )

colMeans( m1 )
colSums( m1 )

# eigenvalues, eigenvectors

eigen( m1 )
e <- eigen( m1 )
e$values
e$vectors

# eigen() decomposition
# $values
# [1]  1.611684e+01 -1.116844e+00 -5.700691e-16
#
# $vectors
# [,1]       [,2]       [,3]
# [1,] -0.4645473 -0.8829060  0.4082483
# [2,] -0.5707955 -0.2395204 -0.8164966
# [3,] -0.6770438  0.4038651  0.4082483

# single value decomposition

svd( m1 )

# $d    singular values of m1
# [1] 1.684810e+01 1.068370e+00 5.543107e-16
#
# $u    left singular vectors of m1
# [,1]        [,2]       [,3]
# [1,] -0.4796712  0.77669099  0.4082483
# [2,] -0.5723678  0.07568647 -0.8164966
# [3,] -0.6650644 -0.62531805  0.4082483
#
# $v    right singular vectors of m1
# [,1]       [,2]       [,3]
# [1,] -0.2148372 -0.8872307  0.4082483
# [2,] -0.5205874 -0.2496440 -0.8164966
# [3,] -0.8263375  0.3879428  0.4082483


# QR decomposition 

qr( m1 )

# $qr
# [,1]      [,2]          [,3]
# [1,] -3.7416574 -8.552360 -1.336306e+01
# [2,]  0.5345225  1.963961  3.927922e+00
# [3,]  0.8017837  0.988693  1.776357e-15
#
# $rank
# [1] 2
#
# $qraux  
# [1] 1.267261e+00 1.149954e+00 1.776357e-15
#
# $pivot
# [1] 1 2 3
#
# attr(,"class")
# [1] "qr"


# inverse 

solve( m1 )

# Error in solve.default(m1) : 
#   Lapack routine dgesv: system is exactly singular: U[3,3] = 0

m3 <- matrix( c( 2, 6, 1, 4 ) , 2, 2 )
m3

# [,1] [,2]
# [1,]    2    1
# [2,]    6    4

sm3 <- solve( m3 )

# [,1] [,2]
# [1,]    2 -0.5
# [2,]   -3  1.0

m3 %*% sm3

# [,1] [,2]
# [1,]    1    0
# [2,]    0    1

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# matrix algebra

m1 <- matrix( c( 1, 2, 3, 4, 5, 6, 7, 8, 9 ) , 3, 3 )

m2 <- matrix( rep( 2, 9 ), 3, 3 )

# [,1] [,2] [,3]

# [1,] 1 4 7

# [2,] 2 5 8

# [3,] 3 6 9

m1 * m1 # element multipliction

# [,1] [,2] [,3]

# [1,] 1 16 49

# [2,] 4 25 64

# [3,] 9 36 81

m1 * m2

# [,1] [,2] [,3]

# [1,] 2 8 14

# [2,] 4 10 16

# [3,] 6 12 18

# Matrix Multiplication

m1 %*% m1

# [,1] [,2] [,3]

# [1,] 30 66 102

# [2,] 36 81 126

# [3,] 42 96 150

# Transpose

t( m1 )

# [,1] [,2] [,3]

# [1,] 1 2 3

# [2,] 4 5 6

# [3,] 7 8 9

# Outer Product

m1[ 1 , ]

m1[ , 1 ]

m1[ 1 , ] %o% m1[ , 1 ]

m1 %o% m1

# , , 1, 1

# [,1] [,2] [,3]

# [1,] 1 4 7

# [2,] 2 5 8

# [3,] 3 6 9

# , , 2, 1

# [,1] [,2] [,3]

# [1,] 2 8 14

# [2,] 4 10 16

# [3,] 6 12 18

# , , 3, 1

# [,1] [,2] [,3]

# [1,] 3 12 21

# [2,] 6 15 24

# [3,] 9 18 27

# , , 1, 2

# [,1] [,2] [,3]

# [1,] 4 16 28

# [2,] 8 20 32

# [3,] 12 24 36

# , , 2, 2

# [,1] [,2] [,3]

# [1,] 5 20 35

# [2,] 10 25 40

# [3,] 15 30 45

# , , 3, 2

# [,1] [,2] [,3]

# [1,] 6 24 42

# [2,] 12 30 48

# [3,] 18 36 54

# , , 1, 3

# [,1] [,2] [,3]

# [1,] 7 28 49

# [2,] 14 35 56

# [3,] 21 42 63

# , , 2, 3

# [,1] [,2] [,3]

# [1,] 8 32 56

# [2,] 16 40 64

# [3,] 24 48 72

# , , 3, 3

# [,1] [,2] [,3]

# [1,] 9 36 63

# [2,] 18 45 72

# [3,] 27 54 81

# kroenecker product

m1 %x% m1

# [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]

# [1,] 1 4 7 4 16 28 7 28 49

# [2,] 2 5 8 8 20 32 14 35 56

# [3,] 3 6 9 12 24 36 21 42 63

# [4,] 2 8 14 5 20 35 8 32 56

# [5,] 4 10 16 10 25 40 16 40 64

# [6,] 6 12 18 15 30 45 24 48 72

# [7,] 3 12 21 6 24 42 9 36 63

# [8,] 6 15 24 12 30 48 18 45 72

# [9,] 9 18 27 18 36 54 27 54 81

m1 %x% m2

# [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]

# [1,] 2 2 2 8 8 8 14 14 14

# [2,] 2 2 2 8 8 8 14 14 14

# [3,] 2 2 2 8 8 8 14 14 14

# [4,] 4 4 4 10 10 10 16 16 16

# [5,] 4 4 4 10 10 10 16 16 16

# [6,] 4 4 4 10 10 10 16 16 16

# [7,] 6 6 6 12 12 12 18 18 18

# [8,] 6 6 6 12 12 12 18 18 18

# [9,] 6 6 6 12 12 12 18 18 18

# cross Product

m1[ , 1 ]

m1[ , 2 ]

crossprod( m1, m2[ , 1 ] )

# [,1]

# [1,] 32

# [2,] 77

# [3,] 122

crossprod( m1 )

# [,1] [,2] [,3]

# [1,] 14 32 50

# [2,] 32 77 122

# [3,] 50 122 194

crossprod( m1, m2 )

# [,1] [,2] [,3]

# [1,] 12 12 12

# [2,] 30 30 30

# [3,] 48 48 48

# Diagonal Matrix with elements of x in the diagonal

diag( nrow = 3 )

# [,1] [,2] [,3]

# [1,] 1 0 0

# [2,] 0 1 0

# [3,] 0 0 1

diag( 3, nrow = 3 )

# [,1] [,2] [,3]

# [1,] 3 0 0

# [2,] 0 3 0

# [3,] 0 0 3

# returns a vector of the principal diagonal elements

diag( m1 )

# [,1] [,2] [,3]

# [1,] 1 0 0

# [2,] 0 2 0

# [3,] 0 0 3

# k * k identity matrix for m1[ , 1 ]

diag( m1[ , 1 ] )

# [,1] [,2] [,3]

# [1,] 1 0 0

# [2,] 0 2 0

# [3,] 0 0

# simple combinations

cbind( m1, m2 )

rbind( m1, m2 )

# means and sums

rowMeans( m1 )

rowSums( m1 )

colMeans( m1 )

colSums( m1 )

# eigenvalues, eigenvectors

eigen( m1 )

e <- eigen( m1 )

e$values

e$vectors

# eigen() decomposition

# $values

# [1] 1.611684e+01 -1.116844e+00 -5.700691e-16

# $vectors

# [,1] [,2] [,3]

# [1,] -0.4645473 -0.8829060 0.4082483

# [2,] -0.5707955 -0.2395204 -0.8164966

# [3,] -0.6770438 0.4038651 0.4082483

# single value decomposition

svd( m1 )

# $d singular values of m1

# [1] 1.684810e+01 1.068370e+00 5.543107e-16

# $u left singular vectors of m1

# [,1] [,2] [,3]

# [1,] -0.4796712 0.77669099 0.4082483

# [2,] -0.5723678 0.07568647 -0.8164966

# [3,] -0.6650644 -0.62531805 0.4082483

# $v right singular vectors of m1

# [,1] [,2] [,3]

# [1,] -0.2148372 -0.8872307 0.4082483

# [2,] -0.5205874 -0.2496440 -0.8164966

# [3,] -0.8263375 0.3879428 0.4082483

# QR decomposition

qr( m1 )

# $qr

# [,1] [,2] [,3]

# [1,] -3.7416574 -8.552360 -1.336306e+01

# [2,] 0.5345225 1.963961 3.927922e+00

# [3,] 0.8017837 0.988693 1.776357e-15

# $rank

# [1] 2

# $qraux

# [1] 1.267261e+00 1.149954e+00 1.776357e-15

# $pivot

# [1] 1 2 3

# attr(,"class")

# [1] "qr"

# inverse

solve( m1 )

# Error in solve.default(m1) :

# Lapack routine dgesv: system is exactly singular: U[3,3] = 0

m3 <- matrix( c( 2, 6, 1, 4 ) , 2, 2 )

# [,1] [,2]

# [1,] 2 1

# [2,] 6 4

sm3 <- solve( m3 )

# [,1] [,2]

# [1,] 2 -0.5

# [2,] -3 1.0

m3 %*% sm3

# [,1] [,2]

# [1,] 1 0

# [2,] 0 1

Basic R commands – 1

Leave a reply

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
# Basic Commands and Statistics with R

rm(list = ls(all = TRUE))
getwd()
#system("ls")
setwd("~/ownCloud/STA_Statistics/basicR/")

search()

options(scipen=100)   # scientific off
options(scipen=0)     # scientific on
options(digits = 3)     

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
# https://stat.ethz.ch/R-manual/R-patched/library/datasets/html/mtcars.html

attach(mtcars)
search()
detach(mtcars)
search()
mtcars         # The data was extracted from the 1974 Motor Trend US magazine 
# ?mtcars

class(mtcars)  # determine the class of an object

str(mtcars)    # Compactly display the internal structure of an R object

# 'data.frame':	32 obs. of  11 variables:

#                     mpg cyl  disp  hp drat    wt  qsec vs am gear carb
# Mazda RX4           21.0   6 160.0 110 3.90 2.620 16.46  0  1    4    4
# Mazda RX4 Wag       21.0   6 160.0 110 3.90 2.875 17.02  0  1    4    4
# Datsun 710          22.8   4 108.0  93 3.85 2.320 18.61  1  1    4    1
# Hornet 4 Drive      21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
# Hornet Sportabout   18.7   8 360.0 175 3.15 3.440 17.02  0  0    3    2
# Valiant             18.1   6 225.0 105 2.76 3.460 20.22  1  0    3    1
# Duster 360          14.3   8 360.0 245 3.21 3.570 15.84  0  0    3    4
# Merc 240D           24.4   4 146.7  62 3.69 3.190 20.00  1  0    4    2
# Merc 230            22.8   4 140.8  95 3.92 3.150 22.90  1  0    4    2
# Merc 280            19.2   6 167.6 123 3.92 3.440 18.30  1  0    4    4
# Merc 280C           17.8   6 167.6 123 3.92 3.440 18.90  1  0    4    4
# Merc 450SE          16.4   8 275.8 180 3.07 4.070 17.40  0  0    3    3
# Merc 450SL          17.3   8 275.8 180 3.07 3.730 17.60  0  0    3    3
# Merc 450SLC         15.2   8 275.8 180 3.07 3.780 18.00  0  0    3    3
# Cadillac Fleetwood  10.4   8 472.0 205 2.93 5.250 17.98  0  0    3    4
# Lincoln Continental 10.4   8 460.0 215 3.00 5.424 17.82  0  0    3    4
# Chrysler Imperial   14.7   8 440.0 230 3.23 5.345 17.42  0  0    3    4
# Fiat 128            32.4   4  78.7  66 4.08 2.200 19.47  1  1    4    1
# Honda Civic         30.4   4  75.7  52 4.93 1.615 18.52  1  1    4    2
# Toyota Corolla      33.9   4  71.1  65 4.22 1.835 19.90  1  1    4    1
# Toyota Corona       21.5   4 120.1  97 3.70 2.465 20.01  1  0    3    1
# Dodge Challenger    15.5   8 318.0 150 2.76 3.520 16.87  0  0    3    2
# AMC Javelin         15.2   8 304.0 150 3.15 3.435 17.30  0  0    3    2
# Camaro Z28          13.3   8 350.0 245 3.73 3.840 15.41  0  0    3    4
# Pontiac Firebird    19.2   8 400.0 175 3.08 3.845 17.05  0  0    3    2
# Fiat X1-9           27.3   4  79.0  66 4.08 1.935 18.90  1  1    4    1
# Porsche 914-2       26.0   4 120.3  91 4.43 2.140 16.70  0  1    5    2
# Lotus Europa        30.4   4  95.1 113 3.77 1.513 16.90  1  1    5    2
# Ford Pantera L      15.8   8 351.0 264 4.22 3.170 14.50  0  1    5    4
# Ferrari Dino        19.7   6 145.0 175 3.62 2.770 15.50  0  1    5    6
# Maserati Bora       15.0   8 301.0 335 3.54 3.570 14.60  0  1    5    8
# Volvo 142E          21.4   4 121.0 109 4.11 2.780 18.60  1  1    4    2

# A data frame with 32 observations on 11 (numeric) variables.

#[, 1]	mpg	Miles/(US) gallon
#[, 2]	cyl	Number of cylinders
#[, 3]	disp	Displacement (cu.in.)
#[, 4]	hp	Gross horsepower
#[, 5]	drat	Rear axle ratio
#[, 6]	wt	Weight (1000 lbs)
#[, 7]	qsec	1/4 mile time
#[, 8]	vs	Engine (0 = V-shaped, 1 = straight)
#[, 9]	am	Transmission (0 = automatic, 1 = manual)
#[,10]	gear	Number of forward gears
#[,11]	carb	Number of carburetors

colnames(mtcars) <- c("mpg","cyl","disp","hp","drat","wt",
                      "qsec","vs","am","gear","carb")

# colnames(mtcars) <- c("miles-per-gallon","cylinders","displacement",
#                       "horsepower","rear-axle-ratio","weight","qsec",
#                       "engine-vs","Transmissionam","gear","carburetors")

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
# data structures

letters
l <- letters
str(l)
# chr [1:26]  "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l" "m" "n" "o" "p" 
#             "q" "r" "s" "t" "u" "v" "w" "x" "y" "z"

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # 
# Vectors

t <- c(1:3,"Hello",NA,FALSE,TRUE)
t
# [1] "1"     "2"     "3"     "Hello" NA      "FALSE" "TRUE" 
str(t)
# chr [1:7] "1" "2" "3" "Hello" NA "FALSE" "TRUE"

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
# Factors

mtcars$am[mtcars$am==1]
which(mtcars$am==1)

am.names <- mtcars$am
am.names[which(am.names==1)] <- "Automatic"
am.names
am.names[which(am.names==0)] <- "Manual"
am.names

am.names.factor <- factor(am.names)
am.names.factor
# [1] Automatic Automatic Automatic Manual    Manual  
# Levels: Automatic Manual

# internally stored as a table of:
# 1 Automatic
# 2 Manual

# Automatic and Manual are the levels of the factor 
levels(am.names.factor)

relevel(am.names.factor, ref="Manual")
# [1] Automatic Automatic Automatic Manual    Manual  
# Levels: Manual Automatic

am.names.factor[1]
as.character(am.names.factor[1])
as.numeric(am.names.factor[1])  # numeric takes the faktor not the level
levels(am.names.factor)[1]      # can be used to get the factor

table(am.names.factor)

is.factor(am.names.factor)

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - # 
# Data Frames

mtcars
str(mtcars)
# 'data.frame':	32 obs. of  11 variables:

df <- data.frame(1:20,60:41,letters[1:20])
df
colnames(df) <- c("n1","n2","letters")
df
t(df)

df$letters      # get the vectors from the dataframe
df$n1
df[,2]
df[1,3]
df[[3]]
levels(df$letters)
is.factor(df[,3])

df <- data.frame(1:20,60:41,letters[1:20], stringsAsFactors = FALSE)
df
is.factor(df[,3])

trees
mtcars
USMortality 
data()    # list of data associated with all current packages in the serch path

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
# Matrix

as.matrix(mtcars)
mtcars.mat <- as.matrix(mtcars) # all elements of a matrix have the same mode 
                                #(numeric, character)
x <- as.vector(mtcars.mat)      # all in order in the vector X
x

mat <- matrix(1:100,nco=10)
mat
as.vector(mat)

mat44 <- matrix(1:(4*4),nco=4)
mat44
as.vector(mat44)

dimnames(mtcars.mat)

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
# Arrays

x <- 1:10000             # this is a matrix
dim(x) <- c(100,100)
x

x <- 1:1000              # array - a matrix with more than 2 dim
dim(x) <- c(10,10,10)
x

x <- 1:(2*3*3)           # array - a matrix with more than 2 dim
dim(x) <- c(2,3,3)
x

str(x)
# int [1:2, 1:3, 1:3] 1 2 3 4 5 6 7 8 9 10 ...

x <- letters[1:(2*3*3)]           # array - a matrix with more than 2 dim
dim(x) <- c(2,3,3)
x
str(x)
# chr [1:2, 1:3, 1:3] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l" 
#                     "m" "n" "o" "p" "q" "r"

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
# Lists - collect different types of data objects

data()

l <- list(mtcars,barley,environmental,ethanol,melanoma)
                                            # most data from lattice package
str(l)

# List of 5
# $ :'data.frame':	32 obs. of  11 variables:
# ..$ mpg : num [1:32] 21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
# ..$ cyl : num [1:32] 6 6 4 6 8 6 8 4 4 6 ...
# ..$ disp: num [1:32] 160 160 108 258 360 ...
# ..$ hp  : num [1:32] 110 110 93 110 175 105 245 62 95 123 ...
# ..$ drat: num [1:32] 3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
# ..$ wt  : num [1:32] 2.62 2.88 2.32 3.21 3.44 ...
# ..$ qsec: num [1:32] 16.5 17 18.6 19.4 17 ...
# ..$ vs  : num [1:32] 0 0 1 1 0 1 0 1 1 1 ...
# ..$ am  : num [1:32] 1 1 1 0 0 0 0 0 0 0 ...
# ..$ gear: num [1:32] 4 4 4 3 3 3 3 4 4 4 ...
# ..$ carb: num [1:32] 4 4 1 1 2 1 4 2 2 4 ...
# $ :'data.frame':	120 obs. of  4 variables:
# ..$ yield  : num [1:120] 27 48.9 27.4 39.9 33 ...
# ..$ variety: Factor w/10 levels "Svansota","No.462",..: 3 3 3 3 3 3 7 7 7 7...
# ..$ year   : Factor w/2 levels "1932","1931": 2 2 2 2 2 2 2 2 2 2...
# ..$ site   : Factor w/6 levels "Grand Rapids",..: 3 6 4 5 1 2 3 6 4 5...
# $ :'data.frame':	111 obs. of  4 variables:
# ..$ ozone      : num [1:111] 41 36 12 18 23 19 8 16 11 14 ...
# ..$ radiation  : num [1:111] 190 118 149 313 299 99 19 256 290 274 ...
# ..$ temperature: num [1:111] 67 72 74 62 65 59 61 69 66 68 ...
# ..$ wind       : num [1:111] 7.4 8 12.6 11.5 8.6 13.8 20.1 9.7 9.2 10.9 ...
# $ :'data.frame':	88 obs. of  3 variables:
# ..$ NOx: num [1:88] 3.74 2.29 1.5 2.88 0.76 ...
# ..$ C  : num [1:88] 12 12 12 12 12 9 9 9 12 12 ...
# ..$ E  : num [1:88] 0.907 0.761 1.108 1.016 1.189 ...
# $ :'data.frame':	37 obs. of  2 variables:
# ..$ year     : num [1:37] 1936 1937 1938 1939 1940 ...
# ..$ incidence: num [1:37] 0.9 0.8 0.8 1.3 1.4 1.2 1.7 1.8 1.6 1.5 ...

l[[1]]
l[[2]]
l[[3]]

l[[1]]

model <- lm(mpg~wt,data=l[[1]])   # building a model from a list object
names(model) 
str(model)                        # the model itselfe is returned as a list

model$coefficients
model[[1]]

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
# some basic R functions

mtcars$mpg
# [1] 21.0 21.0 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 17.8 16.4 17.3 15.2 ...
mtcars$mpg^2
# [1]  441.00  441.00 519.84 457.96 349.69 327.61 204.49  595.36  519.84  ...
sqrt(mtcars$mpg^2)
# [1] 21.0 21.0 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 17.8 16.4 17.3 15.2 ...

pi
# [1] 3.141593
90*pi/180 # radiant conversion
sin(90*pi/180)
cos(90*pi/180)
cos(0*pi/180)

celsius <- 20
9/5*celsius+32

celsius <- -20:40
fahrenheit <- 9/5*celsius+32
plot(celsius,fahrenheit,type="s")

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# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

# Basic Commands and Statistics with R

rm(list = ls(all = TRUE))

getwd()

#system("ls")

setwd("~/ownCloud/STA_Statistics/basicR/")

search()

options(scipen=100) # scientific off

options(scipen=0) # scientific on

options(digits = 3)

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

# https://stat.ethz.ch/R-manual/R-patched/library/datasets/html/mtcars.html

attach(mtcars)

search()

detach(mtcars)

search()

mtcars # The data was extracted from the 1974 Motor Trend US magazine

# ?mtcars

class(mtcars) # determine the class of an object

str(mtcars) # Compactly display the internal structure of an R object

# 'data.frame': 32 obs. of 11 variables:

# mpg cyl disp hp drat wt qsec vs am gear carb

# Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4

# Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4

# Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1

# Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1

# Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 0 3 2

# Valiant 18.1 6 225.0 105 2.76 3.460 20.22 1 0 3 1

# Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 0 3 4

# Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2

# Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2

# Merc 280 19.2 6 167.6 123 3.92 3.440 18.30 1 0 4 4

# Merc 280C 17.8 6 167.6 123 3.92 3.440 18.90 1 0 4 4

# Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 3

# Merc 450SL 17.3 8 275.8 180 3.07 3.730 17.60 0 0 3 3

# Merc 450SLC 15.2 8 275.8 180 3.07 3.780 18.00 0 0 3 3

# Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 0 3 4

# Lincoln Continental 10.4 8 460.0 215 3.00 5.424 17.82 0 0 3 4

# Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 0 3 4

# Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1

# Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2

# Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1

# Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 1 0 3 1

# Dodge Challenger 15.5 8 318.0 150 2.76 3.520 16.87 0 0 3 2

# AMC Javelin 15.2 8 304.0 150 3.15 3.435 17.30 0 0 3 2

# Camaro Z28 13.3 8 350.0 245 3.73 3.840 15.41 0 0 3 4

# Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 0 3 2

# Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 1 4 1

# Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 0 1 5 2

# Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2

# Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.50 0 1 5 4

# Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.50 0 1 5 6

# Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 0 1 5 8

# Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2

# A data frame with 32 observations on 11 (numeric) variables.

#[, 1] mpg Miles/(US) gallon

#[, 2] cyl Number of cylinders

#[, 3] disp Displacement (cu.in.)

#[, 4] hp Gross horsepower

#[, 5] drat Rear axle ratio

#[, 6] wt Weight (1000 lbs)

#[, 7] qsec 1/4 mile time

#[, 8] vs Engine (0 = V-shaped, 1 = straight)

#[, 9] am Transmission (0 = automatic, 1 = manual)

#[,10] gear Number of forward gears

#[,11] carb Number of carburetors

colnames(mtcars) <- c("mpg","cyl","disp","hp","drat","wt",

"qsec","vs","am","gear","carb")

# colnames(mtcars) <- c("miles-per-gallon","cylinders","displacement",

# "horsepower","rear-axle-ratio","weight","qsec",

# "engine-vs","Transmissionam","gear","carburetors")

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

# data structures

letters

l <- letters

str(l)

# chr [1:26] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l" "m" "n" "o" "p"

# "q" "r" "s" "t" "u" "v" "w" "x" "y" "z"

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

# Vectors

t <- c(1:3,"Hello",NA,FALSE,TRUE)

# [1] "1" "2" "3" "Hello" NA "FALSE" "TRUE"

str(t)

# chr [1:7] "1" "2" "3" "Hello" NA "FALSE" "TRUE"

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

# Factors

mtcars$am[mtcars$am==1]

which(mtcars$am==1)

am.names <- mtcars$am

am.names[which(am.names==1)] <- "Automatic"

am.names

am.names[which(am.names==0)] <- "Manual"

am.names

am.names.factor <- factor(am.names)

am.names.factor

# [1] Automatic Automatic Automatic Manual Manual

# Levels: Automatic Manual

# internally stored as a table of:

# 1 Automatic

# 2 Manual

# Automatic and Manual are the levels of the factor

levels(am.names.factor)

relevel(am.names.factor, ref="Manual")

# [1] Automatic Automatic Automatic Manual Manual

# Levels: Manual Automatic

am.names.factor[1]

as.character(am.names.factor[1])

as.numeric(am.names.factor[1]) # numeric takes the faktor not the level

levels(am.names.factor)[1] # can be used to get the factor

table(am.names.factor)

is.factor(am.names.factor)

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

# Data Frames

mtcars

str(mtcars)

# 'data.frame': 32 obs. of 11 variables:

df <- data.frame(1:20,60:41,letters[1:20])

colnames(df) <- c("n1","n2","letters")

t(df)

df$letters # get the vectors from the dataframe

df$n1

df[,2]

df[1,3]

df[[3]]

levels(df$letters)

is.factor(df[,3])

df <- data.frame(1:20,60:41,letters[1:20], stringsAsFactors = FALSE)

is.factor(df[,3])

trees

mtcars

USMortality

data() # list of data associated with all current packages in the serch path

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

# Matrix

as.matrix(mtcars)

mtcars.mat <- as.matrix(mtcars) # all elements of a matrix have the same mode

#(numeric, character)

x <- as.vector(mtcars.mat) # all in order in the vector X

mat <- matrix(1:100,nco=10)

mat

as.vector(mat)

mat44 <- matrix(1:(4*4),nco=4)

mat44

as.vector(mat44)

dimnames(mtcars.mat)

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

# Arrays

x <- 1:10000 # this is a matrix

dim(x) <- c(100,100)

x <- 1:1000 # array - a matrix with more than 2 dim

dim(x) <- c(10,10,10)

x <- 1:(2*3*3) # array - a matrix with more than 2 dim

dim(x) <- c(2,3,3)

str(x)

# int [1:2, 1:3, 1:3] 1 2 3 4 5 6 7 8 9 10 ...

x <- letters[1:(2*3*3)] # array - a matrix with more than 2 dim

dim(x) <- c(2,3,3)

str(x)

# chr [1:2, 1:3, 1:3] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l"

# "m" "n" "o" "p" "q" "r"

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

# Lists - collect different types of data objects

data()

l <- list(mtcars,barley,environmental,ethanol,melanoma)

# most data from lattice package

str(l)

# List of 5

# $ :'data.frame': 32 obs. of 11 variables:

# ..$ mpg : num [1:32] 21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...

# ..$ cyl : num [1:32] 6 6 4 6 8 6 8 4 4 6 ...

# ..$ disp: num [1:32] 160 160 108 258 360 ...

# ..$ hp : num [1:32] 110 110 93 110 175 105 245 62 95 123 ...

# ..$ drat: num [1:32] 3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...

# ..$ wt : num [1:32] 2.62 2.88 2.32 3.21 3.44 ...

# ..$ qsec: num [1:32] 16.5 17 18.6 19.4 17 ...

# ..$ vs : num [1:32] 0 0 1 1 0 1 0 1 1 1 ...

# ..$ am : num [1:32] 1 1 1 0 0 0 0 0 0 0 ...

# ..$ gear: num [1:32] 4 4 4 3 3 3 3 4 4 4 ...

# ..$ carb: num [1:32] 4 4 1 1 2 1 4 2 2 4 ...

# $ :'data.frame': 120 obs. of 4 variables:

# ..$ yield : num [1:120] 27 48.9 27.4 39.9 33 ...

# ..$ variety: Factor w/10 levels "Svansota","No.462",..: 3 3 3 3 3 3 7 7 7 7...

# ..$ year : Factor w/2 levels "1932","1931": 2 2 2 2 2 2 2 2 2 2...

# ..$ site : Factor w/6 levels "Grand Rapids",..: 3 6 4 5 1 2 3 6 4 5...

# $ :'data.frame': 111 obs. of 4 variables:

# ..$ ozone : num [1:111] 41 36 12 18 23 19 8 16 11 14 ...

# ..$ radiation : num [1:111] 190 118 149 313 299 99 19 256 290 274 ...

# ..$ temperature: num [1:111] 67 72 74 62 65 59 61 69 66 68 ...

# ..$ wind : num [1:111] 7.4 8 12.6 11.5 8.6 13.8 20.1 9.7 9.2 10.9 ...

# $ :'data.frame': 88 obs. of 3 variables:

# ..$ NOx: num [1:88] 3.74 2.29 1.5 2.88 0.76 ...

# ..$ C : num [1:88] 12 12 12 12 12 9 9 9 12 12 ...

# ..$ E : num [1:88] 0.907 0.761 1.108 1.016 1.189 ...

# $ :'data.frame': 37 obs. of 2 variables:

# ..$ year : num [1:37] 1936 1937 1938 1939 1940 ...

# ..$ incidence: num [1:37] 0.9 0.8 0.8 1.3 1.4 1.2 1.7 1.8 1.6 1.5 ...

l[[1]]

l[[2]]

l[[3]]

l[[1]]

model <- lm(mpg~wt,data=l[[1]]) # building a model from a list object

names(model)

str(model) # the model itselfe is returned as a list

model$coefficients

model[[1]]

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

# some basic R functions

mtcars$mpg

# [1] 21.0 21.0 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 17.8 16.4 17.3 15.2 ...

mtcars$mpg^2

# [1] 441.00 441.00 519.84 457.96 349.69 327.61 204.49 595.36 519.84 ...

sqrt(mtcars$mpg^2)

# [1] 21.0 21.0 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 17.8 16.4 17.3 15.2 ...

# [1] 3.141593

90*pi/180 # radiant conversion

sin(90*pi/180)

cos(90*pi/180)

cos(0*pi/180)

celsius <- 20

9/5*celsius+32

celsius <- -20:40

fahrenheit <- 9/5*celsius+32

plot(celsius,fahrenheit,type="s")

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
sum(mtcars$mpg)
# [1] 642.9
cumsum(mtcars$mpg)
# [1]  21.0  42.0  64.8  86.2 104.9 123.0 137.3 161.7
cumprod(mtcars$mpg)
# [1] 2.100000e+01 4.410000e+02 1.005480e+04 2.151727e+05 
#     4.023730e+06 7.282951e+07

c(1,2,3,4,5)    # vectors # concatenating function
c(1:5)
c(TRUE,FALSE)
c("TRUE","FALSE") # character vector

x <- runif(5)
x
# [1] 0.832 0.101 0.926 0.253 0.619
sort(x)

order(x)
# [1] 0.101 0.253 0.619 0.832 0.926
x[order(x)]
# [1] 0.101 0.253 0.619 0.832 0.926

x <- c(1:5)
x
y <- c("TRUE","FALSE",NA) 
y
z <- c(x,y)
z
# [1] "1"     "2"     "3"     "4"     "5"     "TRUE"  "FALSE" NA    
rev(z)
# [1] NA      "FALSE" "TRUE"  "5"     "4"     "3"     "2"     "1"   

z[2]
z[2:5]
# [1] "2" "3" "4" "5"
z[z<4]
# [1] "1" "2" "3" NA 
z[z>4]
# [1] "5"     "TRUE"  "FALSE" NA 
z[z>=4]
# [1] "4"     "5"     "TRUE"  "FALSE" NA  
z[-c(3,4)]
# [1] "1"     "2"     "5"     "TRUE"  "FALSE" NA 
z[c(3,4)]
# [1] "3" "4"

z[is.na(z)]
z[is.na(z)]<-0
z
z[z==TRUE]<-1
z[z==FALSE]<-0
z
# [1] "1" "2" "3" "4" "5" "1" "0" "0"

plot(z)
plot(z,type="b")

x <- runif(length(z))*5

plot(x,z,type="b")
plot(x~z,type="b")

plot(z,x,type="b")
lines(z~x,type="b",col="red")

plot(sin((1:360)*pi/180),type="l")
plot(sin((1:360)*pi/180),cos((1:360)*pi/180),type="l")

plot(sin((1:360)*pi/18),cos((1:360)*pi/10),type="l")

plot(sin((1:360)*pi/18),cos((1:360)*pi/10),type="l")

plot(tan((1:360)*pi/180),cos((1:360)*pi/180),type="l")
plot(tan((1:360)*pi/180),sin((1:360)*pi/180),type="l")

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

sum(mtcars$mpg)

# [1] 642.9

cumsum(mtcars$mpg)

# [1] 21.0 42.0 64.8 86.2 104.9 123.0 137.3 161.7

cumprod(mtcars$mpg)

# [1] 2.100000e+01 4.410000e+02 1.005480e+04 2.151727e+05

# 4.023730e+06 7.282951e+07

c(1,2,3,4,5) # vectors # concatenating function

c(1:5)

c(TRUE,FALSE)

c("TRUE","FALSE") # character vector

x <- runif(5)

# [1] 0.832 0.101 0.926 0.253 0.619

sort(x)

order(x)

# [1] 0.101 0.253 0.619 0.832 0.926

x[order(x)]

# [1] 0.101 0.253 0.619 0.832 0.926

x <- c(1:5)

y <- c("TRUE","FALSE",NA)

z <- c(x,y)

# [1] "1" "2" "3" "4" "5" "TRUE" "FALSE" NA

rev(z)

# [1] NA "FALSE" "TRUE" "5" "4" "3" "2" "1"

z[2]

z[2:5]

# [1] "2" "3" "4" "5"

z[z<4]

# [1] "1" "2" "3" NA

z[z>4]

# [1] "5" "TRUE" "FALSE" NA

z[z>=4]

# [1] "4" "5" "TRUE" "FALSE" NA

z[-c(3,4)]

# [1] "1" "2" "5" "TRUE" "FALSE" NA

z[c(3,4)]

# [1] "3" "4"

z[is.na(z)]

z[is.na(z)]<-0

z[z==TRUE]<-1

z[z==FALSE]<-0

# [1] "1" "2" "3" "4" "5" "1" "0" "0"

plot(z)

plot(z,type="b")

x <- runif(length(z))*5

plot(x,z,type="b")

plot(x~z,type="b")

plot(z,x,type="b")

lines(z~x,type="b",col="red")

plot(sin((1:360)*pi/180),type="l")

plot(sin((1:360)*pi/180),cos((1:360)*pi/180),type="l")

plot(sin((1:360)*pi/18),cos((1:360)*pi/10),type="l")

plot(tan((1:360)*pi/180),cos((1:360)*pi/180),type="l")

plot(tan((1:360)*pi/180),sin((1:360)*pi/180),type="l")

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
# some loops

for(i in 1:360){
    plot(cos((1:360)*pi/i),sin((1:360)*pi/i),type="l")
    print(i)
    Sys.sleep(0.1)
}

for(i in 360:1){
  plot(cos((1:360)*pi/i),sin((1:360)*pi/i),type="l")
  print(i)
  Sys.sleep(0.1)
}

for(i in 1:360){
  for(e in 1:360){
  plot(cos((1:360)*pi/i),sin((1:360)*pi/e),type="l")
  print(i)
  Sys.sleep(0.1)
  }
}

for(i in 1:360){
  for(e in 1:360){
    plot(sin((1:360)*pi/i),cos((1:360)*pi/e),type="l")
    print(i)
    Sys.sleep(0.1)
  }
}

for(i in 1:10){
  for(e in 1:10){
    plot(sin((1:360)*pi/i),cos((1:360)*pi/e),type="l")
    mtext(paste("i:",i,"e:",e), side=3, outer=TRUE, line=-3)
    print(paste("i:",i,"e:",e))
    Sys.sleep(0.1)
  }
}

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
# function collection

letters
# "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l" "m" "n" "o" "p" "q" "r" 
# "s" "t" "u" "v" "w" "x" "y" "z"
LETTERS
# "A" "B" "C" "D" "E" "F" "G" "H" "I" "J" "K" "L" "M" "N" "O" "P" "Q" "R" 
# "S" "T" "U" "V" "W" "X" "Y" "Z"
letters[1:15]
# [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l" "m" "n" "o"

plot(mtcars$mpg)
print(mtcars$mpg)

table(mtcars$mpg)
table(mtcars$cyl)
#   4   6   8 
#   11  7   14 

table(mtcars[,9:10])
str(table(mtcars[,9:10])) # table with 2 dimmensions
table(mtcars[,9:11])
str(table(mtcars[,9:11]))
# 'table' int [1:2, 1:3, 1:6] 3 0 0 4 0 0 4 0 2 2 ...
# - attr(*, "dimnames")=List of 3
# ..$ am  : chr [1:2] "0" "1"
# ..$ gear: chr [1:3] "3" "4" "5"
# ..$ carb: chr [1:6] "1" "2" "3" "4" ...

length(mtcars$mpg)
cat(mtcars$mpg)
mean(mtcars$mpg)
median(mtcars$mpg)
range(mtcars$mpg)
unique(mtcars$mpg)

rep(mtcars$mpg,10)

names()
colnames()
rownames()

diff(mtcars$mpg)
plot(diff(mtcars$mpg),type="h",xlab="",ylab="difference")
points(diff(mtcars$mpg),col="red")

sort(mtcars$mpg)
order(mtcars$mpg)
rev(mtcars$mpg)
rev(sort(mtcars$mpg))

cumsum(mtcars$mpg)
cumprod(mtcars$mpg)

rank(mtcars$vs) # Returns the sample ranks of the values in a vector.
(r1 <- rank(x1 <- c(3, 1, 4, 15, 92)))
rank(mtcars$vs, ties.method= "first")  # first occurrence wins 
                                       ## ranks without averaging
rank(mtcars$vs, ties.method= "last")   #  last occurrence wins 
                                       ## ranks without averaging
rank(mtcars$vs, ties.method= "random") # ties broken at random 
                                       ## ranks without averaging
rank(mtcars$vs, ties.method= "random") # and again 
                                       ## ranks without averaging

1:10
7:20
intersect(1:10, 7:20)

match(1:10,7:20)    # match returns a vector of the positions of (first) 
                    # matches of its first argument in its second.

1:10 %in% c(1,3,5,9)
sstr <- c("c","ab","B","bba","c",NA,"@","bla","a","Ba","%")
sstr %in% c(letters, LETTERS)
sstr[sstr %in% c(letters, LETTERS)]

apply()
sapply()
aggregate()
aggregate(state.x77, list(Region = state.region), mean)
tapply()

merge(mtcars$vs,c(1,2))

read.csv()
read.table()

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
# histograms

hist(mtcars$mpg)

# looping with R
par(mfrow=c(3,4))
for(i in 1:length(mtcars[1,])){ 
  hist(mtcars[,i],main=paste("Data: MTcars",colnames(mtcars)[i]),
                              xlab=paste(colnames(mtcars)[i]))
}
par(mfrow=c(1,1))

hist(mtcars$mpg, main="Data: MTcars - mpg Miles per gallon", 
     xlab="mpg Miles per gallon")

hist(mtcars$mpg, breaks=10, main="Data: MTcars - mpg Miles per gallon", 
     xlab="mpg Miles per gallon")

hist(mtcars$mpg, breaks=length(mtcars$mpg), 
     main="Data: MTcars - mpg Miles per gallon", 
     xlab="mpg Miles per gallon")

# probability densities, component
hist(mtcars$mpg, breaks=length(mtcars$mpg), freq=FALSE, 
     main="Data: MTcars - mpg Miles per gallon", xlab="mpg Miles per gallon")

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
#  Boxplot with Scatterplot

par( fig = c( 0, 0.8, 0, 0.8 ), new = TRUE)
plot( mtcars$wt, mtcars$mpg, xlab = "Car Weight",
      ylab = "Miles Per Gallon" )
abline( lm( mpg~wt ), col = "red" )      # regression line (y~x)
lines( lowess( wt, mpg ), col = "blue" ) # lowess line (x,y) 
                                         # LOWESS smoother which uses 
                                         # locally-weighted 
                                         # polynomial regression
model <- lm( mpg~wt )
text( 4, 32, paste( "Intercept", model$coefficients[1] ) )
text( 4, 30, paste( "wt", model$coefficients[2] ) )

par( fig = c( 0, 0.8, 0.55, 1 ), new = TRUE )
boxplot(mtcars$wt, horizontal = TRUE, axes=FALSE, 
                                 col= "green", notch = TRUE )
m.wt <- mean( mtcars$wt )
mtext( paste( "mean wt", m.wt ), side = 3, outer = TRUE, line = -8 )

par( fig = c( 0.65, 1, 0, 0.8 ), new = TRUE)
boxplot( mtcars$mpg, axes = FALSE, col = "green", notch = TRUE)
m.mpg <- mean( mtcars$mpg )
mtext( paste( "mean mpg", m.mpg ), side = 2, outer = TRUE, line = -28)

mtext( "Miles per gallon vs Car Weight", side = 3, outer = TRUE, line = -3 )

par( mfrow = c( 1, 1 ) )

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# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

# some loops

for(i in 1:360){

plot(cos((1:360)*pi/i),sin((1:360)*pi/i),type="l")

print(i)

Sys.sleep(0.1)

}

for(i in 360:1){

plot(cos((1:360)*pi/i),sin((1:360)*pi/i),type="l")

print(i)

Sys.sleep(0.1)

}

for(i in 1:360){

for(e in 1:360){

plot(cos((1:360)*pi/i),sin((1:360)*pi/e),type="l")

print(i)

Sys.sleep(0.1)

}

for(i in 1:360){

for(e in 1:360){

plot(sin((1:360)*pi/i),cos((1:360)*pi/e),type="l")

print(i)

Sys.sleep(0.1)

}

for(i in 1:10){

for(e in 1:10){

plot(sin((1:360)*pi/i),cos((1:360)*pi/e),type="l")

mtext(paste("i:",i,"e:",e), side=3, outer=TRUE, line=-3)

print(paste("i:",i,"e:",e))

Sys.sleep(0.1)

}

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

# function collection

letters

# "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l" "m" "n" "o" "p" "q" "r"

# "s" "t" "u" "v" "w" "x" "y" "z"

LETTERS

# "A" "B" "C" "D" "E" "F" "G" "H" "I" "J" "K" "L" "M" "N" "O" "P" "Q" "R"

# "S" "T" "U" "V" "W" "X" "Y" "Z"

letters[1:15]

# [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l" "m" "n" "o"

plot(mtcars$mpg)

print(mtcars$mpg)

table(mtcars$mpg)

table(mtcars$cyl)

# 4 6 8

# 11 7 14

table(mtcars[,9:10])

str(table(mtcars[,9:10])) # table with 2 dimmensions

table(mtcars[,9:11])

str(table(mtcars[,9:11]))

# 'table' int [1:2, 1:3, 1:6] 3 0 0 4 0 0 4 0 2 2 ...

# - attr(*, "dimnames")=List of 3

# ..$ am : chr [1:2] "0" "1"

# ..$ gear: chr [1:3] "3" "4" "5"

# ..$ carb: chr [1:6] "1" "2" "3" "4" ...

length(mtcars$mpg)

cat(mtcars$mpg)

mean(mtcars$mpg)

median(mtcars$mpg)

range(mtcars$mpg)

unique(mtcars$mpg)

rep(mtcars$mpg,10)

names()

colnames()

rownames()

diff(mtcars$mpg)

plot(diff(mtcars$mpg),type="h",xlab="",ylab="difference")

points(diff(mtcars$mpg),col="red")

sort(mtcars$mpg)

order(mtcars$mpg)

rev(mtcars$mpg)

rev(sort(mtcars$mpg))

cumsum(mtcars$mpg)

cumprod(mtcars$mpg)

rank(mtcars$vs) # Returns the sample ranks of the values in a vector.

(r1 <- rank(x1 <- c(3, 1, 4, 15, 92)))

rank(mtcars$vs, ties.method= "first") # first occurrence wins

## ranks without averaging

rank(mtcars$vs, ties.method= "last") # last occurrence wins

## ranks without averaging

rank(mtcars$vs, ties.method= "random") # ties broken at random

## ranks without averaging

rank(mtcars$vs, ties.method= "random") # and again

## ranks without averaging

1:10

7:20

intersect(1:10, 7:20)

match(1:10,7:20) # match returns a vector of the positions of (first)

# matches of its first argument in its second.

1:10 %in% c(1,3,5,9)

sstr <- c("c","ab","B","bba","c",NA,"@","bla","a","Ba","%")

sstr %in% c(letters, LETTERS)

sstr[sstr %in% c(letters, LETTERS)]

apply()

sapply()

aggregate()

aggregate(state.x77, list(Region = state.region), mean)

tapply()

merge(mtcars$vs,c(1,2))

read.csv()

read.table()

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

# histograms

hist(mtcars$mpg)

# looping with R

par(mfrow=c(3,4))

for(i in 1:length(mtcars[1,])){

hist(mtcars[,i],main=paste("Data: MTcars",colnames(mtcars)[i]),

xlab=paste(colnames(mtcars)[i]))

}

par(mfrow=c(1,1))

hist(mtcars$mpg, main="Data: MTcars - mpg Miles per gallon",

xlab="mpg Miles per gallon")

hist(mtcars$mpg, breaks=10, main="Data: MTcars - mpg Miles per gallon",

xlab="mpg Miles per gallon")

hist(mtcars$mpg, breaks=length(mtcars$mpg),

main="Data: MTcars - mpg Miles per gallon",

xlab="mpg Miles per gallon")

# probability densities, component

hist(mtcars$mpg, breaks=length(mtcars$mpg), freq=FALSE,

main="Data: MTcars - mpg Miles per gallon", xlab="mpg Miles per gallon")

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

# Boxplot with Scatterplot

par( fig = c( 0, 0.8, 0, 0.8 ), new = TRUE)

plot( mtcars$wt, mtcars$mpg, xlab = "Car Weight",

ylab = "Miles Per Gallon" )

abline( lm( mpg~wt ), col = "red" ) # regression line (y~x)

lines( lowess( wt, mpg ), col = "blue" ) # lowess line (x,y)

# LOWESS smoother which uses

# locally-weighted

# polynomial regression

model <- lm( mpg~wt )

text( 4, 32, paste( "Intercept", model$coefficients[1] ) )

text( 4, 30, paste( "wt", model$coefficients[2] ) )

par( fig = c( 0, 0.8, 0.55, 1 ), new = TRUE )

boxplot(mtcars$wt, horizontal = TRUE, axes=FALSE,

col= "green", notch = TRUE )

m.wt <- mean( mtcars$wt )

mtext( paste( "mean wt", m.wt ), side = 3, outer = TRUE, line = -8 )

par( fig = c( 0.65, 1, 0, 0.8 ), new = TRUE)

boxplot( mtcars$mpg, axes = FALSE, col = "green", notch = TRUE)

m.mpg <- mean( mtcars$mpg )

mtext( paste( "mean mpg", m.mpg ), side = 2, outer = TRUE, line = -28)

mtext( "Miles per gallon vs Car Weight", side = 3, outer = TRUE, line = -3 )

par( mfrow = c( 1, 1 ) )

# Martin Stoppacher                                                             #
# office@martinstoppacher.com                                                   #
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #
#################################################################################

# Martin Stoppacher #

# office@martinstoppacher.com #

# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - #

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

Renewable electricity output – Regions

Leave a reply

https://host6.ssl-net.net/martinstoppacher_com/blog/?p=1194

# -------------

# region

# World
# Euro area
# European Union
# Europe & Central Asia
# Arab World
# North America
# Latin America & Caribbean
# Middle East & North Africa
# Sub-Saharan Africa 
# East Asia & Pacific
# South Asia

target.area <- which(renewable.electricity.output$country=="World")
renewable.electricity.output[target.area,]
plot(renewable.electricity.output[target.area,4:3],type="l",
     main=titel,sub=subtitel,ylab="%",xlab="",xlim=c(1980,2020),ylim=c(1,90),
     axes=TRUE)
text(1985, 20, "World",cex=0.7)

target.area <- which(renewable.electricity.output$country=="Euro area")
renewable.electricity.output[target.area,]
lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="red")
text(1985, 12, "Euro area", col="red",cex=0.7)

target.area <- which(renewable.electricity.output$country=="Arab World")
renewable.electricity.output[target.area,]
lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="green")
text(1985, 5, "Arab World", col="green",cex=0.7)

target.area <- which(renewable.electricity.output$country=="North America")
renewable.electricity.output[target.area,]
lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="blue",lty=2)
text(1985, 17, "North America", col="blue",cex=0.7)

target.area <- which(renewable.electricity.output$country=="Latin America & Caribbean")
renewable.electricity.output[target.area,]
lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="yellow")
text(1985, 65, "Latin America & Caribbean", col="yellow",cex=0.7)

# target.area <- which(renewable.electricity.output$country=="Middle East & North Africa")
# renewable.electricity.output[target.area,]
# lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="orange")
# text(1985, 5, "Middle East & North Africa", col="orange",cex=0.7)

target.area <- which(renewable.electricity.output$country=="Sub-Saharan Africa")
renewable.electricity.output[target.area,]
lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="cyan",lty=3)
text(1985, 23, "Sub-Saharan Africa", col="cyan",cex=0.7)

target.area <- which(renewable.electricity.output$country=="East Asia & Pacific")
renewable.electricity.output[target.area,]
lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="magenta",lty=4)
text(1985, 14.5, "East Asia & Pacific", col="magenta",cex=0.7)

target.area <- which(renewable.electricity.output$country=="South Asia")
renewable.electricity.output[target.area,]
lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="pink",lty=5)
text(1985, 28, "South Asia", col="pink",cex=0.7)

# -------------

# region

# World

# Euro area

# European Union

# Europe & Central Asia

# Arab World

# North America

# Latin America & Caribbean

# Middle East & North Africa

# Sub-Saharan Africa

# East Asia & Pacific

# South Asia

target.area <- which(renewable.electricity.output$country=="World")

renewable.electricity.output[target.area,]

plot(renewable.electricity.output[target.area,4:3],type="l",

main=titel,sub=subtitel,ylab="%",xlab="",xlim=c(1980,2020),ylim=c(1,90),

axes=TRUE)

text(1985, 20, "World",cex=0.7)

target.area <- which(renewable.electricity.output$country=="Euro area")

renewable.electricity.output[target.area,]

lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="red")

text(1985, 12, "Euro area", col="red",cex=0.7)

target.area <- which(renewable.electricity.output$country=="Arab World")

renewable.electricity.output[target.area,]

lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="green")

text(1985, 5, "Arab World", col="green",cex=0.7)

target.area <- which(renewable.electricity.output$country=="North America")

renewable.electricity.output[target.area,]

lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="blue",lty=2)

text(1985, 17, "North America", col="blue",cex=0.7)

target.area <- which(renewable.electricity.output$country=="Latin America & Caribbean")

renewable.electricity.output[target.area,]

lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="yellow")

text(1985, 65, "Latin America & Caribbean", col="yellow",cex=0.7)

# target.area <- which(renewable.electricity.output$country=="Middle East & North Africa")

# renewable.electricity.output[target.area,]

# lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="orange")

# text(1985, 5, "Middle East & North Africa", col="orange",cex=0.7)

target.area <- which(renewable.electricity.output$country=="Sub-Saharan Africa")

renewable.electricity.output[target.area,]

lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="cyan",lty=3)

text(1985, 23, "Sub-Saharan Africa", col="cyan",cex=0.7)

target.area <- which(renewable.electricity.output$country=="East Asia & Pacific")

renewable.electricity.output[target.area,]

lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="magenta",lty=4)

text(1985, 14.5, "East Asia & Pacific", col="magenta",cex=0.7)

target.area <- which(renewable.electricity.output$country=="South Asia")

renewable.electricity.output[target.area,]

lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="pink",lty=5)

text(1985, 28, "South Asia", col="pink",cex=0.7)

Renewable electricity output – World Map

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https://host6.ssl-net.net/martinstoppacher_com/blog/?p=1194

# ----------------

library(rworldmap)

options("scipen"=100, "digits"=4)

year <- 2015
target.year <- which(renewable.electricity.output$year==year)
head(renewable.electricity.output[target.year,])

renewable.electricity.output.year <- na.omit(renewable.electricity.output[target.year,])
renewable.electricity.output.year <- renewable.electricity.output.year[which(renewable.electricity.output.year$EG.ELC.RNEW.ZS>0),]

mapped_data <- joinCountryData2Map(renewable.electricity.output.year, joinCode = "ISO2", nameJoinColumn = "iso2c")
par(mai=c(0,0,0.2,0),xaxs="i",yaxs="i")
mapCountryData(mapped_data, nameColumnToPlot = "EG.ELC.RNEW.ZS",mapTitle=paste(titel,subtitel))

mapCountryData(mapped_data, nameColumnToPlot = "EG.ELC.RNEW.ZS",mapRegion="world",mapTitle=paste(titel,subtitel),
               numCats=2,catMethod=c(0:100),addLegend=FALSE,colourPalette=c("red","green"))

# ----------------

library(rworldmap)

options("scipen"=100, "digits"=4)

year <- 2015

target.year <- which(renewable.electricity.output$year==year)

head(renewable.electricity.output[target.year,])

renewable.electricity.output.year <- na.omit(renewable.electricity.output[target.year,])

renewable.electricity.output.year <- renewable.electricity.output.year[which(renewable.electricity.output.year$EG.ELC.RNEW.ZS>0),]

mapped_data <- joinCountryData2Map(renewable.electricity.output.year, joinCode = "ISO2", nameJoinColumn = "iso2c")

par(mai=c(0,0,0.2,0),xaxs="i",yaxs="i")

mapCountryData(mapped_data, nameColumnToPlot = "EG.ELC.RNEW.ZS",mapTitle=paste(titel,subtitel))

mapCountryData(mapped_data, nameColumnToPlot = "EG.ELC.RNEW.ZS",mapRegion="world",mapTitle=paste(titel,subtitel),

numCats=2,catMethod=c(0:100),addLegend=FALSE,colourPalette=c("red","green"))

mapCountryData(mapped_data, nameColumnToPlot = "EG.ELC.RNEW.ZS",mapRegion="world",mapTitle=paste(titel,subtitel),
               numCats=3,catMethod=c(0:100),addLegend=FALSE,colourPalette=c("red","yellow","green"))
legend(-179, -10, legend=c("low", "medium","high"), col=c("red", "yellow","green"), lty=1:3, cex=0.6)

mapCountryData(mapped_data, nameColumnToPlot = "EG.ELC.RNEW.ZS",mapRegion="world",mapTitle=paste(titel,subtitel),

numCats=3,catMethod=c(0:100),addLegend=FALSE,colourPalette=c("red","yellow","green"))

legend(-179, -10, legend=c("low", "medium","high"), col=c("red", "yellow","green"), lty=1:3, cex=0.6)

Renewable electricity output – Statistics

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# Renewable electricity output (% of total electricity output) - EG.ELC.RNEW.ZS

1	# Renewable electricity output (% of total electricity output) - EG.ELC.RNEW.ZS

library("XML")
library("WDI")
library("gridExtra")
library("scatterplot3d")

options(scipen=100) # turning of scientific notation

titel<-"Renewable electricity output"
subtitel<-"(% of total electricity output)"

renewable.electricity.output <- WDI(country="all", indicator="EG.ELC.RNEW.ZS", start=1900, end=2019)
str(renewable.electricity.output)

# 'data.frame':	15840 obs. of  4 variables:
#   $ iso2c         : chr  "1A" "1A" "1A" "1A" ...
# $ country       : chr  "Arab World" "Arab World" "Arab World" "Arab World" ...
# $ EG.ELC.RNEW.ZS: num  NA NA NA NA 2.92 ...
# $ year          : num  2019 2018 2017 2016 2015 ...

head(renewable.electricity.output)

# iso2c    country EG.ELC.RNEW.ZS year
# 1    1A Arab World             NA 2019
# 2    1A Arab World             NA 2018
# 3    1A Arab World             NA 2017
# 4    1A Arab World             NA 2016
# 5    1A Arab World       2.920702 2015
# 6    1A Arab World       3.278073 2014

library("XML")

library("WDI")

library("gridExtra")

library("scatterplot3d")

options(scipen=100) # turning of scientific notation

titel<-"Renewable electricity output"

subtitel<-"(% of total electricity output)"

renewable.electricity.output <- WDI(country="all", indicator="EG.ELC.RNEW.ZS", start=1900, end=2019)

str(renewable.electricity.output)

# 'data.frame': 15840 obs. of 4 variables:

# $ iso2c : chr "1A" "1A" "1A" "1A" ...

# $ country : chr "Arab World" "Arab World" "Arab World" "Arab World" ...

# $ EG.ELC.RNEW.ZS: num NA NA NA NA 2.92 ...

# $ year : num 2019 2018 2017 2016 2015 ...

head(renewable.electricity.output)

# iso2c country EG.ELC.RNEW.ZS year

# 1 1A Arab World NA 2019

# 2 1A Arab World NA 2018

# 3 1A Arab World NA 2017

# 4 1A Arab World NA 2016

# 5 1A Arab World 2.920702 2015

# 6 1A Arab World 3.278073 2014

# selection of the year 2015

year <- 2015
target.year <- which(renewable.electricity.output$year==year)
head(renewable.electricity.output[target.year,])

# iso2c                                     country EG.ELC.RNEW.ZS year
# 5      1A                                  Arab World       2.920702 2015
# 65     S3                      Caribbean small states       8.914780 2015
# 125    B8              Central Europe and the Baltics      20.252851 2015
# 185    V2                  Early-demographic dividend      18.104862 2015
# 245    Z4                         East Asia & Pacific      20.412466 2015
# 305    4E East Asia & Pacific (excluding high income)      23.394930 2015

# selection of the year 2015

year <- 2015

target.year <- which(renewable.electricity.output$year==year)

head(renewable.electricity.output[target.year,])

# iso2c country EG.ELC.RNEW.ZS year

# 5 1A Arab World 2.920702 2015

# 65 S3 Caribbean small states 8.914780 2015

# 125 B8 Central Europe and the Baltics 20.252851 2015

# 185 V2 Early-demographic dividend 18.104862 2015

# 245 Z4 East Asia & Pacific 20.412466 2015

# 305 4E East Asia & Pacific (excluding high income) 23.394930 2015

# income categories

– Low income
– Lower middle income
– Upper middle income
– High income

target.income <- which(renewable.electricity.output$country=="Low income")
renewable.electricity.output[target.income,]
plot(renewable.electricity.output[target.income,4:3],type="l",
     main=titel,sub=subtitel,ylab="%",xlab="",xlim=c(1980,2020),ylim=c(10,90),
     axes=TRUE)
text(1985, 65, "Low income",cex=0.7)

target.income <- which(renewable.electricity.output$country=="Low income")

renewable.electricity.output[target.income,]

plot(renewable.electricity.output[target.income,4:3],type="l",

main=titel,sub=subtitel,ylab="%",xlab="",xlim=c(1980,2020),ylim=c(10,90),

axes=TRUE)

text(1985, 65, "Low income",cex=0.7)

target.income <- which(renewable.electricity.output$country=="Lower middle income")
renewable.electricity.output[target.income,]
lines(renewable.electricity.output[target.income,4:3],type="l",main=titel,ylab="%",xlab="",col="red")
text(1985, 20, "Lower middle income", col="red",cex=0.7)

target.income <- which(renewable.electricity.output$country=="Upper middle income")
renewable.electricity.output[target.income,]
lines(renewable.electricity.output[target.income,4:3],type="l",main=titel,ylab="%",xlab="",col="green")
text(1985, 25, "Upper middle income", col="green",cex=0.7)

target.income <- which(renewable.electricity.output$country=="High income")
renewable.electricity.output[target.income,]
lines(renewable.electricity.output[target.income,4:3],type="l",main=titel,ylab="%",xlab="",col="blue")
text(1985, 15, "High income", col="blue",cex=0.7)

target.income <- which(renewable.electricity.output$country=="Lower middle income")

renewable.electricity.output[target.income,]

lines(renewable.electricity.output[target.income,4:3],type="l",main=titel,ylab="%",xlab="",col="red")

text(1985, 20, "Lower middle income", col="red",cex=0.7)

target.income <- which(renewable.electricity.output$country=="Upper middle income")

renewable.electricity.output[target.income,]

lines(renewable.electricity.output[target.income,4:3],type="l",main=titel,ylab="%",xlab="",col="green")

text(1985, 25, "Upper middle income", col="green",cex=0.7)

target.income <- which(renewable.electricity.output$country=="High income")

renewable.electricity.output[target.income,]

lines(renewable.electricity.output[target.income,4:3],type="l",main=titel,ylab="%",xlab="",col="blue")

text(1985, 15, "High income", col="blue",cex=0.7)

# -------------

# region

# World
# Euro area
# European Union
# Europe & Central Asia
# Arab World
# North America
# Latin America & Caribbean
# Middle East & North Africa
# Sub-Saharan Africa 
# East Asia & Pacific
# South Asia

target.area <- which(renewable.electricity.output$country=="World")
renewable.electricity.output[target.area,]
plot(renewable.electricity.output[target.area,4:3],type="l",
     main=titel,sub=subtitel,ylab="%",xlab="",xlim=c(1980,2020),ylim=c(1,90),
     axes=TRUE)
text(1985, 20, "World",cex=0.7)

target.area <- which(renewable.electricity.output$country=="Euro area")
renewable.electricity.output[target.area,]
lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="red")
text(1985, 12, "Euro area", col="red",cex=0.7)

target.area <- which(renewable.electricity.output$country=="Arab World")
renewable.electricity.output[target.area,]
lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="green")
text(1985, 5, "Arab World", col="green",cex=0.7)

target.area <- which(renewable.electricity.output$country=="North America")
renewable.electricity.output[target.area,]
lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="blue",lty=2)
text(1985, 17, "North America", col="blue",cex=0.7)

target.area <- which(renewable.electricity.output$country=="Latin America & Caribbean")
renewable.electricity.output[target.area,]
lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="yellow")
text(1985, 65, "Latin America & Caribbean", col="yellow",cex=0.7)

# target.area <- which(renewable.electricity.output$country=="Middle East & North Africa")
# renewable.electricity.output[target.area,]
# lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="orange")
# text(1985, 5, "Middle East & North Africa", col="orange",cex=0.7)

target.area <- which(renewable.electricity.output$country=="Sub-Saharan Africa")
renewable.electricity.output[target.area,]
lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="cyan",lty=3)
text(1985, 23, "Sub-Saharan Africa", col="cyan",cex=0.7)

target.area <- which(renewable.electricity.output$country=="East Asia & Pacific")
renewable.electricity.output[target.area,]
lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="magenta",lty=4)
text(1985, 14.5, "East Asia & Pacific", col="magenta",cex=0.7)

target.area <- which(renewable.electricity.output$country=="South Asia")
renewable.electricity.output[target.area,]
lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="pink",lty=5)
text(1985, 28, "South Asia", col="pink",cex=0.7)

# -------------

# region

# World

# Euro area

# European Union

# Europe & Central Asia

# Arab World

# North America

# Latin America & Caribbean

# Middle East & North Africa

# Sub-Saharan Africa

# East Asia & Pacific

# South Asia

target.area <- which(renewable.electricity.output$country=="World")

renewable.electricity.output[target.area,]

plot(renewable.electricity.output[target.area,4:3],type="l",

main=titel,sub=subtitel,ylab="%",xlab="",xlim=c(1980,2020),ylim=c(1,90),

axes=TRUE)

text(1985, 20, "World",cex=0.7)

target.area <- which(renewable.electricity.output$country=="Euro area")

renewable.electricity.output[target.area,]

lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="red")

text(1985, 12, "Euro area", col="red",cex=0.7)

target.area <- which(renewable.electricity.output$country=="Arab World")

renewable.electricity.output[target.area,]

lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="green")

text(1985, 5, "Arab World", col="green",cex=0.7)

target.area <- which(renewable.electricity.output$country=="North America")

renewable.electricity.output[target.area,]

lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="blue",lty=2)

text(1985, 17, "North America", col="blue",cex=0.7)

target.area <- which(renewable.electricity.output$country=="Latin America & Caribbean")

renewable.electricity.output[target.area,]

lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="yellow")

text(1985, 65, "Latin America & Caribbean", col="yellow",cex=0.7)

# target.area <- which(renewable.electricity.output$country=="Middle East & North Africa")

# renewable.electricity.output[target.area,]

# lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="orange")

# text(1985, 5, "Middle East & North Africa", col="orange",cex=0.7)

target.area <- which(renewable.electricity.output$country=="Sub-Saharan Africa")

renewable.electricity.output[target.area,]

lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="cyan",lty=3)

text(1985, 23, "Sub-Saharan Africa", col="cyan",cex=0.7)

target.area <- which(renewable.electricity.output$country=="East Asia & Pacific")

renewable.electricity.output[target.area,]

lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="magenta",lty=4)

text(1985, 14.5, "East Asia & Pacific", col="magenta",cex=0.7)

target.area <- which(renewable.electricity.output$country=="South Asia")

renewable.electricity.output[target.area,]

lines(renewable.electricity.output[target.area,4:3],type="l",main=titel,ylab="%",xlab="",col="pink",lty=5)

text(1985, 28, "South Asia", col="pink",cex=0.7)

Using trigonometric functions in R

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R uses radiant as input for trigonometric functions.

# calculating rad
pi/2
90*pi/180 # transforming degree into radiant
degr<-c(0:360)
degr
rad<-grad*(pi/180)
rad

# calculating rad

pi/2

90*pi/180 # transforming degree into radiant

degr<-c(0:360)

degr

rad<-grad*(pi/180)

rad

Now we can plot the function.

sin(rad)
plot(sin(rad))

1 2	sin(rad) plot(sin(rad))

And by playing with the functions we get a funny graphic output.

plot(asin(sin(rad)))
plot(asin(sin(rad)),type="l")
points(sin(rad))
points(sin(rad)*-1,col="green")
lines(asin(sin(rad))*-1)
lines(1/sin(rad),col="red")
lines(1/sin(rad)*-1,col="blue")
points(x=91,y=0)
points(x=271,y=0)

plot(asin(sin(rad)))

plot(asin(sin(rad)),type="l")

points(sin(rad))

points(sin(rad)*-1,col="green")

lines(asin(sin(rad))*-1)

lines(1/sin(rad),col="red")

lines(1/sin(rad)*-1,col="blue")

points(x=91,y=0)

points(x=271,y=0)

And if we include the tangent, the graphic looks like this:

tan(rad)
tangens <- tan(rad)
tangens[91]<-0
tangens[271]<-0
plot(tangens,type="l")
lines(sin(rad),type="l",col="red")
lines(cos(rad),type="l",col="green")

tan(rad)

tangens <- tan(rad)

tangens[91]<-0

tangens[271]<-0

plot(tangens,type="l")

lines(sin(rad),type="l",col="red")

lines(cos(rad),type="l",col="green")

lines(tangens,type="l",col="red")
lines(1/tangens,type="l",col="green")
# dividing by 10 for visual reasons
lines(tangens/10,type="l",col="red")
lines(1/tangens/10,type="l",col="green")

lines(tangens,type="l",col="red")

lines(1/tangens,type="l",col="green")

# dividing by 10 for visual reasons

lines(tangens/10,type="l",col="red")

lines(1/tangens/10,type="l",col="green")

plot(tangens,type="l")
lines(1/tangens,type="l")
plot(tangens,type="l")
lines(1/tangens,type="l",col="green")

plot(tangens,type="l")

lines(1/tangens,type="l")

plot(tangens,type="l")

lines(1/tangens,type="l",col="green")

Audio file conversion with afconvert (mac)

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I was looking for a simple and elegant way to convert a high amount of audio files from one format (.caf) to another (.aif). The solution i found is a very elegant one and also comes included with your operating system – if using a MAC.

afconvert -f AIFF -d BEI24@48000 "Wow Bass 03.caf" "Wow Bass 03.aif"

1	afconvert -f AIFF -d BEI24@48000 "Wow Bass 03.caf" "Wow Bass 03.aif"

And now here is the most amazing part. It is super easy to execute the conversion of multiple files by just one command line.

for i in *.caf; do afconvert -f AIFF -d BEI24@48000 "$i" "${i%.caf}.aif"; done

1	for i in *.caf; do afconvert -f AIFF -d BEI24@48000 "$i" "${i%.caf}.aif"; done

or to run through subdirectories:

for d in */ ; do cd $d; pwd; cd ..; done
for d in */ ; do cd $d; for i in *.caf; do echo *caf; pwd; done; cd ..; done;
for d in */ ; do cd $d; for i in *.caf; do afconvert -f AIFF -d BEI24@48000 "$i" "${i%.caf}.aif"; done; cd ..; done

for d in */ ; do cd $d; pwd; cd ..; done

for d in */ ; do cd $d; for i in *.caf; do echo *caf; pwd; done; cd ..; done;

for d in */ ; do cd $d; for i in *.caf; do afconvert -f AIFF -d BEI24@48000 "$i" "${i%.caf}.aif"; done; cd ..; done

or with recursion by using find:

find -name "*.caf"
find . -type f -iname '*.caf' -print | while read -r name; do cp "$name" "/.../..."; done
find . -type f -iname '*.caf' -print | while read -r name; do afconvert -f AIFF -d BEI24@48000 "$name" "/Volumes/Daten/Logic/test/${name%.*}.aif"; done

find -name "*.caf"

find . -type f -iname '*.caf' -print | while read -r name; do cp "$name" "/.../..."; done

find . -type f -iname '*.caf' -print | while read -r name; do afconvert -f AIFF -d BEI24@48000 "$name" "/Volumes/Daten/Logic/test/${name%.*}.aif"; done

Key	linear PCM format
LE	Little Endian
BE	Big Endian
F	Floating point
I	Integer
UI	Unsigned integer
8/16/24/32/64	Number of bits

Number of bits	Information Size
8	256
16	65536
24	16777216
32	4294967296
64	18446744073709551616

afconvert -hf

1	afconvert -hf

Audio file and data formats:	data_formats:
‘3gpp’ = 3GP Audio (.3gp)	‘Qclp’ ‘aac ‘ ‘aace’ ‘aach’ ‘aacl’ ‘aacp’ ‘samr’
‘3gp2’ = 3GPP-2 Audio (.3g2)	Qclp’ ‘aac ‘ ‘aace’ ‘aach’ ‘aacl’ ‘aacp’ ‘samr’
‘adts’ = AAC ADTS (.aac, .adts)	‘aac ‘ ‘aach’ ‘aacp’
‘ac-3’ = AC3 (.ac3)	‘ac-3’
‘AIFC’ = AIFC (.aifc, .aiff, .aif)	I8 BEI16 BEI24 BEI32 BEF32 BEF64 UI8 ‘ulaw’ ‘alaw’ ‘MAC3’ ‘MAC6’ ‘ima4’ ‘QDMC’ ‘QDM2’ ‘Qclp’ ‘agsm’
‘AIFF’ = AIFF (.aiff, .aif)	I8 BEI16 BEI24 BEI32
‘amrf’ = AMR (.amr)	‘samr’
‘m4af’ = Apple MPEG-4 Audio (.m4a, .m4r)	‘aac ‘ ‘aace’ ‘aach’ ‘aacl’ ‘aacp’ ‘alac’
‘caff’ = CAF (.caf)	‘.mp1’ ‘.mp2’ ‘.mp3’ ‘QDM2’ ‘QDMC’ ‘Qclp’ ‘Qclq’ ‘aac ‘ ‘aace’ ‘aach’ ‘aacl’ ‘aacp’ ‘alac’ ‘alaw’ ‘dvi8’ ‘ilbc’ ‘ima4’ I8 BEI16 BEI24 BEI32 BEF32 BEF64 LEI16 LEI24 LEI32 LEF32 LEF64 ‘ms\x00\x02’ ‘ms\x00\x11’ ‘ms\x001’ ‘paac’ ‘samr’ ‘ulaw’
‘MPG1’ = MPEG Layer 1 (.mp1, .mpeg, .mpa)	‘.mp1’
‘MPG2’ = MPEG Layer 2 (.mp2, .mpeg, .mpa)	‘.mp2’
‘MPG3’ = MPEG Layer 3 (.mp3, .mpeg, .mpa)	‘.mp3’
‘mp4f’ = MPEG-4 Audio (.mp4)	data_formats: ‘aac ‘ ‘aace’ ‘aach’ ‘aacl’ ‘aacp’
‘NeXT’ = NeXT/Sun (.snd, .au)	I8 BEI16 BEI24 BEI32 BEF32 BEF64 ‘ulaw’
‘Sd2f’ = Sound Designer II (.sd2)	I8 BEI16 BEI24 BEI32
‘WAVE’ = WAVE (.wav)	UI8 LEI16 LEI24 LEI32 LEF32 LEF64 ‘ulaw’ ‘alaw’

Supported Audio File and Data Formats in OS X

access file systems – recursive function r

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I was playing around with recursion. This is a short snippet about iterating through folder structures. It shows all directories and subdirectories within a file path.

library(rlang)  # is_empty() to check if a folder is empty

show.dir <- function(path="/",sleep.time=1){
  if(!is_empty(path)){
    
    print(path);
    print(dir(path,all.files = FALSE, full.names = FALSE, recursive = FALSE));
    Sys.sleep(sleep.time);
        
    #print(charToRaw(paste(dir(path,all.files = FALSE, full.names = FALSE, recursive = FALSE)))); # print HEX for fun

    current.dir <- dir(path,all.files = FALSE, full.names = TRUE, recursive = FALSE);
    
    for(i in 1:length(current.dir)){
      
      #print(i)
      #print(current.dir[i])
    
      if(!is_empty(dir(current.dir[i]))){
      
        #show.dir(current.dir[i])
        #print(dir(current.dir[i]));
        
        #print(charToRaw(paste(dir(current.dir[i]),collapse=""))) # print HEX for fun
        
        #Sys.sleep(sleep.time);
        show.dir(current.dir[i],sleep.time=sleep.time)
        
      }else{print(current.dir[i]);print("empty");}
      
    }
    
  }
}
show.dir(path="/Users/impac/Desktop/test",sleep.time=5)
show.dir()

show.dir(sleep.time=0.3)
show.dir(sleep.time=0.01)

library(rlang) # is_empty() to check if a folder is empty

show.dir <- function(path="/",sleep.time=1){

if(!is_empty(path)){

print(path);

print(dir(path,all.files = FALSE, full.names = FALSE, recursive = FALSE));

Sys.sleep(sleep.time);

#print(charToRaw(paste(dir(path,all.files = FALSE, full.names = FALSE, recursive = FALSE)))); # print HEX for fun

current.dir <- dir(path,all.files = FALSE, full.names = TRUE, recursive = FALSE);

for(i in 1:length(current.dir)){

#print(i)

#print(current.dir[i])

if(!is_empty(dir(current.dir[i]))){

#show.dir(current.dir[i])

#print(dir(current.dir[i]));

#print(charToRaw(paste(dir(current.dir[i]),collapse=""))) # print HEX for fun

#Sys.sleep(sleep.time);

show.dir(current.dir[i],sleep.time=sleep.time)

}else{print(current.dir[i]);print("empty");}

}

show.dir(path="/Users/impac/Desktop/test",sleep.time=5)

show.dir()

show.dir(sleep.time=0.3)

show.dir(sleep.time=0.01)

This is the output from a test directory:

[1] "/Users/impac/Desktop/test"
[1] "t1" "t2" "t3" "t4"
[1] "/Users/impac/Desktop/test/t1"
[1] "tt1" "tt2"
[1] "/Users/impac/Desktop/test/t1/tt1"
[1] "ttt1-3"
[1] "/Users/impac/Desktop/test/t1/tt1/ttt1-3"
[1] "empty"
[1] "/Users/impac/Desktop/test/t1/tt2"
[1] "ttt2-3"
[1] "/Users/impac/Desktop/test/t1/tt2/ttt2-3"
[1] "empty"
[1] "/Users/impac/Desktop/test/t2"
[1] "b1" "b2"
[1] "/Users/impac/Desktop/test/t2/b1"
[1] "empty"
[1] "/Users/impac/Desktop/test/t2/b2"
[1] "empty"
[1] "/Users/impac/Desktop/test/t3"
[1] "empty"
[1] "/Users/impac/Desktop/test/t4"
[1] "empty"

[1] "/Users/impac/Desktop/test"

[1] "t1" "t2" "t3" "t4"

[1] "/Users/impac/Desktop/test/t1"

[1] "tt1" "tt2"

[1] "/Users/impac/Desktop/test/t1/tt1"

[1] "ttt1-3"

[1] "/Users/impac/Desktop/test/t1/tt1/ttt1-3"

[1] "empty"

[1] "/Users/impac/Desktop/test/t1/tt2"

[1] "ttt2-3"

[1] "/Users/impac/Desktop/test/t1/tt2/ttt2-3"

[1] "empty"

[1] "/Users/impac/Desktop/test/t2"

[1] "b1" "b2"

[1] "/Users/impac/Desktop/test/t2/b1"

[1] "empty"

[1] "/Users/impac/Desktop/test/t2/b2"

[1] "empty"

[1] "/Users/impac/Desktop/test/t3"

[1] "empty"

[1] "/Users/impac/Desktop/test/t4"

[1] "empty"

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