Basic Terminology
Prerequisite
Install R from https://cran.r-project.org/, as well as an integrated development environment (IDE) (e.g., editor, build tools):
- RStudio: http://www.rstudio.com/.
R (contributed) packages can be installed via either of the following versions.
Release versions:
comprehensive R Archive Network (CRAN): install.packages(“mypkg”);
bioconductor: devtools::install_bioc(“mypackage”) or BiocManager::install(“mypackage”).
Development versions:
R-Forge: install.packages(“mypkg”, repos = “https://R-Forge.R-project.org”));
GitHub: devtools::install_github(“maintainer/mypkg”).
To work with R,
create a script (a file, e.g. myscript.R) containing the R source code; and
run the script interactively by executing it line-by-line.
To run the current line, press Control+R or right-click and select Run line or selection. If you want to understand a command, enter ?command in R console.
This is a good practice: clean all objects from memory before using an R instance.
rm(list=ls(all=TRUE)) Creating objects
- Scalars
scalar1 <- 1 Run the next line and the value of the object scalar1 appears in the R Console.
scalar1 ## [1] 1- Vectors
vector1 <- array(1,5)
vector1## [1] 1 1 1 1 1# ':' means 'to'
sequence1 <- 1:10
sequence1## [1] 1 2 3 4 5 6 7 8 9 10sequence2 <- c(1,4,-7,10,-20)
sequence2## [1] 1 4 -7 10 -20sequence3 <- seq(1,10,by=2)
sequence3## [1] 1 3 5 7 9# repeat 5 twice
repeated1 <- rep(5,2)
repeated1## [1] 5 5# repeat 1:5 three times
repeated.sequence1 <- rep(1:5,3)
repeated.sequence1## [1] 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5# display the 5th element in the vector
sequence1[5] ## [1] 5# matrix of 4 by 5
matrix1 <- array(1:20,c(4,5))
matrix1## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 5 9 13 17
## [2,] 2 6 10 14 18
## [3,] 3 7 11 15 19
## [4,] 4 8 12 16 20# matrix of 4 by 6 with all 8
matrix2 <- matrix(8,4,6)
matrix2## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 8 8 8 8 8 8
## [2,] 8 8 8 8 8 8
## [3,] 8 8 8 8 8 8
## [4,] 8 8 8 8 8 8# dimension of a matrix
dim(matrix1)## [1] 4 5dim(matrix2)## [1] 4 6# put vector1 as the last row of matrix1
matrix3 <- rbind(matrix1,vector1)
matrix3## [,1] [,2] [,3] [,4] [,5]
## 1 5 9 13 17
## 2 6 10 14 18
## 3 7 11 15 19
## 4 8 12 16 20
## vector1 1 1 1 1 1# display the 2nd row, 3rd column element of matrix
matrix3[2,3] ##
## 10- Strings
string1 <- "Hello!"
string1## [1] "Hello!"string2 <- c(string1, "Happy New Year.")
string2## [1] "Hello!" "Happy New Year."# Combine string1 and string2 with "---" in between
string3 <- paste(string2,collapse="---")
string3## [1] "Hello!---Happy New Year."# Name columns using labels
colnames(matrix3)## NULLlabels <- c("A", "B", "C", "D", "E")
colnames(matrix3) <- paste("Column",labels,sep=" ")
colnames(matrix3)## [1] "Column A" "Column B" "Column C" "Column D" "Column E"# Name rows using 1:5
rownames(matrix3) <- paste("Row",1:5,sep=" ")
rownames(matrix3)## [1] "Row 1" "Row 2" "Row 3" "Row 4" "Row 5"Note: sep is different from collapse.
Basic calculations
- Transpose
scalar1*matrix3## Column A Column B Column C Column D Column E
## Row 1 1 5 9 13 17
## Row 2 2 6 10 14 18
## Row 3 3 7 11 15 19
## Row 4 4 8 12 16 20
## Row 5 1 1 1 1 1t(matrix3) ## Row 1 Row 2 Row 3 Row 4 Row 5
## Column A 1 2 3 4 1
## Column B 5 6 7 8 1
## Column C 9 10 11 12 1
## Column D 13 14 15 16 1
## Column E 17 18 19 20 1- Inverse
matrix3^-1 ## Column A Column B Column C Column D Column E
## Row 1 1.0000000 0.2000000 0.11111111 0.07692308 0.05882353
## Row 2 0.5000000 0.1666667 0.10000000 0.07142857 0.05555556
## Row 3 0.3333333 0.1428571 0.09090909 0.06666667 0.05263158
## Row 4 0.2500000 0.1250000 0.08333333 0.06250000 0.05000000
## Row 5 1.0000000 1.0000000 1.00000000 1.00000000 1.00000000- Element-by-element multiplication
sqrt(matrix3)## Column A Column B Column C Column D Column E
## Row 1 1.000000 2.236068 3.000000 3.605551 4.123106
## Row 2 1.414214 2.449490 3.162278 3.741657 4.242641
## Row 3 1.732051 2.645751 3.316625 3.872983 4.358899
## Row 4 2.000000 2.828427 3.464102 4.000000 4.472136
## Row 5 1.000000 1.000000 1.000000 1.000000 1.000000matrix4 <- matrix(0:24,5,5)
matrix4## [,1] [,2] [,3] [,4] [,5]
## [1,] 0 5 10 15 20
## [2,] 1 6 11 16 21
## [3,] 2 7 12 17 22
## [4,] 3 8 13 18 23
## [5,] 4 9 14 19 24matrix3*matrix4 ## Column A Column B Column C Column D Column E
## Row 1 0 25 90 195 340
## Row 2 2 36 110 224 378
## Row 3 6 49 132 255 418
## Row 4 12 64 156 288 460
## Row 5 4 9 14 19 24- Matrix algebra
matrix3%*%matrix4 ## [,1] [,2] [,3] [,4] [,5]
## Row 1 130 355 580 805 1030
## Row 2 140 390 640 890 1140
## Row 3 150 425 700 975 1250
## Row 4 160 460 760 1060 1360
## Row 5 10 35 60 85 110Consider a matrix from all rows and first three column of matrix4.
sequence3%*%matrix4## [,1] [,2] [,3] [,4] [,5]
## [1,] 70 195 320 445 570sequence3%*%matrix4[,1:3] ## [,1] [,2] [,3]
## [1,] 70 195 320Control flow
IfStatement
if (scalar1>4) {
print("Scalar bigger than 4")
} else print("Scalar smaller or equal 4")## [1] "Scalar smaller or equal 4"Forandwhileloops
matrix5 <- matrix(0,nrow(matrix4),ncol(matrix4))
for (i in 1:nrow(matrix4)){
for (j in 1:ncol(matrix4)){
matrix5[i,j] <- matrix4[i,j]+i*j
}
}
matrix5## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 7 13 19 25
## [2,] 3 10 17 24 31
## [3,] 5 13 21 29 37
## [4,] 7 16 25 34 43
## [5,] 9 19 29 39 49matrix5-matrix4 ## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 2 3 4 5
## [2,] 2 4 6 8 10
## [3,] 3 6 9 12 15
## [4,] 4 8 12 16 20
## [5,] 5 10 15 20 25This is the while-loop equivalent to the for-loop above:
matrix6 <- matrix(0,nrow(matrix4),ncol(matrix4))
i <- 1
while (i<=nrow(matrix4)){
j <- 1
while (j<=nrow(matrix4)){
matrix6[i,j] <- matrix4[i,j]+i*j
j <- j+1
}
i <- i+1
}
matrix5-matrix6## [,1] [,2] [,3] [,4] [,5]
## [1,] 0 0 0 0 0
## [2,] 0 0 0 0 0
## [3,] 0 0 0 0 0
## [4,] 0 0 0 0 0
## [5,] 0 0 0 0 0Random number generation
- Generate random numbers from a normal distribution.
# draws 5 RV
rand.norm <- rnorm(5)
rand.norm## [1] 1.31970588 -0.44335160 2.26050870 -0.07189716 0.96160733# draws 5 RV with mean 5 and standard dev. 3
rnorm(5,mean=5,sd=3) ## [1] 5.061060 5.851887 2.459515 7.089227 7.961723# density at the common cut-off 1.96 ~ 0.05
dnorm(1.96) ## [1] 0.05844094# cumulative distribution function
pnorm(-1.96) ## [1] 0.0249979# quantile function: the inverse of pnorm
qnorm(pnorm(-1.96)) ## [1] -1.96- Generate random numbers from a student-t distribution.
# set degrees of freedom
dof <- 4
# draw 5 RV from Student t distribution
rt(5, df=dof) ## [1] -0.7053972 0.6095279 0.2258550 -0.4576023 -8.2033943# draw 5 RV from Student t distribution with non-centrality
rt(5, df=dof, ncp=7) ## [1] 6.389403 5.620142 7.406423 6.593214 17.165841# density at the common cut-off 1.96
dt(1.96, df=dof) ## [1] 0.06968985# cumulative distribution function
pt(-1.96, df=dof) ## [1] 0.06077732# quantile function: the inverse of pnorm
qt(0.05, df=dof) # quantile ## [1] -2.131847- Generate pseudo random numbers with/out replacement.
# without replacement
sample(1:10)## [1] 7 3 1 9 4 2 5 10 8 6# with replacement
sample(1:10, replace=TRUE)## [1] 9 5 10 2 10 2 5 6 1 5- Control the draws (this is pseudo-random afterall).
The set.seed() function in R is used to create reproducible results when writing code that involves creating variables that take on random values. By using the set.seed() function, you guarantee that the same random values are produced each time you run the code.
your.choice <- 5
set.seed(your.choice)
rnorm(5)## [1] -0.84085548 1.38435934 -1.25549186 0.07014277 1.71144087# By calling the seed you stored, you can retrive the 5 numbers just generated.
set.seed(your.choice)
rnorm(5)## [1] -0.84085548 1.38435934 -1.25549186 0.07014277 1.71144087# Without calling the seed number, you will get another 5 different random numbers
rnorm(5)## [1] -0.6029080 -0.4721664 -0.6353713 -0.2857736 0.1381082Data and dates
R provides some data sets. For example, see available data sets.
data(Orange)
Orange## Tree age circumference
## 1 1 118 30
## 2 1 484 58
## 3 1 664 87
## 4 1 1004 115
## 5 1 1231 120
## 6 1 1372 142
## 7 1 1582 145
## 8 2 118 33
## 9 2 484 69
## 10 2 664 111
## 11 2 1004 156
## 12 2 1231 172
## 13 2 1372 203
## 14 2 1582 203
## 15 3 118 30
## 16 3 484 51
## 17 3 664 75
## 18 3 1004 108
## 19 3 1231 115
## 20 3 1372 139
## 21 3 1582 140
## 22 4 118 32
## 23 4 484 62
## 24 4 664 112
## 25 4 1004 167
## 26 4 1231 179
## 27 4 1372 209
## 28 4 1582 214
## 29 5 118 30
## 30 5 484 49
## 31 5 664 81
## 32 5 1004 125
## 33 5 1231 142
## 34 5 1372 174
## 35 5 1582 177See available objects in this R instance’s memory (ls=list of objects).
ls()## [1] "dof" "i" "j" "labels" "matrix1"
## [6] "matrix2" "matrix3" "matrix4" "matrix5" "matrix6"
## [11] "rand.norm" "repeated.sequence1" "repeated1" "scalar1" "sequence1"
## [16] "sequence2" "sequence3" "string1" "string2" "string3"
## [21] "vector1" "your.choice"Convert part of Orange to time series.
Orange1TS <- ts(Orange[1:6,], start=c(1995, 1), frequency=1)
Orange1TS## Time Series:
## Start = 1995
## End = 2000
## Frequency = 1
## Tree age circumference
## 1995 2 118 30
## 1996 2 484 58
## 1997 2 664 87
## 1998 2 1004 115
## 1999 2 1231 120
## 2000 2 1372 142Some basic ts commands.
start(Orange1TS)## [1] 1995 1end(Orange1TS)## [1] 2000 1# next data - previous data
diff(Orange1TS[,3]) ## Time Series:
## Start = 1996
## End = 2000
## Frequency = 1
## [1] 28 29 28 5 22# Look at the result in R console
lag(Orange1TS[,3],2) ## Time Series:
## Start = 1993
## End = 1998
## Frequency = 1
## [1] 30 58 87 115 120 142cbind(Orange1TS,diff(Orange1TS[,3]),lag(Orange1TS[,3],2))## Time Series:
## Start = 1993
## End = 2000
## Frequency = 1
## Orange1TS.Tree Orange1TS.age Orange1TS.circumference diff(Orange1TS[, 3]) lag(Orange1TS[, 3], 2)
## 1993 NA NA NA NA 30
## 1994 NA NA NA NA 58
## 1995 2 118 30 NA 87
## 1996 2 484 58 28 115
## 1997 2 664 87 29 120
## 1998 2 1004 115 28 142
## 1999 2 1231 120 5 NA
## 2000 2 1372 142 22 NAWriting functions
R makes writing user-defined function very easy. This makes sense whenever you have to repeat a specific sequence of commands on similar objects. Commenting is very useful to remind you of what a function 1) needs as input, 2) does and 3) gives out.
summarize.matrix <- function(mat){
# Plots columns of a matrix into one graph and returns summary statistics
nc <- ncol(mat)
dev.new()
plot(mat[,1], type="l", ylim=c(min(mat),max(mat)))
# Plot the first column of mat using line. Set the y axis between maximum and minimum values
if (nc>1) for (j in 2:nc) lines(mat[,j],col=j)
legend("bottomleft",paste("Column",1:nc,sep=" "), col=1:nc, lty=1, cex=.8)
return(summary(mat))
}
summarize.matrix(matrix1)## V1 V2 V3 V4 V5
## Min. :1.00 Min. :5.00 Min. : 9.00 Min. :13.00 Min. :17.00
## 1st Qu.:1.75 1st Qu.:5.75 1st Qu.: 9.75 1st Qu.:13.75 1st Qu.:17.75
## Median :2.50 Median :6.50 Median :10.50 Median :14.50 Median :18.50
## Mean :2.50 Mean :6.50 Mean :10.50 Mean :14.50 Mean :18.50
## 3rd Qu.:3.25 3rd Qu.:7.25 3rd Qu.:11.25 3rd Qu.:15.25 3rd Qu.:19.25
## Max. :4.00 Max. :8.00 Max. :12.00 Max. :16.00 Max. :20.00summarize.matrix(matrix2)## V1 V2 V3 V4 V5 V6
## Min. :8 Min. :8 Min. :8 Min. :8 Min. :8 Min. :8
## 1st Qu.:8 1st Qu.:8 1st Qu.:8 1st Qu.:8 1st Qu.:8 1st Qu.:8
## Median :8 Median :8 Median :8 Median :8 Median :8 Median :8
## Mean :8 Mean :8 Mean :8 Mean :8 Mean :8 Mean :8
## 3rd Qu.:8 3rd Qu.:8 3rd Qu.:8 3rd Qu.:8 3rd Qu.:8 3rd Qu.:8
## Max. :8 Max. :8 Max. :8 Max. :8 Max. :8 Max. :8summarize.matrix(matrix3)## Column A Column B Column C Column D Column E
## Min. :1.0 Min. :1.0 Min. : 1.0 Min. : 1.0 Min. : 1
## 1st Qu.:1.0 1st Qu.:5.0 1st Qu.: 9.0 1st Qu.:13.0 1st Qu.:17
## Median :2.0 Median :6.0 Median :10.0 Median :14.0 Median :18
## Mean :2.2 Mean :5.4 Mean : 8.6 Mean :11.8 Mean :15
## 3rd Qu.:3.0 3rd Qu.:7.0 3rd Qu.:11.0 3rd Qu.:15.0 3rd Qu.:19
## Max. :4.0 Max. :8.0 Max. :12.0 Max. :16.0 Max. :20summarize.matrix(matrix4)## V1 V2 V3 V4 V5
## Min. :0 Min. :5 Min. :10 Min. :15 Min. :20
## 1st Qu.:1 1st Qu.:6 1st Qu.:11 1st Qu.:16 1st Qu.:21
## Median :2 Median :7 Median :12 Median :17 Median :22
## Mean :2 Mean :7 Mean :12 Mean :17 Mean :22
## 3rd Qu.:3 3rd Qu.:8 3rd Qu.:13 3rd Qu.:18 3rd Qu.:23
## Max. :4 Max. :9 Max. :14 Max. :19 Max. :24summarize.matrix(matrix5)## V1 V2 V3 V4 V5
## Min. :1 Min. : 7 Min. :13 Min. :19 Min. :25
## 1st Qu.:3 1st Qu.:10 1st Qu.:17 1st Qu.:24 1st Qu.:31
## Median :5 Median :13 Median :21 Median :29 Median :37
## Mean :5 Mean :13 Mean :21 Mean :29 Mean :37
## 3rd Qu.:7 3rd Qu.:16 3rd Qu.:25 3rd Qu.:34 3rd Qu.:43
## Max. :9 Max. :19 Max. :29 Max. :39 Max. :49For example, concerning “data(Orange)”,
summarize.matrix(Orange1TS)## Tree age circumference
## Min. :2 Min. : 118.0 Min. : 30.00
## 1st Qu.:2 1st Qu.: 529.0 1st Qu.: 65.25
## Median :2 Median : 834.0 Median :101.00
## Mean :2 Mean : 812.2 Mean : 92.00
## 3rd Qu.:2 3rd Qu.:1174.2 3rd Qu.:118.75
## Max. :2 Max. :1372.0 Max. :142.00More
Much has been programmed before and is provided for free in packages. You need to install them, but the common ones are already available on LSE computers. Load them using library("packagename"):
library(QRM) # This is the collection of data and functions we will focus onSee the code of a self-defined function or a function from a package by typing in its name:
summarize.matrix## function(mat){
## # Plots columns of a matrix into one graph and returns summary statistics
## nc <- ncol(mat)
## dev.new()
## plot(mat[,1], type="l", ylim=c(min(mat),max(mat)))
## # Plot the first column of mat using line. Set the y axis between maximum and minimum values
## if (nc>1) for (j in 2:nc) lines(mat[,j],col=j)
## legend("bottomleft",paste("Column",1:nc,sep=" "), col=1:nc, lty=1, cex=.8)
## return(summary(mat))
## }
## <bytecode: 0x0000026fe5d6b7f8>
## <environment: 0x0000026fdf5cf700>QQplot## function (x, a = 0.5, reference = c("normal", "exp", "student"),
## ...)
## {
## n <- length(x)
## reference <- match.arg(reference)
## plot.points <- ppoints(n, a)
## func <- switch(reference, normal = qnorm, exp = qexp, student = qt)
## xp <- func(plot.points, ...)
## y <- sort(x)
## plot(xp, y, xlab = paste("Theoretical", reference), ylab = "Empirical")
## invisible(list(x = x, y = y))
## }
## <bytecode: 0x0000026feea494c8>
## <environment: namespace:QRM>For more information, references and examples add a ‘?’, e.g. ‘?QQplot’.
QQplot(rexp(1000), reference = "exp", rate = 0.3) 
You can find much reading material online for free. Some good reads can be:
A R introduction: http://cran.r-project.org/doc/manuals/R-intro.pdf
On good coding style: short - http://adv-r.had.co.nz/Style.html
… detailed: http://cran.r-project.org/web/packages/rockchalk/vignettes/Rstyle.pdf