3 Data structures
In R we have objects which are functions and objects which are data.
- Function examples:
sin()integrate()plot()paste()
- Data examples:
42
1:5
“R”
matrix(1:12, nrow=4, ncol=3)
data.frame(a=1:5, tmt=c(“a”,“b”,“a”,“b”,“a”))
list(x=2, y=“abc”, x=1:10)
3.1 Vector
> # Vector of numbers, e.g:
> c(1,1.2,pi,exp(1))
## [1] 1.000 1.200 3.142 2.718
>
> # We can have vectors of other things too, e.g:
> c(TRUE,1==2)
## [1] TRUE FALSE
> c("a","ab","abc")
## [1] "a" "ab" "abc"
>
> # But not combinations, e.g:
> c("a",5,1==2)
## [1] "a" "5" "FALSE"
> # Notice that R just turned everything into characters!3.1.1 Constructing vectors
> # Integers from 9 to 17
> x<-9:17
> x
## [1] 9 10 11 12 13 14 15 16 17
>
> # A sequence of 11 numbers from 0 to 1
> y<-seq(0,1,length=11)
> y
## [1] 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
>
> # The same number or the same vector several times
> z<-rep(1:2, 5)
> z
## [1] 1 2 1 2 1 2 1 2 1 2
>
> # Combine numbers, vectors or both into a new vector
> xz10<-c(x,z,10)
> xz10
## [1] 9 10 11 12 13 14 15 16 17 1 2 1 2 1 2 1 2 1 2 103.1.2 Index and logical index
> # Define a vector with integers from (-5) to 5 and extract the numbers with absolute value less than 3:
> x<- (-5):5
> x
## [1] -5 -4 -3 -2 -1 0 1 2 3 4 5
>
> # by their index in the vector:
> x[4:8]
## [1] -2 -1 0 1 2
>
> # or, by negative selection (set a minus in front of the indices we don't want):
> x[-c(1:3,9:11)]
## [1] -2 -1 0 1 2
>
> # A logical vector can be defined by:
> index<-abs(x)<3
> index
## [1] FALSE FALSE FALSE TRUE TRUE TRUE TRUE TRUE FALSE FALSE FALSE
>
> # Now this vector can be used to extract the wanted numbers:
> x[index]
## [1] -2 -1 0 1 23.2 Matrix
- Similar to vectors we can have matrices of objects of the same type, e.g:
> matrix(c(1,2,3,4,5,6)+pi,nrow=2)
## [,1] [,2] [,3]
## [1,] 4.142 6.142 8.142
## [2,] 5.142 7.142 9.142
>
> matrix(c(1,2,3,4,5,6)+pi,nrow=2)<6
## [,1] [,2] [,3]
## [1,] TRUE FALSE FALSE
## [2,] TRUE FALSE FALSE
>
> # We can create higher order arrays, e.g:
> array(c(1:24), dim=c(4,3,2))
## , , 1
##
## [,1] [,2] [,3]
## [1,] 1 5 9
## [2,] 2 6 10
## [3,] 3 7 11
## [4,] 4 8 12
##
## , , 2
##
## [,1] [,2] [,3]
## [1,] 13 17 21
## [2,] 14 18 22
## [3,] 15 19 23
## [4,] 16 20 243.2.1 Constructing matrices
>
> # Combine rows into a matrix
> A<-rbind(1:3, c(1,1,2))
> A
## [,1] [,2] [,3]
## [1,] 1 2 3
## [2,] 1 1 2
>
> # Or columns
> B<-cbind(1:3, c(1,1,2))
> B
## [,1] [,2]
## [1,] 1 1
## [2,] 2 1
## [3,] 3 2
>
> # Define a matrix from one long vector
> C<-matrix(c(1,0,0,1,1,0,1,1,1), nrow=3, ncol=3)
> C
## [,1] [,2] [,3]
## [1,] 1 1 1
## [2,] 0 1 1
## [3,] 0 0 1
>
> # Can also be done by rows by adding "byrow=TRUE" before the last parenthesis. Try!3.2.2 Index and logical index
> A<-matrix((-4):5, nrow=2, ncol=5)
> A
## [,1] [,2] [,3] [,4] [,5]
## [1,] -4 -2 0 2 4
## [2,] -3 -1 1 3 5
>
>
> # Negative values
> A[A<0]
## [1] -4 -3 -2 -1
>
> # Assignments
> A[A<0]<-0
> A
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0 0 0 2 4
## [2,] 0 0 1 3 5
>
> # Matrix rows can be selected by
> A[2,]
## [1] 0 0 1 3 5
>
> # and similarly for columns
> A[,c(2,4)]
## [,1] [,2]
## [1,] 0 2
## [2,] 0 33.2.3 Properties of vectors and matrices
- The
Rfunctionmode()when applied to a vector or to a matrix detects the type of singles that is stored:
> A<-matrix(rep(c(TRUE,FALSE),2),nrow=2)
>
> B<-rnorm(4)
>
> C<-matrix(LETTERS[1:9],nrow=3)
>
> A;B;C
## [,1] [,2]
## [1,] TRUE TRUE
## [2,] FALSE FALSE
## [1] 1.7138 0.8554 0.7930 -1.3228
## [,1] [,2] [,3]
## [1,] "A" "D" "G"
## [2,] "B" "E" "H"
## [3,] "C" "F" "I"
>
> mode(A); mode(B); mode(C)
## [1] "logical"
## [1] "numeric"
## [1] "character"- Vectors and matrices have lengths: the length is the number of elements:
> x<-matrix(c(NA,2:12),ncol=3)
> x
## [,1] [,2] [,3]
## [1,] NA 5 9
## [2,] 2 6 10
## [3,] 3 7 11
## [4,] 4 8 12
>
> length(x[1,])
## [1] 3
>
> length(x)
## [1] 12
>
> # The dimension of a matrix is the number of rows and columns: The number of columns is the second element:
> dim(x); dim(x)[2]
## [1] 4 3
## [1] 33.2.4 Naming rows and columns in a matrix
- We can add names to a matrix with the
colnames()andrownames()functions:
> x<-matrix(rnorm(12),nrow=4)
> x
## [,1] [,2] [,3]
## [1,] 0.9202 -0.4745 -0.2831
## [2,] 0.1585 -0.2804 -0.6047
## [3,] -1.1698 -1.2134 -0.5080
## [4,] -0.2999 -1.4372 0.8759
>
> colnames(x)<-paste("data",1:3,sep="")
>
> rownames(x)<-paste("obs",1:4,sep="")
>
> x
## data1 data2 data3
## obs1 0.9202 -0.4745 -0.2831
## obs2 0.1585 -0.2804 -0.6047
## obs3 -1.1698 -1.2134 -0.5080
## obs4 -0.2999 -1.4372 0.8759
>
> y<-matrix(rnorm(15),nrow=5)
> y
## [,1] [,2] [,3]
## [1,] 0.05725 0.9804 -1.8222
## [2,] -0.99361 -1.4403 1.7824
## [3,] 0.99407 1.7198 1.9227
## [4,] 0.16685 1.4679 -0.7306
## [5,] 0.72052 -0.8524 -1.3746
>
> colnames(y)<-LETTERS[1:ncol(y)]
>
> rownames(y)<-letters[1:nrow(y)]
>
> y
## A B C
## a 0.05725 0.9804 -1.8222
## b -0.99361 -1.4403 1.7824
## c 0.99407 1.7198 1.9227
## d 0.16685 1.4679 -0.7306
## e 0.72052 -0.8524 -1.37463.2.5 Matrix multiplication
> M<-matrix(rnorm(20),nrow=4,ncol=5)
> N<-matrix(rnorm(15),nrow=5,ncol=3)
>
> M%*%N
## [,1] [,2] [,3]
## [1,] -2.9955 0.6733 -1.020
## [2,] -2.4249 -0.4178 -2.198
## [3,] 0.2123 -1.0215 -3.137
## [4,] 1.0913 -0.8827 -1.053
>
> # Can we perform N*M? No! A and B are not compatible!! Try to run:
> # N%*%M3.2.6 Additional functions
> M<-matrix(rnorm(16),nrow=4,ncol=4)
>
> dim(M)
## [1] 4 4
>
> t(M)
## [,1] [,2] [,3] [,4]
## [1,] 0.10115 -0.12413 0.9378 1.2825
## [2,] 0.29297 0.02105 -1.0539 -0.8166
## [3,] 0.57005 -0.10685 1.3300 0.4510
## [4,] 0.04554 0.78997 0.2430 -0.5366
>
> det(M)
## [1] 0.5723
>
> (invM <- solve(M))
## [,1] [,2] [,3] [,4]
## [1,] 0.9554 1.1337 -0.79049 1.3921
## [2,] 1.7441 0.5640 -0.89636 0.5725
## [3,] 0.6728 -0.5987 0.60243 -0.5515
## [4,] 0.1947 1.3480 -0.01885 0.1289
>
> eigen(M)
## eigen() decomposition
## $values
## [1] 1.6905+0.000i -0.5639+0.801i -0.5639-0.801i 0.3528+0.000i
##
## $vectors
## [,1] [,2] [,3] [,4]
## [1,] -0.33786+0i -0.219463+0.2577i -0.219463-0.2577i 0.6779+0i
## [2,] -0.08072+0i -0.319630-0.4519i -0.319630+0.4519i 0.6352+0i
## [3,] -0.87322+0i 0.005361-0.3768i 0.005361+0.3768i -0.0564+0i
## [4,] -0.34179+0i 0.661115+0.0000i 0.661115+0.0000i 0.3657+0i3.3 Simple Functions
- The above functions are built-in functions. However, it is simple to write your own functions:
