19.4. Test Data¶
This section contains some simple vectors / matrices etc. useful for examples in this document.
19.4.1. Matrices¶
General
> matrix(c(1,1,1,3,0,2), nrow=3)
[,1] [,2]
[1,] 1 3
[2,] 1 0
[3,] 1 2
> matrix(c(0,7,2,0,5,1), nrow=3)
[,1] [,2]
[1,] 0 0
[2,] 7 5
[3,] 2 1
Permutation matrices:
> diag(3)[c(1,3,2), ]
[,1] [,2] [,3]
[1,] 1 0 0
[2,] 0 0 1
[3,] 0 1 0
> x <- c (3,4,1,2)
> diag(length(x))[x, ]
[,1] [,2] [,3] [,4]
[1,] 0 0 1 0
[2,] 0 0 0 1
[3,] 1 0 0 0
[4,] 0 1 0 0
Orthogonal matrices:
> diag(1,nrow=2)
[,1] [,2]
[1,] 1 0
[2,] 0 1
> theta <- pi/4; matrix(c(cos(theta), sin(theta), -sin(theta), cos(theta)), nrow=2)
[,1] [,2]
[1,] 0.7071068 -0.7071068
[2,] 0.7071068 0.7071068
Symmetric positive definite matrices:
> A <- matrix(c(5,1,1,3),2,2)
> A
[,1] [,2]
[1,] 5 1
[2,] 1 3
> eigen(A)$values
[1] 5.414214 2.585786
> A <- matrix(c(4, 12, -16, 12, 37, -43, -16, -43, 98), nrow=3)
> A
[,1] [,2] [,3]
[1,] 4 12 -16
[2,] 12 37 -43
[3,] -16 -43 98
> eigen(A)$values
[1] 123.47723179 15.50396323 0.01880498
Upper triangular matrices:
> A <- matrix(c(2, 0, 0, 6, 1, 0, -8, 5, 3), nrow=3)
> A
[,1] [,2] [,3]
[1,] 2 6 -8
[2,] 0 1 5
[3,] 0 0 3