So I want to do the matrix dot product with two matrices, even if they have different sizes. The problem is, how do I append rows and columns of all 0s to the smaller matrix to make it the same size as the larger one.
So for example, if I have a 2x2 matrix and a 4x4 matrix, I want to see if there's a way in R to code the addition of 2 rows and 2 columns of all 0s. Can someone help out?
Probably not the most elegant way, but I've done a similar task just by adding filler matrices first horizontally and then vertically to fulfill the lacking part to make them comformable. Here's a function as well as an example:
set.seed(1)
a <- matrix(rnorm(8), nrow=2, ncol=4)
b <- matrix(rnorm(10), nrow=5, ncol=2)
#> a
# [,1] [,2] [,3] [,4]
#[1,] -0.6264538 -0.8356286 0.3295078 0.4874291
#[2,] 0.1836433 1.5952808 -0.8204684 0.7383247
#> b
# [,1] [,2]
#[1,] 0.5757814 -2.21469989
#[2,] -0.3053884 1.12493092
#[3,] 1.5117812 -0.04493361
#[4,] 0.3898432 -0.01619026
#[5,] -0.6212406 0.94383621
# Here is a function that adds empty rows and columns of 0s to matrices x and y to make them comformable
# Two matrices x and y, and repeated fill element which is by default 0s
filler <- function(x, y, fill = 0){
# Block of x to add horizontally before vertical block
horizontal.x = matrix(fill,
ncol=ifelse(ncol(x) > ncol(y), 0, ncol(y) - ncol(x)),
nrow=nrow(x)
)
# Block of y to add horizontally before vertical block
horizontal.y = matrix(fill,
ncol=ifelse(ncol(x) > ncol(y), ncol(x) - ncol(y), 0),
nrow=nrow(y)
)
# Vertical block of x to add after the horizontal block
vertical.x = matrix(fill,
ncol=ncol(x) + ncol(horizontal.x),
nrow=ifelse(nrow(x) > nrow(y), 0, nrow(y) - nrow(x))
)
# Vertical block of y to add after the horizontal block
vertical.y = matrix(fill,
ncol=ncol(y) + ncol(horizontal.y),
nrow=ifelse(nrow(x) > nrow(y), nrow(x) - nrow(y), 0)
)
# Bind the blocks together and return both within a list
x <- rbind(cbind(x, horizontal.x), vertical.x)
y <- rbind(cbind(y, horizontal.y), vertical.y)
list(x, y)
}
filler(a, b)
filler(b, a)
filler(b, t(a))
#> filler(a, b)
#[[1]]
# [,1] [,2] [,3] [,4]
#[1,] -0.6264538 -0.8356286 0.3295078 0.4874291
#[2,] 0.1836433 1.5952808 -0.8204684 0.7383247
#[3,] 0.0000000 0.0000000 0.0000000 0.0000000
#[4,] 0.0000000 0.0000000 0.0000000 0.0000000
#[5,] 0.0000000 0.0000000 0.0000000 0.0000000
#
#[[2]]
# [,1] [,2] [,3] [,4]
#[1,] 0.5757814 -2.21469989 0 0
#[2,] -0.3053884 1.12493092 0 0
#[3,] 1.5117812 -0.04493361 0 0
#[4,] 0.3898432 -0.01619026 0 0
#[5,] -0.6212406 0.94383621 0 0
#
#> filler(b, a)
#[[1]]
# [,1] [,2] [,3] [,4]
#[1,] 0.5757814 -2.21469989 0 0
#[2,] -0.3053884 1.12493092 0 0
#[3,] 1.5117812 -0.04493361 0 0
#[4,] 0.3898432 -0.01619026 0 0
#[5,] -0.6212406 0.94383621 0 0
#
#[[2]]
# [,1] [,2] [,3] [,4]
#[1,] -0.6264538 -0.8356286 0.3295078 0.4874291
#[2,] 0.1836433 1.5952808 -0.8204684 0.7383247
#[3,] 0.0000000 0.0000000 0.0000000 0.0000000
#[4,] 0.0000000 0.0000000 0.0000000 0.0000000
#[5,] 0.0000000 0.0000000 0.0000000 0.0000000
#
#> filler(b, t(a))
#[[1]]
# [,1] [,2]
#[1,] 0.5757814 -2.21469989
#[2,] -0.3053884 1.12493092
#[3,] 1.5117812 -0.04493361
#[4,] 0.3898432 -0.01619026
#[5,] -0.6212406 0.94383621
#
#[[2]]
# [,1] [,2]
#[1,] -0.6264538 0.1836433
#[2,] -0.8356286 1.5952808
#[3,] 0.3295078 -0.8204684
#[4,] 0.4874291 0.7383247
#[5,] 0.0000000 0.0000000
ex <- filler(b, t(a))
# This is now defined
ex[[1]] %*% t(ex[[2]])
Suppose you start with two matrices m1 and m2, the bigger being m1
m1 <- matrix(1, 4, 4)
m2 <- matrix(1, 2, 2)
You can create a third matrix of zeros with the same dimensions as the bigger matrix, then fill in the smaller matrix values.
m3 <- matrix(0, dim(m1)[1], dim(m1)[2])
m3[1:nrow(m2), 1:ncol(m2)] <- m2
m3
# [,1] [,2] [,3] [,4]
# [1,] 1 1 0 0
# [2,] 1 1 0 0
# [3,] 0 0 0 0
# [4,] 0 0 0 0
Here's a possible function that you could use to make a square matrix based on a given set of dimensions.
sameDim <- function(x, size, fill = 0L) {
rb <- rbind(x, matrix(fill, size[1]-nrow(x), ncol(x)))
cbind(rb, matrix(fill, nrow(rb), size[2]-ncol(x)))
}
sameDim(m2, dim(m1))
# [,1] [,2] [,3] [,4]
# [1,] 1 1 0 0
# [2,] 1 1 0 0
# [3,] 0 0 0 0
# [4,] 0 0 0 0
