Apply function on each element of a list of matrices - r

I have a list of matrices.
(below is a simplified example, I actually have a list of 3 matrices, the first one being in 2D, while the second and third ones are in 3D)
> a <- matrix(-1:2, ncol = 2)
> b <- array(c(-2:5), dim=c(2, 2, 2))
> c_list <- list(a,b)
> c_list
[[1]]
[,1] [,2]
[1,] -1 1
[2,] 0 2
[[2]]
, , 1
[,1] [,2]
[1,] -2 0
[2,] -1 1
, , 2
[,1] [,2]
[1,] 2 4
[2,] 3 5
I'd like to apply the function max(0,c_list) to each and every element (without a loop), in order to have the same type of object as "c_list" but with the negative values replaced by zeros.
> output
[[1]]
[,1] [,2]
[1,] 0 1
[2,] 0 2
[[2]]
, , 1
[,1] [,2]
[1,] 0 0
[2,] 0 1
, , 2
[,1] [,2]
[1,] 2 4
[2,] 3 5
I've managed to do it for a matrice or for a list with mapply or lapply, but not for a list of matrices.
Answer : either Sotos' answer
output <- lapply(c_list, function(i)replace(i, i < 0, 0))
or Moody_Mudskipper's answer
output <- lapply(c_list,pmax,0)

You can use pmax, it will preserve the format of the source matrix and vectorized so faster than looping with max.
lapply(c_list,pmax,0)

Using apply and lapply:
a <- matrix(-1:2, ncol = 2)
b <- matrix(-3:0, ncol = 2)
c <- list(a,b)
d <- lapply(c, function(m) {
apply(m, c(1, 2), function(x) max(0, x))
})
Output:
> d
[[1]]
[,1] [,2]
[1,] 0 1
[2,] 0 2
[[2]]
[,1] [,2]
[1,] 0 0
[2,] 0 0

Related

Is there a way to multiply the 2d matrices of a 3d array by a scalar in R?

I have a 2x2x10 array of identity matrices, created with
arr = array(diag(2), dim=c(2,2,10))
I'm looking to multiply each 2x2 matrix within that array by a scalar c(1:10)
z = arr[,,1:10] * c(1:10)
However, I'm getting unexpected results. The first three 2x2 matrices of z shown below
, , 1
[,1] [,2]
[1,] 1 0
[2,] 0 4
, , 2
[,1] [,2]
[1,] 5 0
[2,] 0 8
, , 3
[,1] [,2]
[1,] 9 0
[2,] 0 2
Am I missing something?
We need to replicate to make the lengths same
arr[,,1:10] * rep(1:10, each = length(arr[,, 1]))
or else 1 gets multiplied by the first element of arr[, , 1] 2 with the second element of arr[,, 1] and due to recycling the elements of shorter vector is recycled until the length of arr[, , 1:10]
sweep() is designed for this:
sweep(arr, 3, 1:10, `*`)
, , 1
[,1] [,2]
[1,] 1 0
[2,] 0 1
, , 2
[,1] [,2]
[1,] 2 0
[2,] 0 2
, , 3
[,1] [,2]
[1,] 3 0
[2,] 0 3
...

Running Map reduces the dimensions of the matrices

Say I have three lists:
l_zero
[[1]]
[,1] [,2]
[1,] 0 0
[2,] 0 0
[[2]]
[,1] [,2]
[1,] 0 0
[2,] 0 0
l_ind <- list(matrix(c(1,1), ncol = 2), matrix(c(1,1,1,2), ncol = 2))
l_ind
[[1]]
[,1] [,2]
[1,] 1 1
[[2]]
[,1] [,2]
[1,] 1 1
[2,] 1 2
l_val <- list(5, c(4, 7))
l_val
[[1]]
[1] 5
[[2]]
[1] 4 7
I would like to run Map over the three lists with the goal of replacing in l_zero the zeros with the coordinates in l_ind with the values from l_val.
My attempt gives me the following:
Map(function(l_zero, l_ind, l_val) l_zero[l_ind] <- l_val, l_zero = l_zero, l_ind = l_ind, l_val = l_val)
[[1]]
[1] 5
[[2]]
[1] 4 7
As you can see, the original dimensions of the matrices are reduced, but I would like to keep the dimensions of the matrices and just replace the values with the coordinates in l_ind. I tried l_zero[l_ind, drop = FALSE], but that didn't help either.
Can someone help me with this?
Here's a bit simpler method, The [<- replacement function can be used in Map()'s function argument. It takes three arguments, in order.
Map("[<-", l_zero, l_ind, l_val)
# [[1]]
# [,1] [,2]
# [1,] 5 0
# [2,] 0 0
#
# [[2]]
# [,1] [,2]
# [1,] 4 7
# [2,] 0 0
You need to return the modified value from your mapped function (see return(l_zero) below).
l_zero <- replicate(2,matrix(0,2,2),simplify=FALSE)
l_ind <- list(matrix(c(1,1), ncol = 2), matrix(c(1,1,1,2), ncol = 2))
l_val <- list(5, c(4, 7))
ff <- function(l_zero, l_ind, l_val) {
l_zero[l_ind] <- l_val
return(l_zero)
}
Map(ff, l_zero = l_zero, l_ind = l_ind, l_val = l_val)
Results:
## [[1]]
## [,1] [,2]
## [1,] 5 0
## [2,] 0 0
##
## [[2]]
## [,1] [,2]
## [1,] 4 7
## [2,] 0 0

R: Is there a simple and efficient way to get back the list of building block matrices of a block-diagonal matrix?

I'm looking for a (build-in) function, which efficiently returns the list of building blocks of a block-diagonal matrix in the following way (rather than iterating over the slots to get the list manually):
#construct bdiag-matrix
library("Matrix")
listElems <- list(matrix(1:4,ncol=2,nrow=2),matrix(5:8,ncol=2,nrow=2))
mat <- bdiag(listElems)
#get back the list
res <- theFunctionImLookingFor(mat)
The result res yields the building blocks:
[[1]]
[,1] [,2]
[1,] 1 3
[2,] 2 4
[[2]]
[,1] [,2]
[1,] 5 7
[2,] 6 8
Edit: Regarding my use case, the list elements in listElems are square and symmetric matrices. If the block is a diagonal matrix, theFunctionImLookingFor should return a list element for each diagonal element.
However, the function should be able to deal with building block matrices like
[,1] [,2] [,3]
[1,] 1 1 0
[2,] 1 1 1
[3,] 0 1 1
or
[,1] [,2] [,3]
[1,] 1 0 1
[2,] 0 1 1
[3,] 1 1 1
i.e. deal with zeros in blocks, which are not diagonal matrices.
I hope this will work for all your cases, the test at the bottom includes a block that contains zeroes.
theFunctionImLookingFor <- function(mat, plot.graph = FALSE) {
stopifnot(nrow(mat) == ncol(mat))
x <- mat
diag(x) <- 1
edges <- as.matrix(summary(x)[c("i", "j")])
library(igraph)
g <- graph.edgelist(edges, directed = FALSE)
if (plot.graph) plot(g)
groups <- unique(Map(sort, neighborhood(g, nrow(mat))))
sub.Mat <- Map(`[`, list(mat), groups, groups, drop = FALSE)
sub.mat <- Map(as.matrix, sub.Mat)
return(sub.mat)
}
listElems <- list(matrix(1:4,ncol=2,nrow=2),
matrix(5:8,ncol=2,nrow=2),
matrix(c(0, 1, 0, 0, 0, 1, 0, 0, 1),ncol=3,nrow=3),
matrix(1:1,ncol=1, nrow=1))
mat <- bdiag(listElems)
theFunctionImLookingFor(mat, plot.graph = TRUE)
# [[1]]
# [,1] [,2]
# [1,] 1 3
# [2,] 2 4
# [[2]]
# [,1] [,2]
# [1,] 5 7
# [2,] 6 8
# [[3]]
# [,1] [,2] [,3]
# [1,] 0 0 0
# [2,] 1 0 0
# [3,] 0 1 1
# [[4]]
# [,1]
# [1,] 1

How to change elements in one matrix indexed in another matrix?

I have two matrices A and B. Matrix B is a two-column matrix, each row containing one index of an element in matrix A. I want to change those elements in matrix A, which are indexed by each row in matrix B, to 0.
Is there a way to avoid using the loop shown below?
> A <- matrix(1:12, 3, 4)
> B <- matrix(c(1, 2, 2, 2, 3, 4), byrow = TRUE, ncol = 2)
> A
[,1] [,2] [,3] [,4]
[1,] 1 4 7 10
[2,] 2 5 8 11
[3,] 3 6 9 12
> B
[,1] [,2]
[1,] 1 2
[2,] 2 2
[3,] 3 4
> for (i in 1:nrow(B)) {
+ A[B[i, 1], B[i, 2]] <- 0
+ }
> A
[,1] [,2] [,3] [,4]
[1,] 1 0 7 10
[2,] 2 0 8 11
[3,] 3 6 9 0
It's done like this
A[B] <- 0;

Construct dynamic-sized array in R

I was wondering about what are the ways to construct dynamic-size array in R.
For one example, I want to construct a n-vector but its dimension n is dynamically determined. The following code will work:
> x=NULL
> n=2;
> for (i in 1:n) x[i]=i;
> x
[1] 1 2
For another example, I want to construct a n by 2 matrix where the number of rows n is dynamically determined. But I fail even at assigning the first row:
> tmp=c(1,2)
> x=NULL
> x[1,]=tmp
Error in x[1, ] = tmp : incorrect number of subscripts on matrix
> x[1,:]=tmp
Error: unexpected ':' in "x[1,:"
Thanks and regards!
I think the answers you are looking for are rbind() and cbind():
> x=NULL # could also use x <- c()
> rbind(x, c(1,2))
[,1] [,2]
[1,] 1 2
> x <- rbind(x, c(1,2))
> x <- rbind(x, c(1,2)) # now extend row-wise
> x
[,1] [,2]
[1,] 1 2
[2,] 1 2
> x <- cbind(x, c(1,2)) # or column-wise
> x
[,1] [,2] [,3]
[1,] 1 2 1
[2,] 1 2 2
The strategy of trying to assign to "new indices" on the fly as you attempted can be done in some languages but cannot be done that way in R.
You can also use sparse matrices provided in the Matrix package. They would allow assignments of the form M <- sparseMatrix(i=200, j=50, x=234) resulting in a single value at row 200, column 50 and 0's everywhere else.
require(Matrix)
M <- sparseMatrix(i=200, j=50, x=234)
M[1,1]
# [1] 0
M[200, 50]
# [1] 234
But I think the use of sparse matrices is best reserved for later use after mastering regular matrices.
It is possible to dimension the array after we fill it (in a one-dimensional, vector, fashion)
Emulating the 1-dimension snippet of the question, here's the way it can be done with higher dimensions.
> x=c()
> tmp=c(1,2)
> n=6
> for (i in seq(1, by=2, length=n)) x[i:(i+1)] =tmp;
> dim(x) = c(2,n)
> x
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1 1 1 1 1 1
[2,] 2 2 2 2 2 2
>
Rather than using i:(i+1) as index, it may be preferable to use seq(i, length=2) or better yet, seq(i, length=length(tmp)) for a more generic approach, as illustrated below (for a 4 x 7 array example)
> x=c()
> tmp=c(1,2,3,4)
> n=7
> for (i in seq(1, by=length(tmp), length=n))
x[seq(i, length=length(tmp))] = tmp;
> dim(x) = c(length(tmp),n)
> x
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 1 1 1 1 1 1 1
[2,] 2 2 2 2 2 2 2
[3,] 3 3 3 3 3 3 3
[4,] 4 4 4 4 4 4 4
>
We can also obtain a similar result by re-assigning x with cbind/rbind, as follow.
> tmp=c(1,2)
> n=6
> x=rbind(tmp)
> for (i in 1:n) x=rbind(x, tmp);
> x
[,1] [,2]
tmp 1 2
tmp 1 2
tmp 1 2
tmp 1 2
tmp 1 2
tmp 1 2
tmp 1 2
Note: one can get rid of the "tmp" names (these are a side effect of the rbind), with
> dimnames(x)=NULL
You can rbind it:
tmp = c(1,2)
x = NULL
rbind(x, tmp)
I believe this is an approach you need
arr <- array(1)
arr <- append(arr,3)
arr[1] <- 2
print(arr[1])
(found on rosettacode.org)
When I want to dynamically construct an array (matrix), I do it like so:
n <- 500
new.mtrx <- matrix(ncol = 2, nrow = n)
head(new.mtrx)
[,1] [,2]
[1,] NA NA
[2,] NA NA
[3,] NA NA
[4,] NA NA
[5,] NA NA
[6,] NA NA
Your matrix is now ready to accept vectors.
Assuming you already have a vector, you pass that to the matrix() function. Notice how values are "broken" into the matrix (column wise). This can be changed with byrow argument.
matrix(letters, ncol = 2)
[,1] [,2]
[1,] "a" "n"
[2,] "b" "o"
[3,] "c" "p"
[4,] "d" "q"
[5,] "e" "r"
[6,] "f" "s"
[7,] "g" "t"
[8,] "h" "u"
[9,] "i" "v"
[10,] "j" "w"
[11,] "k" "x"
[12,] "l" "y"
[13,] "m" "z"
n = 5
x = c(1,2) %o% rep(1,n)
x
# [,1] [,2] [,3] [,4] [,5]
# [1,] 1 1 1 1 1
# [2,] 2 2 2 2 2
x = rep(1,n) %o% c(1,2)
x
# [,1] [,2]
# [1,] 1 2
# [2,] 1 2
# [3,] 1 2
# [4,] 1 2
# [5,] 1 2

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