Generate all possible permutations of a binary matrix - r

I'm looking to generate all possible 4x4 matrices, where each element can either be a 0 or a 1.
Is there a function in R to do this?


Here is a function that would create such matrices for indices from 0 to 2^16-1:
num2mat = function(num){ matrix(as.integer(intToBits(num)),4,4) }
Here is what it produces:
> num2mat(0)
[,1] [,2] [,3] [,4]
[1,] 0 0 0 0
[2,] 0 0 0 0
[3,] 0 0 0 0
[4,] 0 0 0 0
> num2mat(2^15+2^13+2^10+2^8+2^7+2^5+2^2+1)
[,1] [,2] [,3] [,4]
[1,] 1 0 1 0
[2,] 0 1 0 1
[3,] 1 0 1 0
[4,] 0 1 0 1
> num2mat(2^16-1)
[,1] [,2] [,3] [,4]
[1,] 1 1 1 1
[2,] 1 1 1 1
[3,] 1 1 1 1
[4,] 1 1 1 1

Related

How to set all rows of a list of matrices to zero using if condition statement in R

Suppose I have a matrix, mat. Suppose further that the sum of one row of this matrix is equal to zero. Then, I need to set all the coming rows (the rows after the zero row) to zero. For example,
mat <- c(1,2,0,0,0,
3,4,0,2,1,
0,0,0,1,0,
1,2,0,0,0,
0,1,0,1,0)
mat <- matrix(mat,5,5)
mat
[,1] [,2] [,3] [,4] [,5]
[1,] 1 3 0 1 0
[2,] 2 4 0 2 1
[3,] 0 0 0 0 0
[4,] 0 2 1 0 1
[5,] 0 1 0 0 0
All the entries of row 3 are zero. Hence, I want rows 4, and 5 to become zeros as well. I have a list of matrices and would like to apply the same to all the matrices using the lapply function. For simplicity, I make a list of 3 matrices similar to the mat.
mat <- c(1,2,0,0,0,
3,3,0,2,1,
0,0,0,4,0,
1,3,0,0,0,
0,1,0,1,0)
mat <- matrix(mat,5,5)
mat1 <- c(1,2,0,0,0,
3,4,0,2,1,
0,0,0,1,0,
1,2,0,0,0,
0,1,0,1,0)
mat1 <- matrix(mat1,5,5)
mat2 <- c(1,2,0,0,0,
3,4,0,2,1,
0,0,0,2,0,
1,2,0,0,0,
0,2,0,3,0)
mat2 <- matrix(mat2,5,5)
Mat <- list(mat1, mat2, mat3)

You did not actually post mat3 in your data so I just used mat3 <- matrix(1, 5, 5), i.e. a 5x5 matrix of ones. This was to ensure it could handle cases where there is no row where all values are zero.
This will return a list of matrices where all rows are zero after the first row of zeroes:
lapply(Mat, \(mat) {
first_zero_row <- which(rowSums(mat)==0)[1]
if(!is.na(first_zero_row)) {
mat[first_zero_row:nrow(mat),] <- 0
}
mat
})
Output:
[[1]]
[,1] [,2] [,3] [,4] [,5]
[1,] 1 3 0 1 0
[2,] 2 4 0 2 1
[3,] 0 0 0 0 0
[4,] 0 0 0 0 0
[5,] 0 0 0 0 0
[[2]]
[,1] [,2] [,3] [,4] [,5]
[1,] 1 3 0 1 0
[2,] 2 4 0 2 2
[3,] 0 0 0 0 0
[4,] 0 0 0 0 0
[5,] 0 0 0 0 0
[[3]]
[,1] [,2] [,3] [,4] [,5]
[1,] 1 1 1 1 1
[2,] 1 1 1 1 1
[3,] 1 1 1 1 1
[4,] 1 1 1 1 1
[5,] 1 1 1 1 1

Another option could be:
lapply(Mat, function(x) {x[cumsum(rowSums(x != 0) == 0) != 0, ] <- 0; x})
[[1]]
[,1] [,2] [,3] [,4] [,5]
[1,] 1 3 0 1 0
[2,] 2 3 0 3 1
[3,] 0 0 0 0 0
[4,] 0 0 0 0 0
[5,] 0 0 0 0 0
[[2]]
[,1] [,2] [,3] [,4] [,5]
[1,] 1 3 0 1 0
[2,] 2 4 0 2 1
[3,] 0 0 0 0 0
[4,] 0 0 0 0 0
[5,] 0 0 0 0 0
[[3]]
[,1] [,2] [,3] [,4] [,5]
[1,] 1 3 0 1 0
[2,] 2 4 0 2 2
[3,] 0 0 0 1 0
[4,] 0 2 2 0 3
[5,] 0 1 0 0 0

Transform Identity Matrix

I have identity matrix which can be generated via diag(5)
[,1] [,2] [,3] [,4] [,5]
[1,] 1 0 0 0 0
[2,] 0 1 0 0 0
[3,] 0 0 1 0 0
[4,] 0 0 0 1 0
[5,] 0 0 0 0 1
I want to convert it to the matrix wherein series starts after 1. For example 1st column, values 1 through 5. Second column - values 1 through 4.
Desired Output
[,1] [,2] [,3] [,4] [,5]
[1,] 1 0 0 0 0
[2,] 2 1 0 0 0
[3,] 3 2 1 0 0
[4,] 4 3 2 1 0
[5,] 5 4 3 2 1

Try the code below (given m <- diag(5))
> (row(m) - col(m) + 1)*lower.tri(m,diag = TRUE)
[,1] [,2] [,3] [,4] [,5]
[1,] 1 0 0 0 0
[2,] 2 1 0 0 0
[3,] 3 2 1 0 0
[4,] 4 3 2 1 0
[5,] 5 4 3 2 1
Another option is using apply + cumsum
> apply(lower.tri(m, diag = TRUE), 2, cumsum)
[,1] [,2] [,3] [,4] [,5]
[1,] 1 0 0 0 0
[2,] 2 1 0 0 0
[3,] 3 2 1 0 0
[4,] 4 3 2 1 0
[5,] 5 4 3 2 1

1) If d <- diag(5) is the identity matrix then:
pmax(row(d) - col(d) + 1, 0)
giving:
[,1] [,2] [,3] [,4] [,5]
[1,] 1 0 0 0 0
[2,] 2 1 0 0 0
[3,] 3 2 1 0 0
[4,] 4 3 2 1 0
[5,] 5 4 3 2 1
2) This alternative is slightly longer (though still a one-liner) but also works if the columns of d are rearranged and/or some columns are missing. For example,
dd <- d[, 4:1] # test data
pmax(outer(1:nrow(dd) + 1, max.col(t(dd)), `-`), 0)
giving the same result for d and this for dd:
[,1] [,2] [,3] [,4]
[1,] 0 0 0 1
[2,] 0 0 1 2
[3,] 0 1 2 3
[4,] 1 2 3 4
[5,] 2 3 4 5

A solution based on nested cumsum:
n <- 5
m <- diag(n)
apply(m, 2, function(x) cumsum(cumsum(x)))
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1 0 0 0 0
#> [2,] 2 1 0 0 0
#> [3,] 3 2 1 0 0
#> [4,] 4 3 2 1 0
#> [5,] 5 4 3 2 1

One option could be:
x <- 1:5
embed(c(rep(0, length(x) - 1), x), length(x))
[,1] [,2] [,3] [,4] [,5]
[1,] 1 0 0 0 0
[2,] 2 1 0 0 0
[3,] 3 2 1 0 0
[4,] 4 3 2 1 0
[5,] 5 4 3 2 1

Working with matrix in R. Place an element in matrix

I have a distance matrix. For example :
d<-matrix(c(0,2,3,7,11,0,13,6,8,5,0,12,6,53,12,0), nrow = 4, ncol = 4)
d
[,1] [,2] [,3] [,4]
[1,] 0 11 8 6
[2,] 2 0 5 53
[3,] 3 13 0 12
[4,] 7 6 12 0
I want to create a neighbor matrix where distance is less than or equal to 5. In matrix nb, 1 indicates not a neighbor. However, they have no neighbor (excluding itself, for example, row 1 and row 4. I would like the one with the smallest distance to be their neighbor.
> nb=(d>=5)
> nb*1
[,1] [,2] [,3] [,4]
[1,] 0 1 1 1
[2,] 0 0 1 1
[3,] 0 1 0 1
[4,] 1 1 1 0
Expected result
[,1] [,2] [,3] [,4]
[1,] 0 1 1 0
[2,] 0 0 1 1
[3,] 0 1 0 1
[4,] 1 0 1 0
I have tried and I don't know how to get it efficiently without using loop. This is just an example, my actual data has over 9000 rows. Any suggestion would be helpful. Thank you so much!

I believe the following function does what you want.
fun <- function(Dist, n = 5){
nb <- (Dist > n)*1L
for(i in seq_len(nrow(nb))) {
tmp <- Dist[i, ]
tmp[tmp == 0] <- Inf
nb[i, which.min(tmp)] <- 0L
}
nb
}
fun(d)
# [,1] [,2] [,3] [,4]
#[1,] 0 1 1 0
#[2,] 0 0 0 1
#[3,] 0 1 0 1
#[4,] 1 0 1 0
fun(d, 10)
# [,1] [,2] [,3] [,4]
#[1,] 0 1 0 0
#[2,] 0 0 0 1
#[3,] 0 1 0 1
#[4,] 0 0 1 0

How can I make an identical matrix with a column vector?

I have a column vector with dimensions 4000x1, and I need to make a matrix with that vector, but the matrix needs to have the column vector as a diagonal and the other numbers as zero. Something like this:
Column Vector
> vector <- matrix(c(1:5), ncol=1, nrow=5)
> vector
[,1]
[1,] 1
[2,] 2
[3,] 3
[4,] 4
Matrix
[,1] [,2] [,3] [,4]
a 1 0 0 0
b 0 2 0 0
c 0 0 3 0
How can I produce this output?

This sounds like the diag() function, e.g.,
> my_vect <- 1:5
> diag(my_vect)
[,1] [,2] [,3] [,4] [,5]
[1,] 1 0 0 0 0
[2,] 0 2 0 0 0
[3,] 0 0 3 0 0
[4,] 0 0 0 4 0
[5,] 0 0 0 0 5
By the way, as you have written it vector is actually a 5x1 matrix, so you would need to convert it to, well, a vector:
> diag(as.vector(vector))
[,1] [,2] [,3] [,4] [,5]
[1,] 1 0 0 0 0
[2,] 0 2 0 0 0
[3,] 0 0 3 0 0
[4,] 0 0 0 4 0
[5,] 0 0 0 0 5

use of the [<- operator to modify a line of data

I have some data
data <- diag(5)
I want to use the [<- operator to change a line.
The result should be:
data[1,] <- 2
> data
[,1] [,2] [,3] [,4] [,5]
[1,] 2 2 2 2 2
[2,] 0 1 0 0 0
[3,] 0 0 1 0 0
[4,] 0 0 0 1 0
[5,] 0 0 0 0 1
I know I can do e.g.
`[<-`(data, i=1, j=3, 2)
which gives
[,1] [,2] [,3] [,4] [,5]
[1,] 1 0 8 0 0
[2,] 0 1 0 0 0
[3,] 0 0 1 0 0
[4,] 0 0 0 1 0
[5,] 0 0 0 0 1
but how can I operate on line (or column, same issue)?
I tried j=NULL, j=integer(0), it doesn't work. I could do j=1:5 and get what I want but I am wondering how to mimic data[1,] <- 2 and not data[1,1:5] <- 2.

> `[<-`(data, 1, , 2) # blank 2nd argument
[,1] [,2] [,3] [,4] [,5]
[1,] 2 2 2 2 2
[2,] 0 1 0 0 0
[3,] 0 0 1 0 0
[4,] 0 0 0 1 0
[5,] 0 0 0 0 1

You can use ncol to ensure that all columns are set:
`[<-`(data, i = 1, j = 1:ncol(data), 2)

Resources