I want to do a matrix multiplication with a twist.
I have this matrix:
A <- matrix(c(1,-1,-1,0,-1,0,1,0,0,1,0,0,0,1,-1,1,-1,0,0,-1,1,0,1,0,1,-1,-1,1,-1,1), nrow = 6, ncol = 5)
A
[,1] [,2] [,3] [,4] [,5]
[1,] 1 1 0 0 1
[2,] -1 0 1 -1 -1
[3,] -1 0 -1 1 -1
[4,] 0 1 1 0 1
[5,] -1 0 -1 1 -1
[6,] 0 0 0 0 1
And I want to get two different matrices. The first matrix is this:
C
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0 0 0 2 0 1
[2,] 0 0 2 1 2 0
[3,] 0 2 0 0 4 0
[4,] 2 1 0 0 0 1
[5,] 0 2 4 0 0 0
[6,] 1 0 0 1 0 0
This "convergence matrix" is something like the multiplication of A for its transpose (in R is something like this A%*%t(A)), but with a little twist, during the sum to obtain each cell I only want de sum of the positives values. For example, for the cell C23 the regular sum would be:
(-1)(-1) + (0)(0) + (1)(-1) + (-1)(1) + (-1)(-1) = 0
, but I only want the sum of the positive products, in this example the first [(-1)(-1)] and the last [(-1)(-1)] to obtain 2.
The second matrix is this:
D
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0 2 2 0 2 0
[2,] 2 0 2 1 2 1
[3,] 2 2 0 2 0 1
[4,] 0 1 2 0 2 0
[5,] 2 2 0 2 0 1
[6,] 0 1 1 0 1 0
This "divergence matrix" is similar to the previous one, with the difference that I only want to sum de absolute values of the negative values. For example, for the cell D23 the regular sum would be:
(-1)(-1) + (0)(0) + (1)(-1) + (-1)(1) + (-1)(-1) = 0
, but I only want the sum of the absolute values of negative products, in this example the third abs [(1)(-1)] and the fourth abs[(-1)(-1)] to obtain 2.
I've been trying with apply, sweep and loops but I can't get it. Thanks for your responses.
Another take:
D <- A
D[D<0] = -1i*D[D<0]
D <- Im(tcrossprod(D))
C <- tcrossprod(A) + D
A is defined in the question.
Output:
> D
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0 2 2 0 2 0
[2,] 2 0 2 1 2 1
[3,] 2 2 0 2 0 1
[4,] 0 1 2 0 2 0
[5,] 2 2 0 2 0 1
[6,] 0 1 1 0 1 0
> C
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 3 0 0 2 0 1
[2,] 0 4 2 1 2 0
[3,] 0 2 4 0 4 0
[4,] 2 1 0 3 0 1
[5,] 0 2 4 0 4 0
[6,] 1 0 0 1 0 1