CODEWITHSUNDEEP
rmatrix
digestivee
digestivee

Reputation: 740

Multiply specific columns of one matrix with specific columns of another matrix for many indices

I have two large matrices P and Q around (10k x 50k dim in both, but to test this yourself a random 10x10 matrix for P and Q is sufficient). I have a list of indices, e.g.

i    j
1    4
1    625
1    9207
2    827
...  ...

etc. This means that I need to find the dot product of column 1 in P and column 4 in Q, then column 1 in P and column 625 in Q and so on. I could easily solve this with a for loop but I know they are not very efficient in R. Anyone got any ideas?

edit: asked for a reproducible example

P <- matrix(c(1,0,1,0,0,1,0,1,0), nrow = 3, ncol = 3) 
Q <- matrix(c(0,0,1,0,1,0,1,0,1), nrow = 3, ncol = 3) 
i <- c(1,1,2) 
j <- c(2,1,3)

gives output (if in dot product form)

1: 0
2: 1
3: 1

Upvotes: 1

Views: 37

Answers (2)

lmo
lmo

Reputation: 38520

Using matrix multiplication, you can do

diag(t(P[, i]) %*% Q[, j])
[1] 0 1 1

Here is second a solution with apply.

apply(cbind(i, j), 1, function(x) t(P[, x[1]]) %*% Q[, x[2]])
[1] 0 1 1

To verify these agree in a second example:

set.seed(1234)
A <- matrix(sample(0:10, 100, replace=TRUE), 10, 10)
B <- matrix(sample(0:10, 100, replace=TRUE), 10, 10)

inds <- matrix(sample(10, 10, replace=TRUE), 5)

matrix multiplication

diag(t(A[, inds[,1]]) %*% B[, inds[,2]])
[1] 215 260 306 237 317

and apply

apply(inds, 1, function(x) t(A[, x[1]]) %*% B[, x[2]])
[1] 215 260 306 237 317

Upvotes: 2

minem
minem

Reputation: 3650

P <- matrix(1:50, nrow = 5,ncol = 10) 
Q <- matrix(1:50, nrow = 5, ncol = 10) 
i <- c(1,2,4,7) 
j <- c(5,3,7,2)
P
#      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
# [1,]    1    6   11   16   21   26   31   36   41    46
# [2,]    2    7   12   17   22   27   32   37   42    47
# [3,]    3    8   13   18   23   28   33   38   43    48
# [4,]    4    9   14   19   24   29   34   39   44    49
# [5,]    5   10   15   20   25   30   35   40   45    50
Q
#      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
# [1,]    1    6   11   16   21   26   31   36   41    46
# [2,]    2    7   12   17   22   27   32   37   42    47
# [3,]    3    8   13   18   23   28   33   38   43    48
# [4,]    4    9   14   19   24   29   34   39   44    49
# [5,]    5   10   15   20   25   30   35   40   45    50
P[,i] * Q[, j]
#      [,1] [,2] [,3] [,4]
# [1,]   21   66  496  186
# [2,]   44   84  544  224
# [3,]   69  104  594  264
# [4,]   96  126  646  306
# [5,]  125  150  700  350

Upvotes: 3

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