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ralgorithmmatrixmatrix-multiplication

Algorithm for matrix multiplication

I am required to write a one-loop algorithm for matrix multiplication without using %*%, with the help of colSums().

I have tried working through matrix multiplication traits, but failed to find a pattern which can be attained with colSums().

Solution

  • If you are NOT ALLOWED to use %*% and HAVE TO take colSums anyway, you can try

    matrix(
    colSums(t(a)[, rep(1:nrow(a), each = ncol(b))] * b[, rep(1:ncol(b), nrow(a))]), 
    nrow(a),
    byrow = TRUE
)

    Example: Given two matrices a and b like below

    > set.seed(0)

> (a <- matrix(runif(12), 3))
          [,1]      [,2]      [,3]       [,4]
[1,] 0.8966972 0.5728534 0.8983897 0.62911404
[2,] 0.2655087 0.9082078 0.9446753 0.06178627
[3,] 0.3721239 0.2016819 0.6607978 0.20597457

> (b <- matrix(rnorm(8), 4))
             [,1]       [,2]
[1,] -0.928567035  0.7635935
[2,] -0.294720447 -0.7990092
[3,] -0.005767173 -1.1476570
[4,]  2.404653389 -0.2894616

    we have

    > a %*% b
            [,1]       [,2]
[1,]  0.50614499 -0.9861506
[2,] -0.37108354 -1.6249737
[3,]  0.08650475 -0.6949853

> matrix(
+     colSums(t(a)[, rep(1:nrow(a), each = ncol(b))] * b[, rep(1:ncol(b), nrow(a))]),
+     nrow(a),
+     byrow = TRUE
+ )
            [,1]       [,2]
[1,]  0.50614499 -0.9861506
[2,] -0.37108354 -1.6249737
[3,]  0.08650475 -0.6949853