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Question

I want to transform each column of a matrix M by an operator N. Eigen allows to express this in terms of pre-multiplication:

M.colwise() *= N;

But the multiplication M_j * N is mathematically undefined.

Is there some way to avoid writing a loop?

Answer 1

If you want to multiply each column of M by N from the left, just perform a normal matrix-matrix-multiplication:

M = N * M;

This will evaluate N*M into a temporary which is then moved to M . If you do this a lot and want to re-use the allocated memory for that, declare a temporary matrix M_temp somewhere before and write

M_temp.noalias() = N * M;
M.swap(M_temp);  // M_temp has the old memory of M; Swapping is O(1)

If you are afraid of too much memory consumption, you can write something like

for(long i=0; i<M.cols()-3; i+=4)
    M.middleCols<4>(i) = N * M.middleCols<4>(i);
M.rightCols(M.cols()%4) = N * M.rightCols(M.cols()%4);