Replace non-NaN values with their row indices within matrix

Question

I have the 4x2 matrix A:

A = [2 NaN 5 8; 14 NaN 23 NaN]';

I want to replace the non-NaN values with their associated indices within each column in A. The output looks like this:

out = [1 NaN 3 4; 1 NaN 3 NaN]'; 

I know how to do it for each column manually, but I would like an automatic solution, as I have much larger matrices to handle. Anyone has any idea?

Answer 1

out = bsxfun(@times, A-A+1, (1:size(A,1)).');

How it works:

• A-A+1 replaces actual numbers in A by 1, and keeps NaN as NaN
• (1:size(A,1)).' is a column vector of row indices
• bsxfun(@times, ...) multiplies both of the above with singleton expansion.

As pointed out by @thewaywewalk, in Matlab R2016 onwards bsxfun(@times...) can be replaced by .*, as singleton expansion is enabled by default:

out = (A-A+1) .* (1:size(A,1)).';

An alternative suggested by @Dev-Il is

out = bsxfun(@plus, A*0, (1:size(A,1)).');

This works because multiplying by 0 replaces actual numbers by 0, and keeps NaN as is.