MATLAB: Partially reduced row echelon form

linear algebrarref

Suppose a matrix C and a matrix D. I want to bring the matrix into the form:
where is in reduced row echelon form. Currently, I do this using the following code:
%Our aim is to bring the matrix (C,D) in the form 
% [Ctilde,  Dtilde_1]
% [0-rows , Dtilde_2].
[CtildeT,BVCtilde] = rref([C,speye(q)]);
%Delete Zero Rows in Ctilde
CtildeWZ = CtildeT(:,1:n);
Ctilde = CtildeWZ(any(CtildeWZ~=0,2),:);
T = CtildeT(:,n+1:end);
Dtilde = T*D;
Dtilde_1 = Dtilde(any(CtildeWZ~=0,2),:);
Dtilde_2 = Dtilde(all(CtildeWZ==0,2),:);
the rref function turns out to be a bottleneck for large matrices C. Is there another potentially faster way do compute these matrices?

Best Answer

Hey Christoph,
You may try using the 'fast rref' function created on File Exchange by Armin Ataei. It may perform faster than Matlab's rref.
Link: https://in.mathworks.com/matlabcentral/fileexchange/21583-fast-reduced-row-echelon-form
Note: Code that is shared on MATLAB File Exchange is written by MATLAB users and is not developed or tested by the Mathworks.
Related Question