partially reduced row echelon form

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?

Answer 1

[Athul Prakash]

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.

[Christoph Neumann]

Thanks, this indeed gave me a significant speed up of factor >1000.