sparse RREF

[epsi1on]

Hi @wo80
following our last conversations, for reducing the big equation system into smaller one (with preserving the SPDness of matrix) i ended up implementing the RREF myself. Just need your suggesting on how to start.

Is it easy to reuse the code in CSParse.Net to create code for calculating rref format of matrix. if yes, please, could you tell me how much of code or what pieces i can use from CSparseNet ?

Here is what i do need, this is very much like RREF but maybe simpler:
Assuming there is a rectangular matrix $\hat{J}$ (m row, n columns) and a right hand side $\vec{R}$ where $\hat{J}.\vec{X}=\vec{R}$ where $\vec{x}$ is unknown and $\vec{R}$ is known. rank of $\hat{J}$ is unknown h.
I need to use Gaussian row elimination to convert $\hat{J}$ into a this format:
There be h number of columns, each column have only ONE nonzero on a distinct row. so there are in total h nonzeros in those h columns. each non-zeros should be in a distinct row, which means no two nonzeros are lying on same row.
I think this is very much like RREF but maybe simpler.
Order of h columns is not important, just need to select them in a way to reduce fill-in.

Thanks in advance