Null space of a sparse matrix

calculates null space and range of a rectangular sparse matrix

Description

finds null space and range of a sparse matrix using lu decomposition.  
 
This routine is devoted to find null space of possibly large matrix fast.  
Results may be inaccurate if zero and nonzero singular values are not well separated.

• MATLAB release: MATLAB 7.0.1 (R14SP1)
• Other Files: sparse null/demo.m, ; sparse null/luq.m, ; sparse null/spspaces.m

[John D'Errico]

This fills a hole in Matlab. For sparse matrices, it should be much faster than null(full(...)). Why did I rate it as only a 4?  
 
The help seems reasonable, and if you know what you are doing, it should work.  
 
I don't terribly like the interface though, returning a cell array. You need to remember which element number to use to extract the arrays that you need. Far more logical, easy to use, and self commenting, would be to return a structure with appropriately named fields.  
 
Next, if what you really need is an orthogonal basis for the nullspace, then spspaces will not serve this purpose.  
 
Finally, I'd have preferred additional comments (examples) in the help so that a less experienced user could figure out how to use this code. As it is, that person is likely to be completely lost if all they know is they need to find a sparse basis for the nullspace of the columns of a sparse matrix.

[Tim Davis]

Suggestion for the author: You may want to try using dmperm first. It will split the system into its structurallly over-determined, well-determined, and under-determined parts. That function doesn't make the "coarse decomposition" clear, however. It has contains a bug when used for large matrices. Use cs_dmperm in CSparse instead.