usolve misses solutions

[cshaa]

The usolve function can only find solutions of non-degenerate matrices. On degenerate ones, it automatically sets the free parameters to zero, only returning one solution out of many. For null b it only returns null vectors as a result. Example:

M = [[-2,3,5],[0,-1,2],[0,0,0]]
b = [0,0,0]

math.usolve(M, b)
// returns [[0], [0], [0]]
// correct result [5.5, 2, 1]

(Also, the returned array is two-dimensional for some reason.)

EDIT: Related to #1168. Since all non-square matrices are degenerate.
EDIT: Also true for lsolve and lusolve.

[cshaa]

I couldn't find a general back-substituion algorithm for singular matrices, so I spent some time figuring it out. I wrote this paper explaining why I think my algorithm is correct. Hopefully, I'll make a PR soon.

[josdejong]

Thanks for sharing your work Michal!

[josdejong]

Published now in v7.3.0 🎉