Purpose

LA_GELSS and LA_GELSD compute the minimum-norm least squares solution to one or more real or complex linear systems $A x = b$ using the singular value decomposition of $A$. Matrix $A$ is rectangular and may be rank-deficient. The vectors $b$ and corresponding solution vectors $x$ are the columns of matrices denoted $B$ and $X$, respectively.
The effective rank of $A$ is determined by treating as zero those singular values which are less than ${\bf RCOND}$ times the largest singular value. In addition to $X$, the routines also return the right singular vectors and, optionally, the rank and singular values of $A$.
LA_GELSD combines the singular value decomposition with a divide and conquer technique. For large matrices it is often much faster than LA_GELSS but uses more workspace.