SYNOPSIS
 SUBROUTINE SGELSS(
 M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK, LWORK, INFO )
 INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK
 REAL RCOND
 REAL A( LDA, * ), B( LDB, * ), S( * ), WORK( * )
PURPOSE
SGELSS computes the minimum norm solution to a real linear least squares problem: Minimize 2norm( b  A*x ).using the singular value decomposition (SVD) of A. A is an MbyN matrix which may be rankdeficient.
Several right hand side vectors b and solution vectors x can be handled in a single call; they are stored as the columns of the MbyNRHS right hand side matrix B and the NbyNRHS solution matrix X.
The effective rank of A is determined by treating as zero those singular values which are less than RCOND times the largest singular value.
ARGUMENTS
 M (input) INTEGER
 The number of rows of the matrix A. M >= 0.
 N (input) INTEGER
 The number of columns of the matrix A. N >= 0.
 NRHS (input) INTEGER
 The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
 A (input/output) REAL array, dimension (LDA,N)
 On entry, the MbyN matrix A. On exit, the first min(m,n) rows of A are overwritten with its right singular vectors, stored rowwise.
 LDA (input) INTEGER
 The leading dimension of the array A. LDA >= max(1,M).
 B (input/output) REAL array, dimension (LDB,NRHS)
 On entry, the MbyNRHS right hand side matrix B. On exit, B is overwritten by the NbyNRHS solution matrix X. If m >= n and RANK = n, the residual sumofsquares for the solution in the ith column is given by the sum of squares of elements n+1:m in that column.
 LDB (input) INTEGER
 The leading dimension of the array B. LDB >= max(1,max(M,N)).
 S (output) REAL array, dimension (min(M,N))
 The singular values of A in decreasing order. The condition number of A in the 2norm = S(1)/S(min(m,n)).
 RCOND (input) REAL
 RCOND is used to determine the effective rank of A. Singular values S(i) <= RCOND*S(1) are treated as zero. If RCOND < 0, machine precision is used instead.
 RANK (output) INTEGER
 The effective rank of A, i.e., the number of singular values which are greater than RCOND*S(1).
 WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
 LWORK (input) INTEGER
 The dimension of the array WORK. LWORK >= 1, and also: LWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS ) For good performance, LWORK should generally be larger. If LWORK = 1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value.
> 0: the algorithm for computing the SVD failed to converge; if INFO = i, i offdiagonal elements of an intermediate bidiagonal form did not converge to zero.