
SGELSS(l) ) SGELSS(l)
NAME
SGELSS  compute the minimum norm solution to a real linear least squares problem
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 over
written 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 sumof
squares for the solution in the ith column is given by the sum of squares of ele
ments 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 (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 off
diagonal elements of an intermediate bidiagonal form did not converge to zero.
LAPACK version 3.0 15 June 2000 SGELSS(l) 
