
sgelss.f(3) LAPACK sgelss.f(3)
NAME
sgelss.f 
SYNOPSIS
Functions/Subroutines
subroutine sgelss (M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK, LWORK, INFO)
SGELSS solves overdetermined or underdetermined systems for GE matrices
Function/Subroutine Documentation
subroutine sgelss (integerM, integerN, integerNRHS, real, dimension( lda, * )A, integerLDA,
real, dimension( ldb, * )B, integerLDB, real, dimension( * )S, realRCOND, integerRANK,
real, dimension( * )WORK, integerLWORK, integerINFO)
SGELSS solves overdetermined or underdetermined systems for GE matrices
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.
Parameters:
M
M is INTEGER
The number of rows of the matrix A. M >= 0.
N
N is INTEGER
The number of columns of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
A
A is 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
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B
B is 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
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,max(M,N)).
S
S is 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
RCOND is 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
RANK is INTEGER
The effective rank of A, i.e., the number of singular values
which are greater than RCOND*S(1).
WORK
WORK is REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK
LWORK is 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
INFO is 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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 172 of file sgelss.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 sgelss.f(3) 
