SGELSS (3)  Linux Manuals
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.
NN is INTEGER The number of columns of the matrix A. N >= 0.
NRHSNRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
AA 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.
LDALDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
BB 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.
LDBLDB is INTEGER The leading dimension of the array B. LDB >= max(1,max(M,N)).
SS 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)).
RCONDRCOND 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.
RANKRANK is INTEGER The effective rank of A, i.e., the number of singular values which are greater than RCOND*S(1).
WORKWORK is REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORKLWORK 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.
INFOINFO 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
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