SGELS (3)  Linux Manuals
NAME
sgels.f 
SYNOPSIS
Functions/Subroutines
subroutine sgels (TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK, INFO)
SGELS solves overdetermined or underdetermined systems for GE matrices
Function/Subroutine Documentation
subroutine sgels (characterTRANS, integerM, integerN, integerNRHS, real, dimension( lda, * )A, integerLDA, real, dimension( ldb, * )B, integerLDB, real, dimension( * )WORK, integerLWORK, integerINFO)
SGELS solves overdetermined or underdetermined systems for GE matrices
Purpose:

SGELS solves overdetermined or underdetermined real linear systems involving an MbyN matrix A, or its transpose, using a QR or LQ factorization of A. It is assumed that A has full rank. The following options are provided: 1. If TRANS = 'N' and m >= n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem minimize  B  A*X . 2. If TRANS = 'N' and m < n: find the minimum norm solution of an underdetermined system A * X = B. 3. If TRANS = 'T' and m >= n: find the minimum norm solution of an undetermined system A**T * X = B. 4. If TRANS = 'T' and m < n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem minimize  B  A**T * X . 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.
Parameters:

TRANS
TRANS is CHARACTER*1 = 'N': the linear system involves A; = 'T': the linear system involves A**T.
MM 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, if M >= N, A is overwritten by details of its QR factorization as returned by SGEQRF; if M < N, A is overwritten by details of its LQ factorization as returned by SGELQF.
LDALDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
BB is REAL array, dimension (LDB,NRHS) On entry, the matrix B of right hand side vectors, stored columnwise; B is MbyNRHS if TRANS = 'N', or NbyNRHS if TRANS = 'T'. On exit, if INFO = 0, B is overwritten by the solution vectors, stored columnwise: if TRANS = 'N' and m >= n, rows 1 to n of B contain the least squares solution vectors; the residual sum of squares for the solution in each column is given by the sum of squares of elements N+1 to M in that column; if TRANS = 'N' and m < n, rows 1 to N of B contain the minimum norm solution vectors; if TRANS = 'T' and m >= n, rows 1 to M of B contain the minimum norm solution vectors; if TRANS = 'T' and m < n, rows 1 to M of B contain the least squares solution vectors; the residual sum of squares for the solution in each column is given by the sum of squares of elements M+1 to N in that column.
LDBLDB is INTEGER The leading dimension of the array B. LDB >= MAX(1,M,N).
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 >= max( 1, MN + max( MN, NRHS ) ). For optimal performance, LWORK >= max( 1, MN + max( MN, NRHS )*NB ). where MN = min(M,N) and NB is the optimum block size. 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: if INFO = i, the ith diagonal element of the triangular factor of A is zero, so that A does not have full rank; the least squares solution could not be computed.
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 November 2011
Definition at line 183 of file sgels.f.
Author
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