sgels(3P) Sun Performance Library sgels(3P)NAMEsgels - solve overdetermined or underdetermined real linear systems
involving an M-by-N matrix A, or its transpose, using a QR or LQ fac‐
torization of A
SYNOPSIS
SUBROUTINE SGELS(TRANSA, M, N, NRHS, A, LDA, B, LDB, WORK, LDWORK,
INFO)
CHARACTER * 1 TRANSA
INTEGER M, N, NRHS, LDA, LDB, LDWORK, INFO
REAL A(LDA,*), B(LDB,*), WORK(*)
SUBROUTINE SGELS_64(TRANSA, M, N, NRHS, A, LDA, B, LDB, WORK, LDWORK,
INFO)
CHARACTER * 1 TRANSA
INTEGER*8 M, N, NRHS, LDA, LDB, LDWORK, INFO
REAL A(LDA,*), B(LDB,*), WORK(*)
F95 INTERFACE
SUBROUTINE GELS([TRANSA], [M], [N], [NRHS], A, [LDA], B, [LDB], [WORK],
LDWORK, [INFO])
CHARACTER(LEN=1) :: TRANSA
INTEGER :: M, N, NRHS, LDA, LDB, LDWORK, INFO
REAL, DIMENSION(:) :: WORK
REAL, DIMENSION(:,:) :: A, B
SUBROUTINE GELS_64([TRANSA], [M], [N], [NRHS], A, [LDA], B, [LDB],
[WORK], LDWORK, [INFO])
CHARACTER(LEN=1) :: TRANSA
INTEGER(8) :: M, N, NRHS, LDA, LDB, LDWORK, INFO
REAL, DIMENSION(:) :: WORK
REAL, DIMENSION(:,:) :: A, B
C INTERFACE
#include <sunperf.h>
void sgels (char transa, int m, int n, int nrhs, float* a, int lda,
float* b, int ldb, int* info);
void sgels_64 (char transa, long m, long n, long nrhs, float* a, long
lda, float* b, long ldb, long* info);
PURPOSEsgels solves overdetermined or underdetermined real linear systems
involving an M-by-N matrix A, or its transpose, using a QR or LQ fac‐
torization 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 M-by-NRHS right
hand side matrix B and the N-by-NRHS solution matrix X.
ARGUMENTS
TRANSA (input)
= 'N': the linear system involves A;
= 'T': the linear system involves A**T.
TRANSA is defaulted to 'N' for F95 INTERFACE.
M (input) The number of rows of the matrix A. M >= 0.
N (input) The number of columns of the matrix A. N >= 0.
NRHS (input)
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >=0.
A (input/output)
On entry, the M-by-N 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 fac‐
torization as returned by SGELQF.
LDA (input)
The leading dimension of the array A. LDA >= max(1,M).
B (input/output)
On entry, the matrix B of right hand side vectors, stored
columnwise; B is M-by-NRHS if TRANSA = 'N', or N-by-NRHS if
TRANSA = 'T'. On exit, B is overwritten by the solution vec‐
tors, stored columnwise: if TRANSA = '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 col‐
umn; if TRANSA = 'N' and m < n, rows 1 to N of B contain the
minimum norm solution vectors; if TRANSA = 'T' and m >= n,
rows 1 to M of B contain the minimum norm solution vectors;
if TRANSA = '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.
LDB (input)
The leading dimension of the array B. LDB >= MAX(1,M,N).
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.
LDWORK (input)
The dimension of the array WORK. LDWORK >= max( 1, MN + max(
MN, NRHS ) ). For optimal performance, LDWORK >= max( 1, MN
+ max( MN, NRHS )*NB ). where MN = min(M,N) and NB is the
optimum block size.
If LDWORK = -1, then a workspace query is assumed; the rou‐
tine 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 LDWORK is issued by XERBLA.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
6 Mar 2009 sgels(3P)