sgelss(3P) Sun Performance Library sgelss(3P)NAMEsgelss - compute the minimum norm solution to a real linear least
squares problem
SYNOPSIS
SUBROUTINE SGELSS(M, N, NRHS, A, LDA, B, LDB, SING, RCOND, IRANK,
WORK, LDWORK, INFO)
INTEGER M, N, NRHS, LDA, LDB, IRANK, LDWORK, INFO
REAL RCOND
REAL A(LDA,*), B(LDB,*), SING(*), WORK(*)
SUBROUTINE SGELSS_64(M, N, NRHS, A, LDA, B, LDB, SING, RCOND, IRANK,
WORK, LDWORK, INFO)
INTEGER*8 M, N, NRHS, LDA, LDB, IRANK, LDWORK, INFO
REAL RCOND
REAL A(LDA,*), B(LDB,*), SING(*), WORK(*)
F95 INTERFACE
SUBROUTINE GELSS([M], [N], [NRHS], A, [LDA], B, [LDB], SING, RCOND,
IRANK, [WORK], [LDWORK], [INFO])
INTEGER :: M, N, NRHS, LDA, LDB, IRANK, LDWORK, INFO
REAL :: RCOND
REAL, DIMENSION(:) :: SING, WORK
REAL, DIMENSION(:,:) :: A, B
SUBROUTINE GELSS_64([M], [N], [NRHS], A, [LDA], B, [LDB], SING,
RCOND, IRANK, [WORK], [LDWORK], [INFO])
INTEGER(8) :: M, N, NRHS, LDA, LDB, IRANK, LDWORK, INFO
REAL :: RCOND
REAL, DIMENSION(:) :: SING, WORK
REAL, DIMENSION(:,:) :: A, B
C INTERFACE
#include <sunperf.h>
void sgelss(int m, int n, int nrhs, float *a, int lda, float *b, int
ldb, float *sing, float rcond, int *irank, int *info);
void sgelss_64(long m, long n, long nrhs, float *a, long lda, float *b,
long ldb, float *sing, float rcond, long *irank, long *info);
PURPOSEsgelss computes the minimum norm solution to a real linear least
squares problem:
Minimize 2-norm(| b - A*x |).
using the singular value decomposition (SVD) of A. A is an M-by-N
matrix which may be rank-deficient.
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.
The effective rank of A is determined by treating as zero those singu‐
lar values which are less than RCOND times the largest singular value.
ARGUMENTS
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, the first min(m,n)
rows of A are overwritten with its right singular vectors,
stored rowwise.
LDA (input)
The leading dimension of the array A. LDA >= max(1,M).
B (input/output)
On entry, the M-by-NRHS right hand side matrix B. On exit, B
is overwritten by the N-by-NRHS solution matrix X. If m >= n
and IRANK = n, the residual sum-of-squares for the solution
in the i-th column is given by the sum of squares of elements
n+1:m in that column.
LDB (input)
The leading dimension of the array B. LDB >= max(1,max(M,N)).
SING (output)
The singular values of A in decreasing order. The condition
number of A in the 2-norm = SING(1)/SING(min(m,n)).
RCOND (input)
RCOND is used to determine the effective rank of A. Singular
values SING(i) <= RCOND*SING(1) are treated as zero. If
RCOND < 0, machine precision is used instead.
IRANK (output)
The effective rank of A, i.e., the number of singular values
which are greater than RCOND*SING(1).
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.
LDWORK (input)
The dimension of the array WORK. LDWORK >= 1, and also:
LDWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS ) For
good performance, LDWORK should generally be larger.
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.
> 0: the algorithm for computing the SVD failed to converge;
if INFO = i, i off-diagonal elements of an intermediate bidi‐
agonal form did not converge to zero.
6 Mar 2009 sgelss(3P)
