dgelss - compute the minimum norm solution to a real linear least squares problem
SUBROUTINE DGELSS( M, N, NRHS, A, LDA, B, LDB, SING, RCOND, IRANK, * WORK, LDWORK, INFO) INTEGER M, N, NRHS, LDA, LDB, IRANK, LDWORK, INFO DOUBLE PRECISION RCOND DOUBLE PRECISION A(LDA,*), B(LDB,*), SING(*), WORK(*)
SUBROUTINE DGELSS_64( M, N, NRHS, A, LDA, B, LDB, SING, RCOND, * IRANK, WORK, LDWORK, INFO) INTEGER*8 M, N, NRHS, LDA, LDB, IRANK, LDWORK, INFO DOUBLE PRECISION RCOND DOUBLE PRECISION A(LDA,*), B(LDB,*), SING(*), WORK(*)
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(8) :: RCOND REAL(8), DIMENSION(:) :: SING, WORK REAL(8), 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(8) :: RCOND REAL(8), DIMENSION(:) :: SING, WORK REAL(8), DIMENSION(:,:) :: A, B
#include <sunperf.h>
void dgelss(int m, int n, int nrhs, double *a, int lda, double *b, int ldb, double *sing, double rcond, int *irank, int *info);
void dgelss_64(long m, long n, long nrhs, double *a, long lda, double *b, long ldb, double *sing, double rcond, long *irank, long *info);
dgelss 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 singular values which are less than RCOND times the largest singular value.
min(m,n)
rows of A are overwritten with
its right singular vectors, stored rowwise.
SING(i)
< = RCOND*SING(1) are treated as zero.
If RCOND < 0, machine precision is used instead.
WORK(1)
returns the optimal LDWORK.
If LDWORK = -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 LDWORK is issued by XERBLA.
= 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 bidiagonal form did not converge to zero.