Contents
cgelss - compute the minimum norm solution to a complex
linear least squares problem
SUBROUTINE CGELSS(M, N, NRHS, A, LDA, B, LDB, SING, RCOND, IRANK,
WORK, LDWORK, WORK2, INFO)
COMPLEX A(LDA,*), B(LDB,*), WORK(*)
INTEGER M, N, NRHS, LDA, LDB, IRANK, LDWORK, INFO
REAL RCOND
REAL SING(*), WORK2(*)
SUBROUTINE CGELSS_64(M, N, NRHS, A, LDA, B, LDB, SING, RCOND, IRANK,
WORK, LDWORK, WORK2, INFO)
COMPLEX A(LDA,*), B(LDB,*), WORK(*)
INTEGER*8 M, N, NRHS, LDA, LDB, IRANK, LDWORK, INFO
REAL RCOND
REAL SING(*), WORK2(*)
F95 INTERFACE
SUBROUTINE GELSS([M], [N], [NRHS], A, [LDA], B, [LDB], SING, RCOND,
IRANK, [WORK], [LDWORK], [WORK2], [INFO])
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, B
INTEGER :: M, N, NRHS, LDA, LDB, IRANK, LDWORK, INFO
REAL :: RCOND
REAL, DIMENSION(:) :: SING, WORK2
SUBROUTINE GELSS_64([M], [N], [NRHS], A, [LDA], B, [LDB], SING,
RCOND, IRANK, [WORK], [LDWORK], [WORK2], [INFO])
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, B
INTEGER(8) :: M, N, NRHS, LDA, LDB, IRANK, LDWORK, INFO
REAL :: RCOND
REAL, DIMENSION(:) :: SING, WORK2
C INTERFACE
#include <sunperf.h>
void cgelss(int m, int n, int nrhs, complex *a, int lda,
complex *b, int ldb, float *sing, float rcond, int
*irank, int *info);
void cgelss_64(long m, long n, long nrhs, complex *a, long
lda, complex *b, long ldb, float *sing, float
rcond, long *irank, long *info);
cgelss computes the minimum norm solution to a complex
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.
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 solu-
tion 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 ele-
ments n+1:m in that column.
LDB (input)
The leading dimension of the array B. LDB >=
max(1,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 >= 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 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.
WORK2 (workspace)
dimension(5*min(M,N))
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal 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 con-
verge to zero.