zgelsx - routine is deprecated and has been replaced by routine CGELSY
SUBROUTINE ZGELSX( M, N, NRHS, A, LDA, B, LDB, JPIVOT, RCOND, IRANK, * WORK, WORK2, INFO) DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER M, N, NRHS, LDA, LDB, IRANK, INFO INTEGER JPIVOT(*) DOUBLE PRECISION RCOND DOUBLE PRECISION WORK2(*)
SUBROUTINE ZGELSX_64( M, N, NRHS, A, LDA, B, LDB, JPIVOT, RCOND, * IRANK, WORK, WORK2, INFO) DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER*8 M, N, NRHS, LDA, LDB, IRANK, INFO INTEGER*8 JPIVOT(*) DOUBLE PRECISION RCOND DOUBLE PRECISION WORK2(*)
SUBROUTINE GELSX( [M], [N], [NRHS], A, [LDA], B, [LDB], JPIVOT, * RCOND, IRANK, [WORK], [WORK2], [INFO]) COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B INTEGER :: M, N, NRHS, LDA, LDB, IRANK, INFO INTEGER, DIMENSION(:) :: JPIVOT REAL(8) :: RCOND REAL(8), DIMENSION(:) :: WORK2
SUBROUTINE GELSX_64( [M], [N], [NRHS], A, [LDA], B, [LDB], JPIVOT, * RCOND, IRANK, [WORK], [WORK2], [INFO]) COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B INTEGER(8) :: M, N, NRHS, LDA, LDB, IRANK, INFO INTEGER(8), DIMENSION(:) :: JPIVOT REAL(8) :: RCOND REAL(8), DIMENSION(:) :: WORK2
#include <sunperf.h>
void zgelsx(int m, int n, int nrhs, doublecomplex *a, int lda, doublecomplex *b, int ldb, int *jpivot, double rcond, int *irank, int *info);
void zgelsx_64(long m, long n, long nrhs, doublecomplex *a, long lda, doublecomplex *b, long ldb, long *jpivot, double rcond, long *irank, long *info);
zgelsx routine is deprecated and has been replaced by routine CGELSY.
CGELSX computes the minimum-norm solution to a complex linear least squares problem:
minimize || A * X - B ||
using a complete orthogonal factorization 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 routine first computes a QR factorization with column pivoting: A * P = Q * [ R11 R12 ]
[ 0 R22 ]
with R11 defined as the largest leading submatrix whose estimated condition number is less than 1/RCOND. The order of R11, RANK, is the effective rank of A.
Then, R22 is considered to be negligible, and R12 is annihilated by unitary transformations from the right, arriving at the complete orthogonal factorization:
A * P = Q * [ T11 0 ] * Z
[ 0 0 ]
The minimum-norm solution is then
X = P * Z' [ inv(T11)*Q1'*B ]
[ 0 ]
where Q1 consists of the first RANK columns of Q.
JPIVOT(i)
.ne. 0, the i-th column of A is an
initial column, otherwise it is a free column. Before
the QR factorization of A, all initial columns are
permuted to the leading positions; only the remaining
free columns are moved as a result of column pivoting
during the factorization.
On exit, if JPIVOT(i)
= k, then the i-th column of A*P
was the k-th column of A.
dimension(2*N)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value