zgelsx(3P) Sun Performance Library zgelsx(3P)NAMEzgelsx - routine is deprecated and has been replaced by routine ZGELSY
SYNOPSIS
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(*)
F95 INTERFACE
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
C INTERFACE
#include <sunperf.h>
void zgelsx(int m, int n, int nrhs, doublecomplex *a, int lda, double‐
complex *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);
PURPOSEzgelsx routine is deprecated and has been replaced by routine ZGELSY.
ZGELSX 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 con‐
dition 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.
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 matrices B and X. NRHS >= 0.
A (input/output)
On entry, the M-by-N matrix A. On exit, A has been overwrit‐
ten by details of its complete orthogonal factorization.
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,
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 col‐
umn 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,M,N).
JPIVOT (input/output)
On entry, if 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.
RCOND (input)
RCOND is used to determine the effective rank of A, which is
defined as the order of the largest leading triangular subma‐
trix R11 in the QR factorization with pivoting of A, whose
estimated condition number < 1/RCOND.
IRANK (output)
The effective rank of A, i.e., the order of the submatrix
R11. This is the same as the order of the submatrix T11 in
the complete orthogonal factorization of A.
WORK (workspace)
(min(M,N) + max( N, 2*min(M,N)+NRHS )),
WORK2 (workspace)
dimension(2*N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
6 Mar 2009 zgelsx(3P)
