Contents
cgels - solve overdetermined or underdetermined complex
linear systems involving an M-by-N matrix A, or its
conjugate-transpose, using a QR or LQ factorization of A
SUBROUTINE CGELS(TRANSA, M, N, NRHS, A, LDA, B, LDB, WORK, LDWORK,
INFO)
CHARACTER * 1 TRANSA
COMPLEX A(LDA,*), B(LDB,*), WORK(*)
INTEGER M, N, NRHS, LDA, LDB, LDWORK, INFO
SUBROUTINE CGELS_64(TRANSA, M, N, NRHS, A, LDA, B, LDB, WORK, LDWORK,
INFO)
CHARACTER * 1 TRANSA
COMPLEX A(LDA,*), B(LDB,*), WORK(*)
INTEGER*8 M, N, NRHS, LDA, LDB, LDWORK, INFO
F95 INTERFACE
SUBROUTINE GELS([TRANSA], [M], [N], [NRHS], A, [LDA], B, [LDB], [WORK],
LDWORK, [INFO])
CHARACTER(LEN=1) :: TRANSA
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, B
INTEGER :: M, N, NRHS, LDA, LDB, LDWORK, INFO
SUBROUTINE GELS_64([TRANSA], [M], [N], [NRHS], A, [LDA], B, [LDB],
[WORK], LDWORK, [INFO])
CHARACTER(LEN=1) :: TRANSA
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, B
INTEGER(8) :: M, N, NRHS, LDA, LDB, LDWORK, INFO
C INTERFACE
#include <sunperf.h>
void cgels (char, int, int, int, complex*, int, complex*,
int, int*);
void cgels_64 (char, long, long, long, complex*, long, com-
plex*, long, long*);
cgels solves overdetermined or underdetermined complex
linear systems involving an M-by-N matrix A, or its
conjugate-transpose, using a QR or LQ factorization of A.
It is assumed that A has full rank.
The following options are provided:
1. If TRANS = 'N' and m >= n: find the least squares solu-
tion of
an overdetermined system, i.e., solve the least squares
problem
minimize || B - A*X ||.
2. If TRANS = 'N' and m < n: find the minimum norm solution
of
an underdetermined system A * X = B.
3. If TRANS = 'C' and m >= n: find the minimum norm solu-
tion of
an undetermined system A**H * X = B.
4. If TRANS = 'C' and m < n: find the least squares solu-
tion of
an overdetermined system, i.e., solve the least squares
problem
minimize || B - A**H * X ||.
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.
TRANSA (input)
= 'N': the linear system involves A;
= 'C': the linear system involves A**H.
TRANSA is defaulted to 'N' for F95 INTERFACE.
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. if M >= N, A is
overwritten by details of its QR factorization as
returned by CGEQRF; if M < N, A is overwritten by
details of its LQ factorization as returned by
CGELQF.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,M).
B (input/output)
On entry, the matrix B of right hand side vectors,
stored columnwise; B is M-by-NRHS if TRANSA = 'N',
or N-by-NRHS if TRANSA = 'C'. On exit, B is
overwritten by the solution vectors, stored
columnwise: if TRANSA = 'N' and m >= n, rows 1 to
n of B contain the least squares solution vectors;
the residual sum of squares for the solution in
each column is given by the sum of squares of ele-
ments N+1 to M in that column; if TRANSA = 'N' and
m < n, rows 1 to N of B contain the minimum norm
solution vectors; if TRANSA = 'C' and m >= n, rows
1 to M of B contain the minimum norm solution vec-
tors; if TRANSA = 'C' and m < n, rows 1 to M of B
contain the least squares solution vectors; the
residual sum of squares for the solution in each
column is given by the sum of squares of elements
M+1 to N in that column.
LDB (input)
The leading dimension of the array B. LDB >=
MAX(1,M,N).
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal
LDWORK.
LDWORK (output)
The dimension of the array WORK. LDWORK >= max(
1, MN + max( MN, NRHS ) ). For optimal perfor-
mance, LDWORK >= max( 1, MN + max( MN, NRHS )*NB
). where MN = min(M,N) and NB is the optimum
block size.
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.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value