Contents
dgglse - solve the linear equality-constrained least squares
(LSE) problem
SUBROUTINE DGGLSE(M, N, P, A, LDA, B, LDB, C, D, X, WORK, LDWORK,
INFO)
INTEGER M, N, P, LDA, LDB, LDWORK, INFO
DOUBLE PRECISION A(LDA,*), B(LDB,*), C(*), D(*), X(*),
WORK(*)
SUBROUTINE DGGLSE_64(M, N, P, A, LDA, B, LDB, C, D, X, WORK, LDWORK,
INFO)
INTEGER*8 M, N, P, LDA, LDB, LDWORK, INFO
DOUBLE PRECISION A(LDA,*), B(LDB,*), C(*), D(*), X(*),
WORK(*)
F95 INTERFACE
SUBROUTINE GGLSE([M], [N], [P], A, [LDA], B, [LDB], C, D, X, [WORK],
[LDWORK], [INFO])
INTEGER :: M, N, P, LDA, LDB, LDWORK, INFO
REAL(8), DIMENSION(:) :: C, D, X, WORK
REAL(8), DIMENSION(:,:) :: A, B
SUBROUTINE GGLSE_64([M], [N], [P], A, [LDA], B, [LDB], C, D, X, [WORK],
[LDWORK], [INFO])
INTEGER(8) :: M, N, P, LDA, LDB, LDWORK, INFO
REAL(8), DIMENSION(:) :: C, D, X, WORK
REAL(8), DIMENSION(:,:) :: A, B
C INTERFACE
#include <sunperf.h>
void dgglse(int m, int n, int p, double *a, int lda, double
*b, int ldb, double *c, double *d, double *x, int
*info);
void dgglse_64(long m, long n, long p, double *a, long lda,
double *b, long ldb, double *c, double *d, double
*x, long *info);
dgglse solves the linear equality-constrained least squares
(LSE) problem:
minimize || c - A*x ||_2 subject to B*x = d
where A is an M-by-N matrix, B is a P-by-N matrix, c is a
given M-vector, and d is a given P-vector. It is assumed
that
P <= N <= M+P, and
rank(B) = P and rank( ( A ) ) = N.
( ( B ) )
These conditions ensure that the LSE problem has a unique
solution, which is obtained using a GRQ factorization of the
matrices B and A.
M (input) The number of rows of the matrix A. M >= 0.
N (input) The number of columns of the matrices A and B. N
>= 0.
P (input) The number of rows of the matrix B. 0 <= P <= N <=
M+P.
A (input/output)
On entry, the M-by-N matrix A. On exit, A is des-
troyed.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,M).
B (input/output)
On entry, the P-by-N matrix B. On exit, B is des-
troyed.
LDB (input)
The leading dimension of the array B. LDB >=
max(1,P).
C (input/output)
On entry, C contains the right hand side vector
for the least squares part of the LSE problem. On
exit, the residual sum of squares for the solution
is given by the sum of squares of elements N-P+1
to M of vector C.
D (input/output)
On entry, D contains the right hand side vector
for the constrained equation. On exit, D is des-
troyed.
X (output)
On exit, X is the solution of the LSE problem.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal
LDWORK.
LDWORK (input)
The dimension of the array WORK. LDWORK >=
max(1,M+N+P). For optimum performance LDWORK >=
P+min(M,N)+max(M,N)*NB, where NB is an upper bound
for the optimal blocksizes for SGEQRF, SGERQF,
SORMQR and SORMRQ.
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.