dgglse (3p)

Name

dgglse - constrained least squares (LSE) problem

Synopsis

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);

Description

Oracle Solaris Studio Performance Library                           dgglse(3P)



NAME
       dgglse  -  solve  the  linear  equality-constrained least squares (LSE)
       problem


SYNOPSIS
       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);



PURPOSE
       dgglse solves the linear equality-constrained least squares (LSE) prob-
       lem:

               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-vec-
       tor, 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.


ARGUMENTS
       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 destroyed.


       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 destroyed.


       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  con-
                 strained equation.  On exit, D is destroyed.


       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 DGEQRF,
                 DGERQF, DORMQR and DORMRQ.

                 If LDWORK = -1, then a workspace query is assumed;  the  rou-
                 tine  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 illegal value.




                                  7 Nov 2015                        dgglse(3P)