zgglse (3p)

Name

zgglse - constrained least squares (LSE) problem

Synopsis

SUBROUTINE ZGGLSE(M, N, P, A, LDA, B, LDB, C, D, X, WORK, LDWORK,
INFO)

DOUBLE COMPLEX A(LDA,*), B(LDB,*), C(*), D(*), X(*), WORK(*)
INTEGER M, N, P, LDA, LDB, LDWORK, INFO

SUBROUTINE ZGGLSE_64(M, N, P, A, LDA, B, LDB, C, D, X, WORK, LDWORK,
INFO)

DOUBLE COMPLEX A(LDA,*), B(LDB,*), C(*), D(*), X(*), WORK(*)
INTEGER*8 M, N, P, LDA, LDB, LDWORK, INFO




F95 INTERFACE
SUBROUTINE GGLSE(M, N, P, A, LDA, B, LDB, C, D, X, WORK,
LDWORK, INFO)

COMPLEX(8), DIMENSION(:) :: C, D, X, WORK
COMPLEX(8), DIMENSION(:,:) :: A, B
INTEGER :: M, N, P, LDA, LDB, LDWORK, INFO

SUBROUTINE GGLSE_64(M, N, P, A, LDA, B, LDB, C, D, X, WORK,
LDWORK, INFO)

COMPLEX(8), DIMENSION(:) :: C, D, X, WORK
COMPLEX(8), DIMENSION(:,:) :: A, B
INTEGER(8) :: M, N, P, LDA, LDB, LDWORK, INFO




C INTERFACE
#include <sunperf.h>

void zgglse(int m, int n, int p, doublecomplex *a, int lda,  doublecom-
plex *b, int ldb, doublecomplex *c, doublecomplex *d, double-
complex *x, int *info);

void zgglse_64(long m, long n, long p, doublecomplex *a, long lda, dou-
blecomplex  *b, long ldb, doublecomplex *c, doublecomplex *d,
doublecomplex *x, long *info);

Description

Oracle Solaris Studio Performance Library                           zgglse(3P)



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


SYNOPSIS
       SUBROUTINE ZGGLSE(M, N, P, A, LDA, B, LDB, C, D, X, WORK, LDWORK,
             INFO)

       DOUBLE COMPLEX A(LDA,*), B(LDB,*), C(*), D(*), X(*), WORK(*)
       INTEGER M, N, P, LDA, LDB, LDWORK, INFO

       SUBROUTINE ZGGLSE_64(M, N, P, A, LDA, B, LDB, C, D, X, WORK, LDWORK,
             INFO)

       DOUBLE COMPLEX A(LDA,*), B(LDB,*), C(*), D(*), X(*), WORK(*)
       INTEGER*8 M, N, P, LDA, LDB, LDWORK, INFO




   F95 INTERFACE
       SUBROUTINE GGLSE(M, N, P, A, LDA, B, LDB, C, D, X, WORK,
              LDWORK, INFO)

       COMPLEX(8), DIMENSION(:) :: C, D, X, WORK
       COMPLEX(8), DIMENSION(:,:) :: A, B
       INTEGER :: M, N, P, LDA, LDB, LDWORK, INFO

       SUBROUTINE GGLSE_64(M, N, P, A, LDA, B, LDB, C, D, X, WORK,
              LDWORK, INFO)

       COMPLEX(8), DIMENSION(:) :: C, D, X, WORK
       COMPLEX(8), DIMENSION(:,:) :: A, B
       INTEGER(8) :: M, N, P, LDA, LDB, LDWORK, INFO




   C INTERFACE
       #include <sunperf.h>

       void zgglse(int m, int n, int p, doublecomplex *a, int lda,  doublecom-
                 plex *b, int ldb, doublecomplex *c, doublecomplex *d, double-
                 complex *x, int *info);

       void zgglse_64(long m, long n, long p, doublecomplex *a, long lda, dou-
                 blecomplex  *b, long ldb, doublecomplex *c, doublecomplex *d,
                 doublecomplex *x, long *info);



PURPOSE
       zgglse 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 ZGEQRF,
                 ZGERQF, ZUNMQR and ZUNMRQ.

                 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                        zgglse(3P)