• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

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, doublecomplex *b, int ldb, doublecomplex *c, doublecomplex *d, doublecomplex *x, int *info);

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

PURPOSE

zgglse 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.

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 constrained 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 CGEQRF, CGERQF, CUNMQR and CUNMRQ.

  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 illegal value.