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

NAME

zggglm - solve a general Gauss-Markov linear model (GLM) problem

SYNOPSIS

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

  SUBROUTINE ZGGGLM_64( N, M, P, A, LDA, B, LDB, D, X, Y, WORK, 
 *      LDWORK, INFO)
  DOUBLE COMPLEX A(LDA,*), B(LDB,*), D(*), X(*), Y(*), WORK(*)
  INTEGER*8 N, M, P, LDA, LDB, LDWORK, INFO

F95 INTERFACE

  SUBROUTINE GGGLM( [N], [M], [P], A, [LDA], B, [LDB], D, X, Y, [WORK], 
 *       [LDWORK], [INFO])
  COMPLEX(8), DIMENSION(:) :: D, X, Y, WORK
  COMPLEX(8), DIMENSION(:,:) :: A, B
  INTEGER :: N, M, P, LDA, LDB, LDWORK, INFO

  SUBROUTINE GGGLM_64( [N], [M], [P], A, [LDA], B, [LDB], D, X, Y, 
 *       [WORK], [LDWORK], [INFO])
  COMPLEX(8), DIMENSION(:) :: D, X, Y, WORK
  COMPLEX(8), DIMENSION(:,:) :: A, B
  INTEGER(8) :: N, M, P, LDA, LDB, LDWORK, INFO

C INTERFACE

#include <sunperf.h>

void zggglm(int n, int m, int p, doublecomplex *a, int lda, doublecomplex *b, int ldb, doublecomplex *d, doublecomplex *x, doublecomplex *y, int *info);

void zggglm_64(long n, long m, long p, doublecomplex *a, long lda, doublecomplex *b, long ldb, doublecomplex *d, doublecomplex *x, doublecomplex *y, long *info);

PURPOSE

zggglm solves a general Gauss-Markov linear model (GLM) problem:

        minimize || y ||_2   subject to   d = A*x + B*y

            x

where A is an N-by-M matrix, B is an N-by-P matrix, and d is a given N-vector. It is assumed that M <= N <= M+P, and

           rank(A) = M    and    rank( A B ) = N.

Under these assumptions, the constrained equation is always consistent, and there is a unique solution x and a minimal 2-norm solution y, which is obtained using a generalized QR factorization of A and B.

In particular, if matrix B is square nonsingular, then the problem GLM is equivalent to the following weighted linear least squares problem

             minimize || inv(B)*(d-A*x) ||_2

                 x

where inv(B) denotes the inverse of B.

ARGUMENTS

• N (input)
  The number of rows of the matrices A and B. N > = 0.

• M (input)
  The number of columns of the matrix A. 0 < = M < = N.

• P (input)
  The number of columns of the matrix B. P > = N-M.

• A (input/output)
  On entry, the N-by-M matrix A. On exit, A is destroyed.

• LDA (input)
  The leading dimension of the array A. LDA > = max(1,N).

• B (input/output)
  On entry, the N-by-P matrix B. On exit, B is destroyed.

• LDB (input)
  The leading dimension of the array B. LDB > = max(1,N).

• D (input/output)
  On entry, D is the left hand side of the GLM equation. On exit, D is destroyed.

• X (output)
  On exit, X and Y are the solutions of the GLM problem.

• Y (output)
  On exit, X and Y are the solutions of the GLM 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,N+M+P). For optimum performance, LDWORK > = M+min(N,P)+max(N,P)*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.