zggglm (3p)

Name

zggglm - 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, doublecom-
plex *b, int ldb, doublecomplex *d, doublecomplex *x, double-
complex *y, int *info);

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

Description

Oracle Solaris Studio Performance Library                           zggglm(3P)



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, doublecom-
                 plex *b, int ldb, doublecomplex *d, doublecomplex *x, double-
                 complex *y, int *info);

       void zggglm_64(long n, long m, long p, doublecomplex *a, long lda, dou-
                 blecomplex *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  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                        zggglm(3P)