sgglse (3p)

Name

sgglse - constrained least squares (LSE) problem

Synopsis

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

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

SUBROUTINE SGGLSE_64(M, N, P, A, LDA, B, LDB, C, D, X, WORK, LDWORK,
INFO)

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




C INTERFACE
#include <sunperf.h>

void sgglse(int m, int n, int p, float *a, int lda, float *b, int  ldb,
float *c, float *d, float *x, int *info);

void  sgglse_64(long  m,  long n, long p, float *a, long lda, float *b,
long ldb, float *c, float *d, float *x, long *info);

Description

Oracle Solaris Studio Performance Library                           sgglse(3P)



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


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

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

       SUBROUTINE SGGLSE_64(M, N, P, A, LDA, B, LDB, C, D, X, WORK, LDWORK,
             INFO)

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




   C INTERFACE
       #include <sunperf.h>

       void sgglse(int m, int n, int p, float *a, int lda, float *b, int  ldb,
                 float *c, float *d, float *x, int *info);

       void  sgglse_64(long  m,  long n, long p, float *a, long lda, float *b,
                 long ldb, float *c, float *d, float *x, long *info);



PURPOSE
       sgglse 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 SGEQRF,
                 SGERQF, SORMQR and SORMRQ.

                 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                        sgglse(3P)