NAME

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

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

        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 SGEQRF, SGERQF, SORMQR and SORMRQ.

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)