NAME

SYNOPSIS

  SUBROUTINE SGGGLM( N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LDWORK, 
 *      INFO)
  INTEGER N, M, P, LDA, LDB, LDWORK, INFO
  REAL A(LDA,*), B(LDB,*), D(*), X(*), Y(*), WORK(*)
 
  SUBROUTINE SGGGLM_64( N, M, P, A, LDA, B, LDB, D, X, Y, WORK, 
 *      LDWORK, INFO)
  INTEGER*8 N, M, P, LDA, LDB, LDWORK, INFO
  REAL A(LDA,*), B(LDB,*), D(*), X(*), Y(*), WORK(*)
 

F95 INTERFACE

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

C INTERFACE

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

void sggglm_64(long n, long m, long p, float *a, long lda, float *b, long ldb, float *d, float *x, float *y, long *info);

PURPOSE

        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)

See the description of X.

* 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 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)