SGGLSE (3lapack)

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

SYNOPSIS

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

      INTEGER        INFO, LDA, LDB, LWORK, M, N, P

      REAL           A( LDA, * ), B( LDB, * ), C( * ), D( * ), WORK( * ), X(
                     * )

PURPOSE

  SGGLSE solves the linear equality-constrained least squares (LSE) problem:

          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) INTEGER
          The number of rows of the matrix A.  M >= 0.

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

  P       (input) INTEGER
          The number of rows of the matrix B. 0 <= P <= N <= M+P.

  A       (input/output) REAL array, dimension (LDA,N)
          On entry, the M-by-N matrix A.  On exit, A is destroyed.

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

  B       (input/output) REAL array, dimension (LDB,N)
          On entry, the P-by-N matrix B.  On exit, B is destroyed.

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

  C       (input/output) REAL array, dimension (M)
          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) REAL array, dimension (P)
          On entry, D contains the right hand side vector for the constrained
          equation.  On exit, D is destroyed.

  X       (output) REAL array, dimension (N)
          On exit, X is the solution of the LSE problem.

  WORK    (workspace/output) REAL array, dimension (LWORK)
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

  LWORK   (input) INTEGER
          The dimension of the array WORK. LWORK >= max(1,M+N+P).  For
          optimum performance LWORK >= P+min(M,N)+max(M,N)*NB, where NB is an
          upper bound for the optimal blocksizes for SGEQRF, SGERQF, SORMQR
          and SORMRQ.

  INFO    (output) INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.