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sgglse

 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,
                         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 || A*x - c ||_2   subject to B*x = d

      using a generalized RQ factorization of matrices A and B,
      where A is M-by-N, B is P-by-N, assume P <= N <= M+P, and
      ||.||_2 denotes vector 2-norm. It is assumed that

                           rank(B) = P
      (1)

      and the null spaces of A and B intersect only trivially,
      i.e.,

       intersection of Null(A) and Null(B) = {0} <=> rank( ( A ) )
      = N  (2)
                                                         ( ( B ) )

      where N(A) denotes the null space of matrix A. Conditions
      (1) and (2) ensure that the problem LSE has a unique solu-
      tion.

 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.  Assume that P <= N <= M+P.

      P       (input) INTEGER
              The number of rows of the matrix B.  P >= 0.

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

      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 des-
              troyed.

      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) 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 >=
              N+P+max(N,M,P).  For optimum performance LWORK >=
              N+P+max(M,P,N)*max(NB1,NB2), where NB1 is the
              optimal blocksize for the QR factorization of M-by-N
              matrix A.  NB2 is the optimal blocksize for the RQ
              factorization of P-by-N matrix B.

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