dgglse.f(3)

NAME
dgglse.f -

SYNOPSIS

  Functions/Subroutines
subroutine dgglse (M, N, P, A, LDA, B, LDB, C, D, X, WORK, LWORK, INFO)
DGGLSE solves overdetermined or underdetermined systems for OTHER matrices

Function/Subroutine Documentation

  subroutine dgglse (integerM, integerN, integerP, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( * )C, double precision, dimension( * )D, double precision, dimension( * )X, double precision, dimension( * )WORK, integerLWORK, integerINFO)

DGGLSE solves overdetermined or underdetermined systems for OTHER matrices

Purpose:

     DGGLSE 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 generalized RQ factorization of the
     matrices (B, A) given by
        B = (0 R)*Q,   A = Z*T*Q.

Parameters:
    M

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

    N

              N is INTEGER
              The number of columns of the matrices A and B. N >= 0.

    P

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

    A

              A is DOUBLE PRECISION array, dimension (LDA,N)
              On entry, the M-by-N matrix A.
              On exit, the elements on and above the diagonal of the array
              contain the min(M,N)-by-N upper trapezoidal matrix T.

    LDA

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

    B

              B is DOUBLE PRECISION array, dimension (LDB,N)
              On entry, the P-by-N matrix B.
              On exit, the upper triangle of the subarray B(1:P,N-P+1:N)
              contains the P-by-P upper triangular matrix R.

    LDB

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

    C

              C is DOUBLE PRECISION 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

              D is DOUBLE PRECISION array, dimension (P)
              On entry, D contains the right hand side vector for the
              constrained equation.
              On exit, D is destroyed.

    X

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

    WORK

              WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is 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
              DGEQRF, SGERQF, DORMQR and SORMRQ.
              If LWORK = -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 LWORK is issued by XERBLA.

    INFO

              INFO is INTEGER
              = 0:  successful exit.
              < 0:  if INFO = -i, the i-th argument had an illegal value.
              = 1:  the upper triangular factor R associated with B in the
                    generalized RQ factorization of the pair (B, A) is
                    singular, so that rank(B) < P; the least squares
                    solution could not be computed.
              = 2:  the (N-P) by (N-P) part of the upper trapezoidal factor
                    T associated with A in the generalized RQ factorization
                    of the pair (B, A) is singular, so that
                    rank( (A) ) < N; the least squares solution could not
                        ( (B) )
                    be computed.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2011

Definition at line 180 of file dgglse.f.

Author

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