dggglm.f(3)

NAME
dggglm.f -

SYNOPSIS

  Functions/Subroutines
subroutine DGGGLM (N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LWORK, INFO)
DGGEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Function/Subroutine Documentation

  subroutine DGGGLM (INTEGERN, INTEGERM, INTEGERP, DOUBLE PRECISION, dimension( lda, * )A, INTEGERLDA, DOUBLE PRECISION, dimension( ldb, * )B, INTEGERLDB, DOUBLE PRECISION, dimension( * )D, DOUBLE PRECISION, dimension( * )X, DOUBLE PRECISION, dimension( * )Y, DOUBLE PRECISION, dimension( * )WORK, INTEGERLWORK, INTEGERINFO)

DGGEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Purpose:

     DGGGLM solves a general Gauss-Markov linear model (GLM) problem:
             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 the matrices (A, B) given by
        A = Q*(R),   B = Q*T*Z.
              (0)
     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.

Parameters:
    N

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

    M

              M is INTEGER
              The number of columns of the matrix A.  0 <= M <= N.

    P

              P is INTEGER
              The number of columns of the matrix B.  P >= N-M.

    A

              A is DOUBLE PRECISION array, dimension (LDA,M)
              On entry, the N-by-M matrix A.
              On exit, the upper triangular part of the array A contains
              the M-by-M upper triangular matrix R.

    LDA

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

    B

              B is DOUBLE PRECISION array, dimension (LDB,P)
              On entry, the N-by-P matrix B.
              On exit, if N <= P, the upper triangle of the subarray
              B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T;
              if N > P, the elements on and above the (N-P)th subdiagonal
              contain the N-by-P upper trapezoidal matrix T.

    LDB

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

    D

              D is DOUBLE PRECISION array, dimension (N)
              On entry, D is the left hand side of the GLM equation.
              On exit, D is destroyed.

    X

              X is DOUBLE PRECISION array, dimension (M)

    Y

              Y is DOUBLE PRECISION array, dimension (P)
              On exit, X and Y are the solutions of the GLM 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,N+M+P).
              For optimum performance, LWORK >= M+min(N,P)+max(N,P)*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 A in the
                    generalized QR factorization of the pair (A, B) is
                    singular, so that rank(A) < M; the least squares
                    solution could not be computed.
              = 2:  the bottom (N-M) by (N-M) part of the upper trapezoidal
                    factor T associated with B in the generalized QR
                    factorization of the pair (A, B) is singular, so that
                    rank( A B ) < N; the least squares solution could not
                    be computed.

Author:
    Univ'. of Tennessee

    Univ'. of California Berkeley

    Univ'. of Colorado Denver

    NAG Ltd'.

Date:
    November 2011

Definition at line 185 of file dggglm.f'.

Author

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