Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - solves a general Gauss-Markov linear model (GLM) problem

SYNOPSIS

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

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

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

PURPOSE

       SGGGLM 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.

ARGUMENTS

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

        M       (input) INTEGER
                The number of columns of the matrix A.  0 <= M <= N.

        P       (input) INTEGER
                The number of columns of the matrix B.  P >= N-M.

        A       (input/output) REAL 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     (input) INTEGER
                The leading dimension of the array A. LDA >= max(1,N).

        B       (input/output) REAL 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     (input) INTEGER
                The leading dimension of the array B. LDB >= max(1,N).

        D       (input/output) REAL array, dimension (N)
                On entry, D is the left hand side of the GLM equation.
                On exit, D is destroyed.

        X       (output) REAL array, dimension (M)
                Y       (output) REAL array, dimension (P)
                On exit, X and Y are the solutions of the GLM problem.

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

        LWORK   (input) 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
                SGEQRF, SGERQF, SORMQR 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    (output) 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.

 LAPACK driver routine (version 3.3.1)      April 2011                            SGGGLM(3lapack)