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

NAME

       LAPACK-3 - computes an RQ factorization of a real M-by-N matrix A

SYNOPSIS

       SUBROUTINE DGERQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )

           INTEGER        INFO, LDA, LWORK, M, N

           DOUBLE         PRECISION A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

       DGERQF computes an RQ factorization of a real M-by-N matrix A:
        A = R * Q.

ARGUMENTS

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

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

        A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
                On entry, the M-by-N matrix A.
                On exit,
                if m <= n, the upper triangle of the subarray
                A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R;
                if m >= n, the elements on and above the (m-n)-th subdiagonal
                contain the M-by-N upper trapezoidal matrix R;
                the remaining elements, with the array TAU, represent the
                orthogonal matrix Q as a product of min(m,n) elementary
                reflectors (see Further Details).
                LDA     (input) INTEGER
                The leading dimension of the array A.  LDA >= max(1,M).

        TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))
                The scalar factors of the elementary reflectors (see Further
                Details).

        WORK    (workspace/output) DOUBLE PRECISION 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,M).
                For optimum performance LWORK >= M*NB, where NB is
                the optimal blocksize.
                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

FURTHER DETAILS

        The matrix Q is represented as a product of elementary reflectors
           Q = H(1) H(2) . . . H(k), where k = min(m,n).
        Each H(i) has the form
           H(i) = I - tau * v * v**T
        where tau is a real scalar, and v is a real vector with
        v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
        A(m-k+i,1:n-k+i-1), and tau in TAU(i).

 LAPACK routine (version 3.3.1)             April 2011                            DGERQF(3lapack)