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

NAME

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

SYNOPSIS

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

           INTEGER        INFO, LDA, LWORK, M, N

           REAL           A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

       SGEQRF computes a QR factorization of a real M-by-N matrix A:
        A = Q * R.

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) REAL 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 R (R is
                upper triangular if m >= n); the elements below the diagonal,
                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) REAL array, dimension (min(M,N))
                The scalar factors of the elementary reflectors (see Further
                Details).

        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).
                For optimum performance LWORK >= N*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(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
        and tau in TAU(i).

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