sgelqf(3F)

NAME
     SGELQF - compute an LQ factorization of a real M-by-N matrix A

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

         INTEGER        INFO, LDA, LWORK, M, N

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

PURPOSE
     SGELQF computes an LQ factorization of a real M-by-N matrix A:  A = L *
     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) REAL array, dimension (LDA,N)
             On entry, the M-by-N matrix A.  On exit, the elements on and
             below the diagonal of the array contain the m-by-min(m,n) lower
             trapezoidal matrix L (L is lower triangular if m <= n); the
             elements above the diagonal, with the array TAU, represent the
             orthogonal matrix Q as a product of 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 (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.

     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(k) . . . H(2) H(1), where k = min(m,n).

     Each H(i) has the form
        H(i) = I - tau * v * v'

     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:n) is stored on exit in A(i,i+1:n), and
     tau in TAU(i).