sgeql2(3F)

NAME
     SGEQL2 - compute a QL factorization of a real m by n matrix A

SYNOPSIS
     SUBROUTINE SGEQL2( M, N, A, LDA, TAU, WORK, INFO )

         INTEGER        INFO, LDA, M, N

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

PURPOSE
     SGEQL2 computes a QL factorization of a real m by n matrix A:  A = Q * L.


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, if m >= n, the lower
             triangle of the subarray A(m-n+1:m,1:n) contains the n by n lower
             triangular matrix L; if m <= n, the elements on and below the
             (n-m)-th superdiagonal contain the m by n lower trapezoidal
             matrix L; the remaining elements, 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) REAL array, dimension (N)

     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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
     A(1:m-k+i-1,n-k+i), and tau in TAU(i).