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 ille­
               gal 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


       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).


Man(1) output converted with man2html