DGEQL2(3)      LAPACK routine of NEC Numeric Library Collection      DGEQL2(3)



NAME
       DGEQL2

SYNOPSIS
       SUBROUTINE DGEQL2 (M, N, A, LDA, TAU, WORK, INFO)



PURPOSE
            DGEQL2 computes a QL factorization of a real m by n matrix A:
            A = Q * L.




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

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

           A         (input/output)
                     A is DOUBLE PRECISION 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)
                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,M).

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

           WORK      (output)
                     WORK is DOUBLE PRECISION array, dimension (N)

           INFO      (output)
                     INFO is 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**T

             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).



LAPACK routine                  31 October 2017                      DGEQL2(3)