NAME

       dgeql2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dgeql2 (M, N, A, LDA, TAU, WORK, INFO)
           DGEQL2 computes the QL factorization of a general rectangular matrix using an
           unblocked algorithm.

Function/Subroutine Documentation

   subroutine dgeql2 (integerM, integerN, double precision, dimension( lda, * )A, integerLDA,
       double precision, dimension( * )TAU, double precision, dimension( * )WORK, integerINFO)
       DGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked
       algorithm.

       Purpose:

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

       Parameters:
           M

                     M is INTEGER
                     The number of rows of the matrix A.  M >= 0.

           N

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

           A

                     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

                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,M).

           TAU

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

           WORK

                     WORK is DOUBLE PRECISION array, dimension (N)

           INFO

                     INFO is INTEGER
                     = 0: successful exit
                     < 0: if INFO = -i, the i-th argument had an illegal value

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       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).

       Definition at line 124 of file dgeql2.f.

Author

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