ZGEQL2(3)      LAPACK routine of NEC Numeric Library Collection      ZGEQL2(3)



NAME
       ZGEQL2

SYNOPSIS
       SUBROUTINE ZGEQL2 (M, N, A, LDA, TAU, WORK, INFO)



PURPOSE
            ZGEQL2 computes a QL factorization of a complex 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 COMPLEX*16 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
                     unitary 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 COMPLEX*16 array, dimension (min(M,N))
                     The scalar factors of the elementary reflectors (see Further
                     Details).

           WORK      (output)
                     WORK is COMPLEX*16 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**H

             where tau is a complex scalar, and v is a complex 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                      ZGEQL2(3)