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



NAME
       ZGEQLF

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



PURPOSE
            ZGEQLF 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 (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK     (input)
                     LWORK is INTEGER
                     The dimension of the array WORK.  LWORK >= max(1,N).
                     For optimum performance LWORK >= N*NB, where NB is
                     the optimal blocksize.

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal size of the WORK array, returns
                     this value as the first entry of the WORK array, and no error
                     message related to LWORK is issued by XERBLA.

           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                      ZGEQLF(3)