CGELQ2(3)      LAPACK routine of NEC Numeric Library Collection      CGELQ2(3)



NAME
       CGELQ2

SYNOPSIS
       SUBROUTINE CGELQ2 (M, N, A, LDA, TAU, WORK, INFO)



PURPOSE
            CGELQ2 computes an LQ factorization of a complex m by n matrix A:
            A = L * Q.




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 array, dimension (LDA,N)
                     On entry, the m by n matrix A.
                     On exit, the elements on and below the diagonal of the array
                     contain the m by min(m,n) lower trapezoidal matrix L (L is
                     lower triangular if m <= n); the elements above the diagonal,
                     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 array, dimension (min(M,N))
                     The scalar factors of the elementary reflectors (see Further
                     Details).

           WORK      (output)
                     WORK is COMPLEX array, dimension (M)

           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 . . . H(2)**H H(1)**H, 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(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
             A(i,i+1:n), and tau in TAU(i).



LAPACK routine                  31 October 2017                      CGELQ2(3)