ZGERQ2(3)      LAPACK routine of NEC Numeric Library Collection      ZGERQ2(3)



NAME
       ZGERQ2

SYNOPSIS
       SUBROUTINE ZGERQ2 (M, N, A, LDA, TAU, WORK, INFO)



PURPOSE
            ZGERQ2 computes an RQ factorization of a complex m by n matrix A:
            A = R * 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*16 array, dimension (LDA,N)
                     On entry, the m by n matrix A.
                     On exit, if m <= n, the upper triangle of the subarray
                     A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
                     if m >= n, the elements on and above the (m-n)-th subdiagonal
                     contain the m by n upper trapezoidal matrix R; 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 (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(1)**H H(2)**H . . . H(k)**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(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
             exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).



LAPACK routine                  31 October 2017                      ZGERQ2(3)