zgerq2(3F)

NAME
     ZGERQ2 - compute an RQ factorization of a complex m by n matrix A

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

         INTEGER        INFO, LDA, M, N

         COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
     ZGERQ2 computes an RQ factorization of a complex m by n matrix A:  A = R
     * Q.


ARGUMENTS
     M       (input) INTEGER
             The number of rows of the matrix A.  M >= 0.

     N       (input) INTEGER
             The number of columns of the matrix A.  N >= 0.

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

     TAU     (output) COMPLEX*16 array, dimension (min(M,N))
             The scalar factors of the elementary reflectors (see Further
             Details).

     WORK    (workspace) COMPLEX*16 array, dimension (M)

     INFO    (output) 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(2)' . . . H(k)', where k = min(m,n).

     Each H(i) has the form

        H(i) = I - tau * v * v'
     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).