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zunmrq

 NAME
      ZUNMRQ - overwrite the general complex M-by-N matrix C with
      SIDE = 'L' SIDE = 'R' TRANS = 'N'

 SYNOPSIS
      SUBROUTINE ZUNMRQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C,
                         LDC, WORK, LWORK, INFO )

          CHARACTER      SIDE, TRANS

          INTEGER        INFO, K, LDA, LDC, LWORK, M, N

          COMPLEX*16     A( LDA, * ), C( LDC, * ), TAU( * ), WORK(
                         LWORK )

 PURPOSE
      ZUNMRQ overwrites the general complex M-by-N matrix C with
      TRANS = 'C':      Q**H * C       C * Q**H

      where Q is a complex unitary matrix defined as the product
      of k elementary reflectors

            Q = H(1)' H(2)' . . . H(k)'

      as returned by ZGERQF. Q is of order M if SIDE = 'L' and of
      order N if SIDE = 'R'.

 ARGUMENTS
      SIDE    (input) CHARACTER*1
              = 'L': apply Q or Q**H from the Left;
              = 'R': apply Q or Q**H from the Right.

      TRANS   (input) CHARACTER*1
              = 'N':  No transpose, apply Q;
              = 'C':  Transpose, apply Q**H.

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

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

      K       (input) INTEGER
              The number of elementary reflectors whose product
              defines the matrix Q.  If SIDE = 'L', M >= K >= 0;
              if SIDE = 'R', N >= K >= 0.

      A       (input) COMPLEX*16 array, dimension
              (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-
              th row must contain the vector which defines the
              elementary reflector H(i), for i = 1,2,...,k, as

              returned by ZGERQF in the last k rows of its array
              argument A.  A is modified by the routine but
              restored on exit.

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

      TAU     (input) COMPLEX*16 array, dimension (K)
              TAU(i) must contain the scalar factor of the elemen-
              tary reflector H(i), as returned by ZGERQF.

      C       (input/output) COMPLEX*16 array, dimension (LDC,N)
              On entry, the M-by-N matrix C.  On exit, C is
              overwritten by Q*C or Q**H*C or C*Q**H or C*Q.

      LDC     (input) INTEGER
              The leading dimension of the array C. LDC >=
              max(1,M).

      WORK    (workspace) COMPLEX*16 array, dimension (LWORK)
              On exit, if INFO = 0, WORK(1) returns the optimal
              LWORK.

      LWORK   (input) INTEGER
              The dimension of the array WORK.  If SIDE = 'L',
              LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M).
              For optimum performance LWORK >= N*NB if SIDE = 'L',
              and LWORK >= M*NB if SIDE = 'R', where NB is the
              optimal blocksize.

      INFO    (output) INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal
              value