CXML
        	    
LAPACK version 3.0
zunmrq(3)

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

SYNTAX
  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( * )

DESCRIPTION
  ZUNMRQ overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE
  = 'R' TRANS = 'N': Q * C C * Q 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 elementary 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/output) 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.

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