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zunmtr

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

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

          CHARACTER      SIDE, TRANS, UPLO

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

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

 PURPOSE
      ZUNMTR 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 of order nq, with nq = m
      if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the
      product of nq-1 elementary reflectors, as returned by
      ZHETRD:

      if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);

      if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).

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

      UPLO    (input) CHARACTER*1
              = 'U': Upper triangle of A contains elementary
              reflectors from ZHETRD; = 'L': Lower triangle of A
              contains elementary reflectors from ZHETRD.

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

      A       (input) COMPLEX*16 array, dimension
              (LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The vec-
              tors which define the elementary reflectors, as

              returned by ZHETRD.

      LDA     (input) INTEGER
              The leading dimension of the array A.  LDA >=
              max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE =
              'R'.

      TAU     (input) COMPLEX*16 array, dimension
              (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i) must
              contain the scalar factor of the elementary reflec-
              tor H(i), as returned by ZHETRD.

      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