ZUPMTR(3)                  MathKeisan LAPACK routine                 ZUPMTR(3)



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

SYNOPSIS
       SUBROUTINE ZUPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK, INFO
                          )

           CHARACTER      SIDE, TRANS, UPLO

           INTEGER        INFO, LDC, M, N

           COMPLEX*16     AP( * ), C( LDC, * ), TAU( * ), WORK( * )

PURPOSE
       ZUPMTR 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 ele-
       mentary reflectors, as returned by ZHPTRD using packed storage:

       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 triangular packed storage used in previous call to
               ZHPTRD; = 'L': Lower triangular packed storage used in previous
               call to ZHPTRD.

       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.

       AP      (input) COMPLEX*16 array, dimension
               (M*(M+1)/2) if SIDE = 'L' (N*(N+1)/2) if SIDE = 'R' The vectors
               which  define the elementary reflectors, as returned by ZHPTRD.
               AP is modified by the routine but restored on exit.

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

       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
               (N) if SIDE = 'L' (M) if SIDE = 'R'

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



 LAPACK routine (version 3.1)    November 2006                       ZUPMTR(3)