ZUPMTR(3)      LAPACK routine of NEC Numeric Library Collection      ZUPMTR(3)



NAME
       ZUPMTR

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



PURPOSE
            ZUPMTR 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 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 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)
                     SIDE is CHARACTER*1
                     = 'L': apply Q or Q**H from the Left;
                     = 'R': apply Q or Q**H from the Right.

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

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

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

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

           WORK      (output)
                     WORK is COMPLEX*16 array, dimension
                                              (N) if SIDE = 'L'
                                              (M) if SIDE = 'R'

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



LAPACK routine                  31 October 2017                      ZUPMTR(3)