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



NAME
       CUNMRZ

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



PURPOSE
            CUNMRZ 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 CTZRZF. Q is of order M if SIDE = 'L' and of order N
            if SIDE = 'R'.




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.

           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.

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

           L         (input)
                     L is INTEGER
                     The number of columns of the matrix A containing
                     the meaningful part of the Householder reflectors.
                     If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.

           A         (input)
                     A is COMPLEX 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
                     CTZRZF in the last k rows of its array argument A.
                     A is modified by the routine but restored on exit.

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

           TAU       (input)
                     TAU is COMPLEX array, dimension (K)
                     TAU(i) must contain the scalar factor of the elementary
                     reflector H(i), as returned by CTZRZF.

           C         (input/output)
                     C is COMPLEX 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 array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

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



LAPACK routine                  31 October 2017                      CUNMRZ(3)