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



NAME
       CUNMHR

SYNOPSIS
       SUBROUTINE CUNMHR (SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, LDC,
           WORK, LWORK, INFO)



PURPOSE
            CUNMHR 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
            IHI-ILO elementary reflectors, as returned by CGEHRD:

            Q = H(ilo) H(ilo+1) . . . H(ihi-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.

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

           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.

           ILO       (input)
                     ILO is INTEGER

           IHI       (input)
                     IHI is INTEGER

                     ILO and IHI must have the same values as in the previous call
                     of CGEHRD. Q is equal to the unit matrix except in the
                     submatrix Q(ilo+1:ihi,ilo+1:ihi).
                     If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and
                     ILO = 1 and IHI = 0, if M = 0;
                     if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and
                     ILO = 1 and IHI = 0, if N = 0.

           A         (input)
                     A is COMPLEX array, dimension
                                          (LDA,M) if SIDE = 'L'
                                          (LDA,N) if SIDE = 'R'
                     The vectors which define the elementary reflectors, as
                     returned by CGEHRD.

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

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

           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                      CUNMHR(3)