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



NAME
       CUNMTR

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



PURPOSE
            CUNMTR 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 CHETRD:

            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 triangle of A contains elementary reflectors
                            from CHETRD;
                     = 'L': Lower triangle of A contains elementary reflectors
                            from CHETRD.

           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.

           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 CHETRD.

           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 CHETRD.

           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                      CUNMTR(3)