NAME

       dormhr.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dormhr (SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
           DORMHR

Function/Subroutine Documentation

   subroutine dormhr (character SIDE, character TRANS, integer M, integer N, integer ILO, integer
       IHI, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( *
       ) TAU, double precision, dimension( ldc, * ) C, integer LDC, double precision, dimension(
       * ) WORK, integer LWORK, integer INFO)
       DORMHR

       Purpose:

            DORMHR overwrites the general real M-by-N matrix C with

                            SIDE = 'L'     SIDE = 'R'
            TRANS = 'N':      Q * C          C * Q
            TRANS = 'T':      Q**T * C       C * Q**T

            where Q is a real orthogonal 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 DGEHRD:

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

       Parameters:
           SIDE

                     SIDE is CHARACTER*1
                     = 'L': apply Q or Q**T from the Left;
                     = 'R': apply Q or Q**T from the Right.

           TRANS

                     TRANS is CHARACTER*1
                     = 'N':  No transpose, apply Q;
                     = 'T':  Transpose, apply Q**T.

           M

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

           N

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

           ILO

                     ILO is INTEGER

           IHI

                     IHI is INTEGER

                     ILO and IHI must have the same values as in the previous call
                     of DGEHRD. 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

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

           LDA

                     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

                     TAU is DOUBLE PRECISION 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 DGEHRD.

           C

                     C is DOUBLE PRECISION array, dimension (LDC,N)
                     On entry, the M-by-N matrix C.
                     On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

           LDC

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

           WORK

                     WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     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

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

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

Author

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