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dormhr

 NAME
      DORMHR - overwrite the general real M-by-N matrix C with
      SIDE = 'L' SIDE = 'R' TRANS = 'N'

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

          CHARACTER      SIDE, TRANS

          INTEGER        IHI, ILO, INFO, LDA, LDC, LWORK, M, N

          DOUBLE         PRECISION A( LDA, * ), C( LDC, * ), TAU(
                         * ), WORK( LWORK )

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

 ARGUMENTS
      SIDE    (input) CHARACTER*1
              = 'L': apply Q or Q**T from the Left;
              = 'R': apply Q or Q**T from the Right.

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

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

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

      ILO     (input) INTEGER
              IHI     (input) 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', 1 <= ILO and
              min(M,ILO) <= IHI <= M; if SIDE = 'R', 1 <= ILO and
              min(N,ILO) <= IHI <= N;

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

      TAU     (input) DOUBLE PRECISION array, dimension
              (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i) must
              contain the scalar factor of the elementary reflec-
              tor H(i), as returned by DGEHRD.

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

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

      LWORK   (input) 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.

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