dormhr(3F)

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',
             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) 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 reflector 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/output) 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