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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 )



     #include <sunperf.h>

     void dormhr(char side, char trans, int m, int  n,  int  ilo,
               int  ihi, double *da, int lda, double *tau, double
               *dc,
                int ldc, int *info) ;

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  subma-
               trix  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,  dimen-
               sion (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 ille-
               gal value

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