DORMR3  -  overwrite the general real m by n matrix C with
       Q * C if SIDE = 'L' and TRANS = 'N', or  Q'* C if  SIDE  =
       'L'  and  TRANS = 'T', or  C * Q if SIDE = 'R' and TRANS =
       'N', or  C * Q' if SIDE = 'R' and TRANS = 'T',


SYNOPSIS

       SUBROUTINE DORMR3( SIDE, TRANS, M, N, K, L, A,  LDA,  TAU,
                          C, LDC, WORK, INFO )

           CHARACTER      SIDE, TRANS

           INTEGER        INFO, K, L, LDA, LDC, M, N

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


PURPOSE

       DORMR3 overwrites the general real m by n matrix C with  Q
       *  C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L'
       and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS  =  'N',
       or C * Q' if SIDE = 'R' and TRANS = 'T', where Q is a real
       orthogonal matrix defined as the product of  k  elementary
       reflectors

             Q = H(1) H(2) . . . H(k)

       as  returned  by DTZRZF. Q is of order m if SIDE = 'L' and
       of order n if SIDE = 'R'.


ARGUMENTS

       SIDE    (input) CHARACTER*1
               = 'L': apply Q or Q' from the Left
               = 'R': apply Q or Q' from the Right

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

       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.

       K       (input) INTEGER
               The number of elementary reflectors whose  product
               defines the matrix Q.  If SIDE = 'L', M >= K >= 0;
               if SIDE = 'R', N >= K >= 0.

       L       (input) INTEGER
               The number of columns of the matrix  A  containing
               the meaningful part of the Householder reflectors.

               >= 0.

       A       (input) DOUBLE PRECISION array, dimension
               (LDA,M)  if  SIDE = 'L', (LDA,N) if SIDE = 'R' The
               i-th row must contain the vector which defines the
               elementary  reflector  H(i), for i = 1,2,...,k, as
               returned by DTZRZF in the last k rows of its array
               argument  A.   A  is  modified  by the routine but
               restored on exit.

       LDA     (input) INTEGER
               The leading dimension  of  the  array  A.  LDA  >=
               max(1,K).

       TAU     (input) DOUBLE PRECISION array, dimension (K)
               TAU(i)  must contain the scalar factor of the ele­
               mentary reflector H(i), as returned by DTZRZF.

       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'*C or C*Q' or C*Q.

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

       WORK    (workspace) DOUBLE PRECISION array, dimension
               (N) if SIDE = 'L', (M) if SIDE = 'R'

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


FURTHER DETAILS

       Based on contributions by
         A. Petitet, Computer  Science  Dept.,  Univ.  of  Tenn.,
       Knoxville, USA


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