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


SYNOPSIS

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

           CHARACTER      SIDE, TRANS

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

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


PURPOSE

       DORMRZ 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 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**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.

       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.
               If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >=  L
               >= 0.

               (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**H*C or C*Q**H 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.

               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    (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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