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


SYNOPSIS

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

           CHARACTER      SIDE, TRANS

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

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


PURPOSE

       DORMRQ 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 DGERQF. 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.

       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 DGERQF in the last k rows of its array

               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 DGERQF.

       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.

               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


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