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


SYNOPSIS

       SUBROUTINE DORMQR( 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

       DORMQR 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 DGEQRF. 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,K)
               The i-th column  must  contain  the  vector  which
               defines  the  elementary  reflector  H(i), for i =
               1,2,...,k, as returned by DGEQRF in  the  first  k
               columns of its array argument A.  A is modified by


       LDA     (input) INTEGER
               The leading dimension of the array A.  If  SIDE  =
               'L',  LDA  >=  max(1,M);  if  SIDE  =  'R', LDA >=
               max(1,N).

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

       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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