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NAME
     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(
               LWORK )



     #include <sunperf.h>

     void dormrq(char side, char trans, int m, int n, int k, dou-
               ble  *da,  int  lda,  double *tau, double *dc, int
               ldc, int *info) ;

PURPOSE
     DORMRQ 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 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
               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 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,  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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