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

SYNOPSIS
     SUBROUTINE DORMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU,  C,
               LDC, WORK, LWORK, INFO )

     CHARACTER SIDE, TRANS, UPLO

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

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



     #include <sunperf.h>

     void dormtr(char side, char uplo, char trans, int m, int  n,
               double  *da, int lda, double *tau, double *dc, int
               ldc, int *info) ;

PURPOSE
     DORMTR 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 of order nq, with nq = m
     if  SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the
     product  of  nq-1  elementary  reflectors,  as  returned  by
     DSYTRD:

     if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);

     if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).


ARGUMENTS
     SIDE      (input) CHARACTER*1
               = 'L': apply Q or Q**T from the Left;
               = 'R': apply Q or Q**T from the Right.

     UPLO      (input) CHARACTER*1
               = 'U': Upper triangle  of  A  contains  elementary
               reflectors from DSYTRD; = 'L': Lower triangle of A
               contains elementary reflectors from DSYTRD.

     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.

     A         (input) DOUBLE PRECISION array, dimension
               (LDA,M) if SIDE = 'L' (LDA,N) if SIDE  =  'R'  The
               vectors which define the elementary reflectors, as
               returned by DSYTRD.

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

     TAU       (input) DOUBLE PRECISION array, dimension
               (M-1) if SIDE = 'L' (N-1) if  SIDE  =  'R'  TAU(i)
               must  contain  the scalar factor of the elementary
               reflector H(i), as returned by DSYTRD.

     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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