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( * )


PURPOSE

       DORMTR 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 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.

               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,
               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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