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


SYNOPSIS

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

           CHARACTER      SIDE, TRANS, UPLO

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

           REAL           A(  LDA,  *  ),  C( LDC, * ), TAU( * ),
                          WORK( * )


PURPOSE

       SORMTR 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
       SSYTRD:

       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 SSYTRD; = 'L': Lower triangle of A
               contains elementary reflectors from SSYTRD.

       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) REAL array, dimension
               (LDA,M)  if  SIDE  = 'L' (LDA,N) if SIDE = 'R' The
               vectors which define the elementary reflectors, as
               returned by SSYTRD.

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

       TAU     (input) REAL 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 SSYTRD.

       C       (input/output) REAL 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) REAL 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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