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


SYNOPSIS

       SUBROUTINE SOPMTR( SIDE, UPLO, TRANS, M, N,  AP,  TAU,  C,
                          LDC, WORK, INFO )

           CHARACTER      SIDE, TRANS, UPLO

           INTEGER        INFO, LDC, M, N

           REAL           AP( * ), C( LDC, * ), TAU( * ), WORK( *
                          )


PURPOSE

       SOPMTR 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
       SSPTRD using packed storage:

       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  triangular  packed storage used in
               previous call to SSPTRD; = 'L':  Lower  triangular
               packed storage used in previous call to SSPTRD.

       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.

       AP      (input) REAL array, dimension
               (M*(M+1)/2)  if  SIDE  = 'L' (N*(N+1)/2) if SIDE =
               'R'  The  vectors  which  define  the   elementary
               reflectors, as returned by SSPTRD.  AP is modified


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

       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) REAL array, dimension
               (N) if SIDE = 'L' (M) if SIDE = 'R'

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille­
               gal value


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