PRACE NPT

      SUBROUTINE DGEMM ( TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB,

     $                   BETA, C, LDC )

      Use numerics

*     .. Scalar Arguments ..

      CHARACTER*1        TRANSA, TRANSB

      INTEGER            M, N, K, LDA, LDB, LDC

      Real(l_)   ALPHA, BETA

*     .. Array Arguments ..

      Real(l_)   A( LDA, * ), B( LDB, * ), C( LDC, * )

*     ..

*

*  Purpose

*  =======

*

*  DGEMM  performs one of the matrix-matrix operations

*

*     C := alpha*op( A )*op( B ) + beta*C,

*

*  where  op( X ) is one of

*

*     op( X ) = X   or   op( X ) = X',

*

*  alpha and beta are scalars, and A, B and C are matrices, with op( A )

*  an m by k matrix,  op( B )  a  k by n matrix and  C an m by n matrix.

*

*  Parameters

*  ==========

*

*  TRANSA - CHARACTER*1.

*           On entry, TRANSA specifies the form of op( A ) to be used in

*           the matrix multiplication as follows:

*

*              TRANSA = 'N' or 'n',  op( A ) = A.

*

*              TRANSA = 'T' or 't',  op( A ) = A'.

*

*              TRANSA = 'C' or 'c',  op( A ) = A'.

*

*           Unchanged on exit.

*

*  TRANSB - CHARACTER*1.

*           On entry, TRANSB specifies the form of op( B ) to be used in

*           the matrix multiplication as follows:

*

*              TRANSB = 'N' or 'n',  op( B ) = B.

*

*              TRANSB = 'T' or 't',  op( B ) = B'.

*

*              TRANSB = 'C' or 'c',  op( B ) = B'.

*

*           Unchanged on exit.

*

*  M      - INTEGER.

*           On entry,  M  specifies  the number  of rows  of the  matrix

*           op( A )  and of the  matrix  C.  M  must  be at least  zero.

*           Unchanged on exit.

*

*  N      - INTEGER.

*           On entry,  N  specifies the number  of columns of the matrix

*           op( B ) and the number of columns of the matrix C. N must be

*           at least zero.

*           Unchanged on exit.

*

*  K      - INTEGER.

*           On entry,  K  specifies  the number of columns of the matrix

*           op( A ) and the number of rows of the matrix op( B ). K must

*           be at least  zero.

*           Unchanged on exit.

*

*  ALPHA  - DOUBLE PRECISION.

*           On entry, ALPHA specifies the scalar alpha.

*           Unchanged on exit.

*

*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is

*           k  when  TRANSA = 'N' or 'n',  and is  m  otherwise.

*           Before entry with  TRANSA = 'N' or 'n',  the leading  m by k

*           part of the array  A  must contain the matrix  A,  otherwise

*           the leading  k by m  part of the array  A  must contain  the

*           matrix A.

*           Unchanged on exit.

*

*  LDA    - INTEGER.

*           On entry, LDA specifies the first dimension of A as declared

*           in the calling (sub) program. When  TRANSA = 'N' or 'n' then

*           LDA must be at least  max( 1, m ), otherwise  LDA must be at

*           least  max( 1, k ).

*           Unchanged on exit.

*

*  B      - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is

*           n  when  TRANSB = 'N' or 'n',  and is  k  otherwise.

*           Before entry with  TRANSB = 'N' or 'n',  the leading  k by n

*           part of the array  B  must contain the matrix  B,  otherwise

*           the leading  n by k  part of the array  B  must contain  the

*           matrix B.

*           Unchanged on exit.

*

*  LDB    - INTEGER.

*           On entry, LDB specifies the first dimension of B as declared

*           in the calling (sub) program. When  TRANSB = 'N' or 'n' then

*           LDB must be at least  max( 1, k ), otherwise  LDB must be at

*           least  max( 1, n ).

*           Unchanged on exit.

*

*  BETA   - DOUBLE PRECISION.

*           On entry,  BETA  specifies the scalar  beta.  When  BETA  is

*           supplied as zero then C need not be set on input.

*           Unchanged on exit.

*

*  C      - DOUBLE PRECISION array of DIMENSION ( LDC, n ).

*           Before entry, the leading  m by n  part of the array  C must

*           contain the matrix  C,  except when  beta  is zero, in which

*           case C need not be set on entry.

*           On exit, the array  C  is overwritten by the  m by n  matrix

*           ( alpha*op( A )*op( B ) + beta*C ).

*

*  LDC    - INTEGER.

*           On entry, LDC specifies the first dimension of C as declared

*           in  the  calling  (sub)  program.   LDC  must  be  at  least

*           max( 1, m ).

*           Unchanged on exit.

*

*

*  Level 3 Blas routine.

*

*  -- Written on 8-February-1989.

*     Jack Dongarra, Argonne National Laboratory.

*     Iain Duff, AERE Harwell.

*     Jeremy Du Croz, Numerical Algorithms Group Ltd.

*     Sven Hammarling, Numerical Algorithms Group Ltd.

*

*

*     .. External Functions ..

      LOGICAL            LSAME

      EXTERNAL           LSAME

*     .. External Subroutines ..

      EXTERNAL           XERBLA

*     .. Intrinsic Functions ..

      INTRINSIC          MAX

*     .. Local Scalars ..

      LOGICAL            NOTA, NOTB

      INTEGER            I, INFO, J, L, NCOLA, NROWA, NROWB

      Real(l_)   TEMP

*     .. Parameters ..

      Real(l_)   ONE         , ZERO

      PARAMETER( ONE = 1.0_l_, ZERO = 0.0_l_ )

*     ..

*     .. Executable Statements ..

*

*     Set  NOTA  and  NOTB  as  true if  A  and  B  respectively are not

*     transposed and set  NROWA, NCOLA and  NROWB  as the number of rows

*     and  columns of  A  and the  number of  rows  of  B  respectively.

*

      NOTA  = LSAME( TRANSA, 'N' )

      NOTB  = LSAME( TRANSB, 'N' )

      IF( NOTA )THEN

         NROWA = M

         NCOLA = K

      ELSE

         NROWA = K

         NCOLA = M

      END IF

      IF( NOTB )THEN

         NROWB = K

      ELSE

         NROWB = N

      END IF

*

*     Test the input parameters.

*

      INFO = 0

      IF(      ( .NOT.NOTA                 ).AND.

     $         ( .NOT.LSAME( TRANSA, 'C' ) ).AND.

     $         ( .NOT.LSAME( TRANSA, 'T' ) )      )THEN

         INFO = 1

      ELSE IF( ( .NOT.NOTB                 ).AND.

     $         ( .NOT.LSAME( TRANSB, 'C' ) ).AND.

     $         ( .NOT.LSAME( TRANSB, 'T' ) )      )THEN

         INFO = 2

      ELSE IF( M  .LT.0               )THEN

         INFO = 3

      ELSE IF( N  .LT.0               )THEN

         INFO = 4

      ELSE IF( K  .LT.0               )THEN

         INFO = 5

      ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN

         INFO = 8

      ELSE IF( LDB.LT.MAX( 1, NROWB ) )THEN

         INFO = 10

      ELSE IF( LDC.LT.MAX( 1, M     ) )THEN

         INFO = 13

      END IF

      IF( INFO.NE.0 )THEN

         CALL XERBLA( 'DGEMM ', INFO )

         RETURN

      END IF

*

*     Quick return if possible.

*

      IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.

     $    ( ( ( ALPHA.EQ.ZERO ).OR.( K.EQ.0 ) ).AND.( BETA.EQ.ONE ) ) )

     $   RETURN

*

*     And if  alpha.eq.zero.

*

      IF( ALPHA.EQ.ZERO )THEN

         IF( BETA.EQ.ZERO )THEN

!$omp parallel do

            DO 20, J = 1, N

               DO 10, I = 1, M

                  C( I, J ) = ZERO

   10          CONTINUE

   20       CONTINUE

         ELSE

!$omp parallel do

            DO 40, J = 1, N

               DO 30, I = 1, M

                  C( I, J ) = BETA*C( I, J )

   30          CONTINUE

   40       CONTINUE

         END IF

         RETURN

      END IF

*

*     Start the operations.

*

      IF( NOTB )THEN

         IF( NOTA )THEN

*

*           Form  C := alpha*A*B + beta*C.

*

!$omp parallel do private(temp)

            DO 90, J = 1, N

               IF( BETA.EQ.ZERO )THEN

                  DO 50, I = 1, M

                     C( I, J ) = ZERO

   50             CONTINUE

               ELSE IF( BETA.NE.ONE )THEN

                  DO 60, I = 1, M

                     C( I, J ) = BETA*C( I, J )

   60             CONTINUE

               END IF

               DO 80, L = 1, K

                  IF( B( L, J ).NE.ZERO )THEN

                     TEMP = ALPHA*B( L, J )

                     DO 70, I = 1, M

                        C( I, J ) = C( I, J ) + TEMP*A( I, L )

   70                CONTINUE

                  END IF

   80          CONTINUE

   90       CONTINUE

         ELSE

*

*           Form  C := alpha*A'*B + beta*C

*

!$omp parallel do private(temp)

            DO 120, J = 1, N

               DO 110, I = 1, M

                  TEMP = ZERO

                  DO 100, L = 1, K

                     TEMP = TEMP + A( L, I )*B( L, J )

  100             CONTINUE

                  IF( BETA.EQ.ZERO )THEN

                     C( I, J ) = ALPHA*TEMP

                  ELSE

                     C( I, J ) = ALPHA*TEMP + BETA*C( I, J )

                  END IF

  110          CONTINUE

  120       CONTINUE

         END IF

      ELSE

         IF( NOTA )THEN

*

*           Form  C := alpha*A*B' + beta*C

*

!$omp parallel do private(temp)

            DO 170, J = 1, N

               IF( BETA.EQ.ZERO )THEN

                  DO 130, I = 1, M

                     C( I, J ) = ZERO

  130             CONTINUE

               ELSE IF( BETA.NE.ONE )THEN

                  DO 140, I = 1, M

                     C( I, J ) = BETA*C( I, J )

  140             CONTINUE

               END IF

               DO 160, L = 1, K

                  IF( B( J, L ).NE.ZERO )THEN

                     TEMP = ALPHA*B( J, L )

                     DO 150, I = 1, M

                        C( I, J ) = C( I, J ) + TEMP*A( I, L )

  150                CONTINUE

                  END IF

  160          CONTINUE

  170       CONTINUE

         ELSE

*

*           Form  C := alpha*A'*B' + beta*C

*

!$omp parallel do private(temp)

            DO 200, J = 1, N

               DO 190, I = 1, M

                  TEMP = ZERO

                  DO 180, L = 1, K

                     TEMP = TEMP + A( L, I )*B( J, L )

  180             CONTINUE

                  IF( BETA.EQ.ZERO )THEN

                     C( I, J ) = ALPHA*TEMP

                  ELSE

                     C( I, J ) = ALPHA*TEMP + BETA*C( I, J )

                  END IF

  190          CONTINUE

  200       CONTINUE

         END IF

      END IF

*

      RETURN

*

*     End of DGEMM .

*

      END