SUBROUTINE DTRMMF ( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA,

     $                   B, LDB )

*     .. Scalar Arguments ..

      CHARACTER*1        SIDE, UPLO, TRANSA, DIAG

      INTEGER            M, N, LDA, LDB

      DOUBLE PRECISION   ALPHA

*     .. Array Arguments ..

      DOUBLE PRECISION   A( LDA, * ), B( LDB, * )

*     ..

*

*  Purpose

*  =======

*

*  DTRMM  performs one of the matrix-matrix operations

*

*     B := alpha*op( A )*B,   or   B := alpha*B*op( A ),

*

*  where  alpha  is a scalar,  B  is an m by n matrix,  A  is a unit, or

*  non-unit,  upper or lower triangular matrix  and  op( A )  is one  of

*

*     op( A ) = A   or   op( A ) = A'.

*

*  Parameters

*  ==========

*

*  SIDE   - CHARACTER*1.

*           On entry,  SIDE specifies whether  op( A ) multiplies B from

*           the left or right as follows:

*

*              SIDE = 'L' or 'l'   B := alpha*op( A )*B.

*

*              SIDE = 'R' or 'r'   B := alpha*B*op( A ).

*

*           Unchanged on exit.

*

*  UPLO   - CHARACTER*1.

*           On entry, UPLO specifies whether the matrix A is an upper or

*           lower triangular matrix as follows:

*

*              UPLO = 'U' or 'u'   A is an upper triangular matrix.

*

*              UPLO = 'L' or 'l'   A is a lower triangular matrix.

*

*           Unchanged on exit.

*

*  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.

*

*  DIAG   - CHARACTER*1.

*           On entry, DIAG specifies whether or not A is unit triangular

*           as follows:

*

*              DIAG = 'U' or 'u'   A is assumed to be unit triangular.

*

*              DIAG = 'N' or 'n'   A is not assumed to be unit

*                                  triangular.

*

*           Unchanged on exit.

*

*  M      - INTEGER.

*           On entry, M specifies the number of rows of B. M must be at

*           least zero.

*           Unchanged on exit.

*

*  N      - INTEGER.

*           On entry, N specifies the number of columns of B.  N must be

*           at least zero.

*           Unchanged on exit.

*

*  ALPHA  - DOUBLE PRECISION.

*           On entry,  ALPHA specifies the scalar  alpha. When  alpha is

*           zero then  A is not referenced and  B need not be set before

*           entry.

*           Unchanged on exit.

*

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

*           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'.

*           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k

*           upper triangular part of the array  A must contain the upper

*           triangular matrix  and the strictly lower triangular part of

*           A is not referenced.

*           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k

*           lower triangular part of the array  A must contain the lower

*           triangular matrix  and the strictly upper triangular part of

*           A is not referenced.

*           Note that when  DIAG = 'U' or 'u',  the diagonal elements of

*           A  are not referenced either,  but are assumed to be  unity.

*           Unchanged on exit.

*

*  LDA    - INTEGER.

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

*           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then

*           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r'

*           then LDA must be at least max( 1, n ).

*           Unchanged on exit.

*

*  B      - DOUBLE PRECISION array of DIMENSION ( LDB, n ).

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

*           contain the matrix  B,  and  on exit  is overwritten  by the

*           transformed matrix.

*

*  LDB    - INTEGER.

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

*           in  the  calling  (sub)  program.   LDB  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            LSIDE, NOUNIT, UPPER

      INTEGER            I, INFO, J, K, NROWA

      DOUBLE PRECISION   TEMP

*     .. Parameters ..

      DOUBLE PRECISION   ONE         , ZERO

      PARAMETER        ( ONE = 1.0D+0, ZERO = 0.0D+0 )

*     ..

*     .. Executable Statements ..

*

*     Test the input parameters.

*

      LSIDE  = LSAME( SIDE  , 'L' )

      IF( LSIDE )THEN

         NROWA = M

      ELSE

         NROWA = N

      END IF

      NOUNIT = LSAME( DIAG  , 'N' )

      UPPER  = LSAME( UPLO  , 'U' )

*

      INFO   = 0

      IF(      ( .NOT.LSIDE                ).AND.

     $         ( .NOT.LSAME( SIDE  , 'R' ) )      )THEN

         INFO = 1

      ELSE IF( ( .NOT.UPPER                ).AND.

     $         ( .NOT.LSAME( UPLO  , 'L' ) )      )THEN

         INFO = 2

      ELSE IF( ( .NOT.LSAME( TRANSA, 'N' ) ).AND.

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

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

         INFO = 3

      ELSE IF( ( .NOT.LSAME( DIAG  , 'U' ) ).AND.

     $         ( .NOT.LSAME( DIAG  , 'N' ) )      )THEN

         INFO = 4

      ELSE IF( M  .LT.0               )THEN

         INFO = 5

      ELSE IF( N  .LT.0               )THEN

         INFO = 6

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

         INFO = 9

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

         INFO = 11

      END IF

      IF( INFO.NE.0 )THEN

         CALL XERBLA( 'DTRMM ', INFO )

         RETURN

      END IF

*

*     Quick return if possible.

*

      IF( N.EQ.0 )

     $   RETURN

*

*     And when  alpha.eq.zero.

*

      IF( ALPHA.EQ.ZERO )THEN

         DO 20, J = 1, N

            DO 10, I = 1, M

               B( I, J ) = ZERO

   10       CONTINUE

   20    CONTINUE

         RETURN

      END IF

*

*     Start the operations.

*

      IF( LSIDE )THEN

         IF( LSAME( TRANSA, 'N' ) )THEN

*

*           Form  B := alpha*A*B.

*

            IF( UPPER )THEN

               DO 50, J = 1, N

                  DO 40, K = 1, M

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

                        TEMP = ALPHA*B( K, J )

                        DO 30, I = 1, K - 1

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

   30                   CONTINUE

                        IF( NOUNIT )

     $                     TEMP = TEMP*A( K, K )

                        B( K, J ) = TEMP

                     END IF

   40             CONTINUE

   50          CONTINUE

            ELSE

               DO 80, J = 1, N

                  DO 70 K = M, 1, -1

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

                        TEMP      = ALPHA*B( K, J )

                        B( K, J ) = TEMP

                        IF( NOUNIT )

     $                     B( K, J ) = B( K, J )*A( K, K )

                        DO 60, I = K + 1, M

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

   60                   CONTINUE

                     END IF

   70             CONTINUE

   80          CONTINUE

            END IF

         ELSE

*

*           Form  B := alpha*A'*B.

*

            IF( UPPER )THEN

               DO 110, J = 1, N

                  DO 100, I = M, 1, -1

                     TEMP = B( I, J )

                     IF( NOUNIT )

     $                  TEMP = TEMP*A( I, I )

                     DO 90, K = 1, I - 1

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

   90                CONTINUE

                     B( I, J ) = ALPHA*TEMP

  100             CONTINUE

  110          CONTINUE

            ELSE

               DO 140, J = 1, N

                  DO 130, I = 1, M

                     TEMP = B( I, J )

                     IF( NOUNIT )

     $                  TEMP = TEMP*A( I, I )

                     DO 120, K = I + 1, M

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

  120                CONTINUE

                     B( I, J ) = ALPHA*TEMP

  130             CONTINUE

  140          CONTINUE

            END IF

         END IF

      ELSE

         IF( LSAME( TRANSA, 'N' ) )THEN

*

*           Form  B := alpha*B*A.

*

            IF( UPPER )THEN

               DO 180, J = N, 1, -1

                  TEMP = ALPHA

                  IF( NOUNIT )

     $               TEMP = TEMP*A( J, J )

                  DO 150, I = 1, M

                     B( I, J ) = TEMP*B( I, J )

  150             CONTINUE

                  DO 170, K = 1, J - 1

                     IF( A( K, J ).NE.ZERO )THEN

                        TEMP = ALPHA*A( K, J )

                        DO 160, I = 1, M

                           B( I, J ) = B( I, J ) + TEMP*B( I, K )

  160                   CONTINUE

                     END IF

  170             CONTINUE

  180          CONTINUE

            ELSE

               DO 220, J = 1, N

                  TEMP = ALPHA

                  IF( NOUNIT )

     $               TEMP = TEMP*A( J, J )

                  DO 190, I = 1, M

                     B( I, J ) = TEMP*B( I, J )

  190             CONTINUE

                  DO 210, K = J + 1, N

                     IF( A( K, J ).NE.ZERO )THEN

                        TEMP = ALPHA*A( K, J )

                        DO 200, I = 1, M

                           B( I, J ) = B( I, J ) + TEMP*B( I, K )

  200                   CONTINUE

                     END IF

  210             CONTINUE

  220          CONTINUE

            END IF

         ELSE

*

*           Form  B := alpha*B*A'.

*

            IF( UPPER )THEN

               DO 260, K = 1, N

                  DO 240, J = 1, K - 1

                     IF( A( J, K ).NE.ZERO )THEN

                        TEMP = ALPHA*A( J, K )

                        DO 230, I = 1, M

                           B( I, J ) = B( I, J ) + TEMP*B( I, K )

  230                   CONTINUE

                     END IF

  240             CONTINUE

                  TEMP = ALPHA

                  IF( NOUNIT )

     $               TEMP = TEMP*A( K, K )

                  IF( TEMP.NE.ONE )THEN

                     DO 250, I = 1, M

                        B( I, K ) = TEMP*B( I, K )

  250                CONTINUE

                  END IF

  260          CONTINUE

            ELSE

               DO 300, K = N, 1, -1

                  DO 280, J = K + 1, N

                     IF( A( J, K ).NE.ZERO )THEN

                        TEMP = ALPHA*A( J, K )

                        DO 270, I = 1, M

                           B( I, J ) = B( I, J ) + TEMP*B( I, K )

  270                   CONTINUE

                     END IF

  280             CONTINUE

                  TEMP = ALPHA

                  IF( NOUNIT )

     $               TEMP = TEMP*A( K, K )

                  IF( TEMP.NE.ONE )THEN

                     DO 290, I = 1, M

                        B( I, K ) = TEMP*B( I, K )

  290                CONTINUE

                  END IF

  300          CONTINUE

            END IF

         END IF

      END IF

*

      RETURN

*

*     End of DTRMM .

*

      END