SUBROUTINE DTRSMF ( 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

*  =======

*

*  DTRSM  solves one of the matrix equations

*

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

*

*  where alpha is a scalar, X and B are m by n matrices, 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'.

*

*  The matrix X is overwritten on B.

*

*  Parameters

*  ==========

*

*  SIDE   - CHARACTER*1.

*           On entry, SIDE specifies whether op( A ) appears on the left

*           or right of X as follows:

*

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

*

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

*

*           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  right-hand  side  matrix  B,  and  on exit  is

*           overwritten by the solution matrix  X.

*

*  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( 'DTRSM ', 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*inv( A )*B.

*

            IF( UPPER )THEN

               DO 60, J = 1, N

                  IF( ALPHA.NE.ONE )THEN

                     DO 30, I = 1, M

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

   30                CONTINUE

                  END IF

                  DO 50, K = M, 1, -1

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

                        IF( NOUNIT )

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

                        DO 40, I = 1, K - 1

                           B( I, J ) = B( I, J ) - B( K, J )*A( I, K )

   40                   CONTINUE

                     END IF

   50             CONTINUE

   60          CONTINUE

            ELSE

               DO 100, J = 1, N

                  IF( ALPHA.NE.ONE )THEN

                     DO 70, I = 1, M

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

   70                CONTINUE

                  END IF

                  DO 90 K = 1, M

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

                        IF( NOUNIT )

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

                        DO 80, I = K + 1, M

                           B( I, J ) = B( I, J ) - B( K, J )*A( I, K )

   80                   CONTINUE

                     END IF

   90             CONTINUE

  100          CONTINUE

            END IF

         ELSE

*

*           Form  B := alpha*inv( A' )*B.

*

            IF( UPPER )THEN

               DO 130, J = 1, N

                  DO 120, I = 1, M

                     TEMP = ALPHA*B( I, J )

                     DO 110, K = 1, I - 1

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

  110                CONTINUE

                     IF( NOUNIT )

     $                  TEMP = TEMP/A( I, I )

                     B( I, J ) = TEMP

  120             CONTINUE

  130          CONTINUE

            ELSE

               DO 160, J = 1, N

                  DO 150, I = M, 1, -1

                     TEMP = ALPHA*B( I, J )

                     DO 140, K = I + 1, M

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

  140                CONTINUE

                     IF( NOUNIT )

     $                  TEMP = TEMP/A( I, I )

                     B( I, J ) = TEMP

  150             CONTINUE

  160          CONTINUE

            END IF

         END IF

      ELSE

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

*

*           Form  B := alpha*B*inv( A ).

*

            IF( UPPER )THEN

               DO 210, J = 1, N

                  IF( ALPHA.NE.ONE )THEN

                     DO 170, I = 1, M

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

  170                CONTINUE

                  END IF

                  DO 190, K = 1, J - 1

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

                        DO 180, I = 1, M

                           B( I, J ) = B( I, J ) - A( K, J )*B( I, K )

  180                   CONTINUE

                     END IF

  190             CONTINUE

                  IF( NOUNIT )THEN

                     TEMP = ONE/A( J, J )

                     DO 200, I = 1, M

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

  200                CONTINUE

                  END IF

  210          CONTINUE

            ELSE

               DO 260, J = N, 1, -1

                  IF( ALPHA.NE.ONE )THEN

                     DO 220, I = 1, M

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

  220                CONTINUE

                  END IF

                  DO 240, K = J + 1, N

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

                        DO 230, I = 1, M

                           B( I, J ) = B( I, J ) - A( K, J )*B( I, K )

  230                   CONTINUE

                     END IF

  240             CONTINUE

                  IF( NOUNIT )THEN

                     TEMP = ONE/A( J, J )

                     DO 250, I = 1, M

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

  250                CONTINUE

                  END IF

  260          CONTINUE

            END IF

         ELSE

*

*           Form  B := alpha*B*inv( A' ).

*

            IF( UPPER )THEN

               DO 310, K = N, 1, -1

                  IF( NOUNIT )THEN

                     TEMP = ONE/A( K, K )

                     DO 270, I = 1, M

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

  270                CONTINUE

                  END IF

                  DO 290, J = 1, K - 1

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

                        TEMP = A( J, K )

                        DO 280, I = 1, M

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

  280                   CONTINUE

                     END IF

  290             CONTINUE

                  IF( ALPHA.NE.ONE )THEN

                     DO 300, I = 1, M

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

  300                CONTINUE

                  END IF

  310          CONTINUE

            ELSE

               DO 360, K = 1, N

                  IF( NOUNIT )THEN

                     TEMP = ONE/A( K, K )

                     DO 320, I = 1, M

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

  320                CONTINUE

                  END IF

                  DO 340, J = K + 1, N

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

                        TEMP = A( J, K )

                        DO 330, I = 1, M

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

  330                   CONTINUE

                     END IF

  340             CONTINUE

                  IF( ALPHA.NE.ONE )THEN

                     DO 350, I = 1, M

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

  350                CONTINUE

                  END IF

  360          CONTINUE

            END IF

         END IF

      END IF

*

      RETURN

*

*     End of DTRSM .

*

      END