SUBROUTINE DTPSVF( UPLO, TRANS, DIAG, N, AP, X, INCX )

*     .. Scalar Arguments ..

      INTEGER            INCX, N

      CHARACTER*1        DIAG, TRANS, UPLO

*     .. Array Arguments ..

      DOUBLE PRECISION   AP( * ), X( * )

*     ..

*

*  Purpose

*  =======

*

*  DTPSV  solves one of the systems of equations

*

*     A*x = b,   or   A'*x = b,

*

*  where b and x are n element vectors and A is an n by n unit, or

*  non-unit, upper or lower triangular matrix, supplied in packed form.

*

*  No test for singularity or near-singularity is included in this

*  routine. Such tests must be performed before calling this routine.

*

*  Parameters

*  ==========

*

*  UPLO   - CHARACTER*1.

*           On entry, UPLO specifies whether the matrix 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.

*

*  TRANS  - CHARACTER*1.

*           On entry, TRANS specifies the equations to be solved as

*           follows:

*

*              TRANS = 'N' or 'n'   A*x = b.

*

*              TRANS = 'T' or 't'   A'*x = b.

*

*              TRANS = 'C' or 'c'   A'*x = b.

*

*           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.

*

*  N      - INTEGER.

*           On entry, N specifies the order of the matrix A.

*           N must be at least zero.

*           Unchanged on exit.

*

*  AP     - DOUBLE PRECISION array of DIMENSION at least

*           ( ( n*( n + 1 ) )/2 ).

*           Before entry with  UPLO = 'U' or 'u', the array AP must

*           contain the upper triangular matrix packed sequentially,

*           column by column, so that AP( 1 ) contains a( 1, 1 ),

*           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )

*           respectively, and so on.

*           Before entry with UPLO = 'L' or 'l', the array AP must

*           contain the lower triangular matrix packed sequentially,

*           column by column, so that AP( 1 ) contains a( 1, 1 ),

*           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )

*           respectively, and so on.

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

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

*           Unchanged on exit.

*

*  X      - DOUBLE PRECISION array of dimension at least

*           ( 1 + ( n - 1 )*abs( INCX ) ).

*           Before entry, the incremented array X must contain the n

*           element right-hand side vector b. On exit, X is overwritten

*           with the solution vector x.

*

*  INCX   - INTEGER.

*           On entry, INCX specifies the increment for the elements of

*           X. INCX must not be zero.

*           Unchanged on exit.

*

*

*  Level 2 Blas routine.

*

*  -- Written on 22-October-1986.

*     Jack Dongarra, Argonne National Lab.

*     Jeremy Du Croz, Nag Central Office.

*     Sven Hammarling, Nag Central Office.

*     Richard Hanson, Sandia National Labs.

*

*

*     .. Parameters ..

      DOUBLE PRECISION   ZERO

      PARAMETER        ( ZERO = 0.0D+0 )

*     .. Local Scalars ..

      DOUBLE PRECISION   TEMP

      INTEGER            I, INFO, IX, J, JX, K, KK, KX

      LOGICAL            NOUNIT

*     .. External Functions ..

      LOGICAL            LSAME

      EXTERNAL           LSAME

*     .. External Subroutines ..

      EXTERNAL           XERBLA

*     ..

*     .. Executable Statements ..

*

*     Test the input parameters.

*

      INFO = 0

      IF     ( .NOT.LSAME( UPLO , 'U' ).AND.

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

         INFO = 1

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

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

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

         INFO = 2

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

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

         INFO = 3

      ELSE IF( N.LT.0 )THEN

         INFO = 4

      ELSE IF( INCX.EQ.0 )THEN

         INFO = 7

      END IF

      IF( INFO.NE.0 )THEN

         CALL XERBLA( 'DTPSV ', INFO )

         RETURN

      END IF

*

*     Quick return if possible.

*

      IF( N.EQ.0 )

     $   RETURN

*

      NOUNIT = LSAME( DIAG, 'N' )

*

*     Set up the start point in X if the increment is not unity. This

*     will be  ( N - 1 )*INCX  too small for descending loops.

*

      IF( INCX.LE.0 )THEN

         KX = 1 - ( N - 1 )*INCX

      ELSE IF( INCX.NE.1 )THEN

         KX = 1

      END IF

*

*     Start the operations. In this version the elements of AP are

*     accessed sequentially with one pass through AP.

*

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

*

*        Form  x := inv( A )*x.

*

         IF( LSAME( UPLO, 'U' ) )THEN

            KK = ( N*( N + 1 ) )/2

            IF( INCX.EQ.1 )THEN

               DO 20, J = N, 1, -1

                  IF( X( J ).NE.ZERO )THEN

                     IF( NOUNIT )

     $                  X( J ) = X( J )/AP( KK )

                     TEMP = X( J )

                     K    = KK     - 1

                     DO 10, I = J - 1, 1, -1

                        X( I ) = X( I ) - TEMP*AP( K )

                        K      = K      - 1

   10                CONTINUE

                  END IF

                  KK = KK - J

   20          CONTINUE

            ELSE

               JX = KX + ( N - 1 )*INCX

               DO 40, J = N, 1, -1

                  IF( X( JX ).NE.ZERO )THEN

                     IF( NOUNIT )

     $                  X( JX ) = X( JX )/AP( KK )

                     TEMP = X( JX )

                     IX   = JX

                     DO 30, K = KK - 1, KK - J + 1, -1

                        IX      = IX      - INCX

                        X( IX ) = X( IX ) - TEMP*AP( K )

   30                CONTINUE

                  END IF

                  JX = JX - INCX

                  KK = KK - J

   40          CONTINUE

            END IF

         ELSE

            KK = 1

            IF( INCX.EQ.1 )THEN

               DO 60, J = 1, N

                  IF( X( J ).NE.ZERO )THEN

                     IF( NOUNIT )

     $                  X( J ) = X( J )/AP( KK )

                     TEMP = X( J )

                     K    = KK     + 1

                     DO 50, I = J + 1, N

                        X( I ) = X( I ) - TEMP*AP( K )

                        K      = K      + 1

   50                CONTINUE

                  END IF

                  KK = KK + ( N - J + 1 )

   60          CONTINUE

            ELSE

               JX = KX

               DO 80, J = 1, N

                  IF( X( JX ).NE.ZERO )THEN

                     IF( NOUNIT )

     $                  X( JX ) = X( JX )/AP( KK )

                     TEMP = X( JX )

                     IX   = JX

                     DO 70, K = KK + 1, KK + N - J

                        IX      = IX      + INCX

                        X( IX ) = X( IX ) - TEMP*AP( K )

   70                CONTINUE

                  END IF

                  JX = JX + INCX

                  KK = KK + ( N - J + 1 )

   80          CONTINUE

            END IF

         END IF

      ELSE

*

*        Form  x := inv( A' )*x.

*

         IF( LSAME( UPLO, 'U' ) )THEN

            KK = 1

            IF( INCX.EQ.1 )THEN

               DO 100, J = 1, N

                  TEMP = X( J )

                  K    = KK

                  DO 90, I = 1, J - 1

                     TEMP = TEMP - AP( K )*X( I )

                     K    = K    + 1

   90             CONTINUE

                  IF( NOUNIT )

     $               TEMP = TEMP/AP( KK + J - 1 )

                  X( J ) = TEMP

                  KK     = KK   + J

  100          CONTINUE

            ELSE

               JX = KX

               DO 120, J = 1, N

                  TEMP = X( JX )

                  IX   = KX

                  DO 110, K = KK, KK + J - 2

                     TEMP = TEMP - AP( K )*X( IX )

                     IX   = IX   + INCX

  110             CONTINUE

                  IF( NOUNIT )

     $               TEMP = TEMP/AP( KK + J - 1 )

                  X( JX ) = TEMP

                  JX      = JX   + INCX

                  KK      = KK   + J

  120          CONTINUE

            END IF

         ELSE

            KK = ( N*( N + 1 ) )/2

            IF( INCX.EQ.1 )THEN

               DO 140, J = N, 1, -1

                  TEMP = X( J )

                  K = KK

                  DO 130, I = N, J + 1, -1

                     TEMP = TEMP - AP( K )*X( I )

                     K    = K    - 1

  130             CONTINUE

                  IF( NOUNIT )

     $               TEMP = TEMP/AP( KK - N + J )

                  X( J ) = TEMP

                  KK     = KK   - ( N - J + 1 )

  140          CONTINUE

            ELSE

               KX = KX + ( N - 1 )*INCX

               JX = KX

               DO 160, J = N, 1, -1

                  TEMP = X( JX )

                  IX   = KX

                  DO 150, K = KK, KK - ( N - ( J + 1 ) ), -1

                     TEMP = TEMP - AP( K )*X( IX )

                     IX   = IX   - INCX

  150             CONTINUE

                  IF( NOUNIT )

     $               TEMP = TEMP/AP( KK - N + J )

                  X( JX ) = TEMP

                  JX      = JX   - INCX

                  KK      = KK   - (N - J + 1 )

  160          CONTINUE

            END IF

         END IF

      END IF

*

      RETURN

*

*     End of DTPSV .

*

      END