kusano 2b45e8
      SUBROUTINE DTRSVF ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )
kusano 2b45e8
*     .. Scalar Arguments ..
kusano 2b45e8
      INTEGER            INCX, LDA, N
kusano 2b45e8
      CHARACTER*1        DIAG, TRANS, UPLO
kusano 2b45e8
*     .. Array Arguments ..
kusano 2b45e8
      DOUBLE PRECISION   A( LDA, * ), X( * )
kusano 2b45e8
*     ..
kusano 2b45e8
*
kusano 2b45e8
*  Purpose
kusano 2b45e8
*  =======
kusano 2b45e8
*
kusano 2b45e8
*  DTRSV  solves one of the systems of equations
kusano 2b45e8
*
kusano 2b45e8
*     A*x = b,   or   A'*x = b,
kusano 2b45e8
*
kusano 2b45e8
*  where b and x are n element vectors and A is an n by n unit, or
kusano 2b45e8
*  non-unit, upper or lower triangular matrix.
kusano 2b45e8
*
kusano 2b45e8
*  No test for singularity or near-singularity is included in this
kusano 2b45e8
*  routine. Such tests must be performed before calling this routine.
kusano 2b45e8
*
kusano 2b45e8
*  Parameters
kusano 2b45e8
*  ==========
kusano 2b45e8
*
kusano 2b45e8
*  UPLO   - CHARACTER*1.
kusano 2b45e8
*           On entry, UPLO specifies whether the matrix is an upper or
kusano 2b45e8
*           lower triangular matrix as follows:
kusano 2b45e8
*
kusano 2b45e8
*              UPLO = 'U' or 'u'   A is an upper triangular matrix.
kusano 2b45e8
*
kusano 2b45e8
*              UPLO = 'L' or 'l'   A is a lower triangular matrix.
kusano 2b45e8
*
kusano 2b45e8
*           Unchanged on exit.
kusano 2b45e8
*
kusano 2b45e8
*  TRANS  - CHARACTER*1.
kusano 2b45e8
*           On entry, TRANS specifies the equations to be solved as
kusano 2b45e8
*           follows:
kusano 2b45e8
*
kusano 2b45e8
*              TRANS = 'N' or 'n'   A*x = b.
kusano 2b45e8
*
kusano 2b45e8
*              TRANS = 'T' or 't'   A'*x = b.
kusano 2b45e8
*
kusano 2b45e8
*              TRANS = 'C' or 'c'   A'*x = b.
kusano 2b45e8
*
kusano 2b45e8
*           Unchanged on exit.
kusano 2b45e8
*
kusano 2b45e8
*  DIAG   - CHARACTER*1.
kusano 2b45e8
*           On entry, DIAG specifies whether or not A is unit
kusano 2b45e8
*           triangular as follows:
kusano 2b45e8
*
kusano 2b45e8
*              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
kusano 2b45e8
*
kusano 2b45e8
*              DIAG = 'N' or 'n'   A is not assumed to be unit
kusano 2b45e8
*                                  triangular.
kusano 2b45e8
*
kusano 2b45e8
*           Unchanged on exit.
kusano 2b45e8
*
kusano 2b45e8
*  N      - INTEGER.
kusano 2b45e8
*           On entry, N specifies the order of the matrix A.
kusano 2b45e8
*           N must be at least zero.
kusano 2b45e8
*           Unchanged on exit.
kusano 2b45e8
*
kusano 2b45e8
*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
kusano 2b45e8
*           Before entry with  UPLO = 'U' or 'u', the leading n by n
kusano 2b45e8
*           upper triangular part of the array A must contain the upper
kusano 2b45e8
*           triangular matrix and the strictly lower triangular part of
kusano 2b45e8
*           A is not referenced.
kusano 2b45e8
*           Before entry with UPLO = 'L' or 'l', the leading n by n
kusano 2b45e8
*           lower triangular part of the array A must contain the lower
kusano 2b45e8
*           triangular matrix and the strictly upper triangular part of
kusano 2b45e8
*           A is not referenced.
kusano 2b45e8
*           Note that when  DIAG = 'U' or 'u', the diagonal elements of
kusano 2b45e8
*           A are not referenced either, but are assumed to be unity.
kusano 2b45e8
*           Unchanged on exit.
kusano 2b45e8
*
kusano 2b45e8
*  LDA    - INTEGER.
kusano 2b45e8
*           On entry, LDA specifies the first dimension of A as declared
kusano 2b45e8
*           in the calling (sub) program. LDA must be at least
kusano 2b45e8
*           max( 1, n ).
kusano 2b45e8
*           Unchanged on exit.
kusano 2b45e8
*
kusano 2b45e8
*  X      - DOUBLE PRECISION array of dimension at least
kusano 2b45e8
*           ( 1 + ( n - 1 )*abs( INCX ) ).
kusano 2b45e8
*           Before entry, the incremented array X must contain the n
kusano 2b45e8
*           element right-hand side vector b. On exit, X is overwritten
kusano 2b45e8
*           with the solution vector x.
kusano 2b45e8
*
kusano 2b45e8
*  INCX   - INTEGER.
kusano 2b45e8
*           On entry, INCX specifies the increment for the elements of
kusano 2b45e8
*           X. INCX must not be zero.
kusano 2b45e8
*           Unchanged on exit.
kusano 2b45e8
*
kusano 2b45e8
*
kusano 2b45e8
*  Level 2 Blas routine.
kusano 2b45e8
*
kusano 2b45e8
*  -- Written on 22-October-1986.
kusano 2b45e8
*     Jack Dongarra, Argonne National Lab.
kusano 2b45e8
*     Jeremy Du Croz, Nag Central Office.
kusano 2b45e8
*     Sven Hammarling, Nag Central Office.
kusano 2b45e8
*     Richard Hanson, Sandia National Labs.
kusano 2b45e8
*
kusano 2b45e8
*
kusano 2b45e8
*     .. Parameters ..
kusano 2b45e8
      DOUBLE PRECISION   ZERO
kusano 2b45e8
      PARAMETER        ( ZERO = 0.0D+0 )
kusano 2b45e8
*     .. Local Scalars ..
kusano 2b45e8
      DOUBLE PRECISION   TEMP
kusano 2b45e8
      INTEGER            I, INFO, IX, J, JX, KX
kusano 2b45e8
      LOGICAL            NOUNIT
kusano 2b45e8
*     .. External Functions ..
kusano 2b45e8
      LOGICAL            LSAME
kusano 2b45e8
      EXTERNAL           LSAME
kusano 2b45e8
*     .. External Subroutines ..
kusano 2b45e8
      EXTERNAL           XERBLA
kusano 2b45e8
*     .. Intrinsic Functions ..
kusano 2b45e8
      INTRINSIC          MAX
kusano 2b45e8
*     ..
kusano 2b45e8
*     .. Executable Statements ..
kusano 2b45e8
*
kusano 2b45e8
*     Test the input parameters.
kusano 2b45e8
*
kusano 2b45e8
      INFO = 0
kusano 2b45e8
      IF     ( .NOT.LSAME( UPLO , 'U' ).AND.
kusano 2b45e8
     $         .NOT.LSAME( UPLO , 'L' )      )THEN
kusano 2b45e8
         INFO = 1
kusano 2b45e8
      ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND.
kusano 2b45e8
     $         .NOT.LSAME( TRANS, 'T' ).AND.
kusano 2b45e8
     $         .NOT.LSAME( TRANS, 'C' )      )THEN
kusano 2b45e8
         INFO = 2
kusano 2b45e8
      ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND.
kusano 2b45e8
     $         .NOT.LSAME( DIAG , 'N' )      )THEN
kusano 2b45e8
         INFO = 3
kusano 2b45e8
      ELSE IF( N.LT.0 )THEN
kusano 2b45e8
         INFO = 4
kusano 2b45e8
      ELSE IF( LDA.LT.MAX( 1, N ) )THEN
kusano 2b45e8
         INFO = 6
kusano 2b45e8
      ELSE IF( INCX.EQ.0 )THEN
kusano 2b45e8
         INFO = 8
kusano 2b45e8
      END IF
kusano 2b45e8
      IF( INFO.NE.0 )THEN
kusano 2b45e8
         CALL XERBLA( 'DTRSV ', INFO )
kusano 2b45e8
         RETURN
kusano 2b45e8
      END IF
kusano 2b45e8
*
kusano 2b45e8
*     Quick return if possible.
kusano 2b45e8
*
kusano 2b45e8
      IF( N.EQ.0 )
kusano 2b45e8
     $   RETURN
kusano 2b45e8
*
kusano 2b45e8
      NOUNIT = LSAME( DIAG, 'N' )
kusano 2b45e8
*
kusano 2b45e8
*     Set up the start point in X if the increment is not unity. This
kusano 2b45e8
*     will be  ( N - 1 )*INCX  too small for descending loops.
kusano 2b45e8
*
kusano 2b45e8
      IF( INCX.LE.0 )THEN
kusano 2b45e8
         KX = 1 - ( N - 1 )*INCX
kusano 2b45e8
      ELSE IF( INCX.NE.1 )THEN
kusano 2b45e8
         KX = 1
kusano 2b45e8
      END IF
kusano 2b45e8
*
kusano 2b45e8
*     Start the operations. In this version the elements of A are
kusano 2b45e8
*     accessed sequentially with one pass through A.
kusano 2b45e8
*
kusano 2b45e8
      IF( LSAME( TRANS, 'N' ) )THEN
kusano 2b45e8
*
kusano 2b45e8
*        Form  x := inv( A )*x.
kusano 2b45e8
*
kusano 2b45e8
         IF( LSAME( UPLO, 'U' ) )THEN
kusano 2b45e8
            IF( INCX.EQ.1 )THEN
kusano 2b45e8
               DO 20, J = N, 1, -1
kusano 2b45e8
                  IF( X( J ).NE.ZERO )THEN
kusano 2b45e8
                     IF( NOUNIT )
kusano 2b45e8
     $                  X( J ) = X( J )/A( J, J )
kusano 2b45e8
                     TEMP = X( J )
kusano 2b45e8
                     DO 10, I = J - 1, 1, -1
kusano 2b45e8
                        X( I ) = X( I ) - TEMP*A( I, J )
kusano 2b45e8
   10                CONTINUE
kusano 2b45e8
                  END IF
kusano 2b45e8
   20          CONTINUE
kusano 2b45e8
            ELSE
kusano 2b45e8
               JX = KX + ( N - 1 )*INCX
kusano 2b45e8
               DO 40, J = N, 1, -1
kusano 2b45e8
                  IF( X( JX ).NE.ZERO )THEN
kusano 2b45e8
                     IF( NOUNIT )
kusano 2b45e8
     $                  X( JX ) = X( JX )/A( J, J )
kusano 2b45e8
                     TEMP = X( JX )
kusano 2b45e8
                     IX   = JX
kusano 2b45e8
                     DO 30, I = J - 1, 1, -1
kusano 2b45e8
                        IX      = IX      - INCX
kusano 2b45e8
                        X( IX ) = X( IX ) - TEMP*A( I, J )
kusano 2b45e8
   30                CONTINUE
kusano 2b45e8
                  END IF
kusano 2b45e8
                  JX = JX - INCX
kusano 2b45e8
   40          CONTINUE
kusano 2b45e8
            END IF
kusano 2b45e8
         ELSE
kusano 2b45e8
            IF( INCX.EQ.1 )THEN
kusano 2b45e8
               DO 60, J = 1, N
kusano 2b45e8
                  IF( X( J ).NE.ZERO )THEN
kusano 2b45e8
                     IF( NOUNIT )
kusano 2b45e8
     $                  X( J ) = X( J )/A( J, J )
kusano 2b45e8
                     TEMP = X( J )
kusano 2b45e8
                     DO 50, I = J + 1, N
kusano 2b45e8
                        X( I ) = X( I ) - TEMP*A( I, J )
kusano 2b45e8
   50                CONTINUE
kusano 2b45e8
                  END IF
kusano 2b45e8
   60          CONTINUE
kusano 2b45e8
            ELSE
kusano 2b45e8
               JX = KX
kusano 2b45e8
               DO 80, J = 1, N
kusano 2b45e8
                  IF( X( JX ).NE.ZERO )THEN
kusano 2b45e8
                     IF( NOUNIT )
kusano 2b45e8
     $                  X( JX ) = X( JX )/A( J, J )
kusano 2b45e8
                     TEMP = X( JX )
kusano 2b45e8
                     IX   = JX
kusano 2b45e8
                     DO 70, I = J + 1, N
kusano 2b45e8
                        IX      = IX      + INCX
kusano 2b45e8
                        X( IX ) = X( IX ) - TEMP*A( I, J )
kusano 2b45e8
   70                CONTINUE
kusano 2b45e8
                  END IF
kusano 2b45e8
                  JX = JX + INCX
kusano 2b45e8
   80          CONTINUE
kusano 2b45e8
            END IF
kusano 2b45e8
         END IF
kusano 2b45e8
      ELSE
kusano 2b45e8
*
kusano 2b45e8
*        Form  x := inv( A' )*x.
kusano 2b45e8
*
kusano 2b45e8
         IF( LSAME( UPLO, 'U' ) )THEN
kusano 2b45e8
            IF( INCX.EQ.1 )THEN
kusano 2b45e8
               DO 100, J = 1, N
kusano 2b45e8
                  TEMP = X( J )
kusano 2b45e8
                  DO 90, I = 1, J - 1
kusano 2b45e8
                     TEMP = TEMP - A( I, J )*X( I )
kusano 2b45e8
   90             CONTINUE
kusano 2b45e8
                  IF( NOUNIT )
kusano 2b45e8
     $               TEMP = TEMP/A( J, J )
kusano 2b45e8
                  X( J ) = TEMP
kusano 2b45e8
  100          CONTINUE
kusano 2b45e8
            ELSE
kusano 2b45e8
               JX = KX
kusano 2b45e8
               DO 120, J = 1, N
kusano 2b45e8
                  TEMP = X( JX )
kusano 2b45e8
                  IX   = KX
kusano 2b45e8
                  DO 110, I = 1, J - 1
kusano 2b45e8
                     TEMP = TEMP - A( I, J )*X( IX )
kusano 2b45e8
                     IX   = IX   + INCX
kusano 2b45e8
  110             CONTINUE
kusano 2b45e8
                  IF( NOUNIT )
kusano 2b45e8
     $               TEMP = TEMP/A( J, J )
kusano 2b45e8
                  X( JX ) = TEMP
kusano 2b45e8
                  JX      = JX   + INCX
kusano 2b45e8
  120          CONTINUE
kusano 2b45e8
            END IF
kusano 2b45e8
         ELSE
kusano 2b45e8
            IF( INCX.EQ.1 )THEN
kusano 2b45e8
               DO 140, J = N, 1, -1
kusano 2b45e8
                  TEMP = X( J )
kusano 2b45e8
                  DO 130, I = N, J + 1, -1
kusano 2b45e8
                     TEMP = TEMP - A( I, J )*X( I )
kusano 2b45e8
  130             CONTINUE
kusano 2b45e8
                  IF( NOUNIT )
kusano 2b45e8
     $               TEMP = TEMP/A( J, J )
kusano 2b45e8
                  X( J ) = TEMP
kusano 2b45e8
  140          CONTINUE
kusano 2b45e8
            ELSE
kusano 2b45e8
               KX = KX + ( N - 1 )*INCX
kusano 2b45e8
               JX = KX
kusano 2b45e8
               DO 160, J = N, 1, -1
kusano 2b45e8
                  TEMP = X( JX )
kusano 2b45e8
                  IX   = KX
kusano 2b45e8
                  DO 150, I = N, J + 1, -1
kusano 2b45e8
                     TEMP = TEMP - A( I, J )*X( IX )
kusano 2b45e8
                     IX   = IX   - INCX
kusano 2b45e8
  150             CONTINUE
kusano 2b45e8
                  IF( NOUNIT )
kusano 2b45e8
     $               TEMP = TEMP/A( J, J )
kusano 2b45e8
                  X( JX ) = TEMP
kusano 2b45e8
                  JX      = JX   - INCX
kusano 2b45e8
  160          CONTINUE
kusano 2b45e8
            END IF
kusano 2b45e8
         END IF
kusano 2b45e8
      END IF
kusano 2b45e8
*
kusano 2b45e8
      RETURN
kusano 2b45e8
*
kusano 2b45e8
*     End of DTRSV .
kusano 2b45e8
*
kusano 2b45e8
      END