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      SUBROUTINE ZTPSVF( UPLO, TRANS, DIAG, N, AP, X, INCX )
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*     .. Scalar Arguments ..
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      INTEGER            INCX, N
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      CHARACTER*1        DIAG, TRANS, UPLO
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*     .. Array Arguments ..
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      COMPLEX*16         AP( * ), X( * )
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*     ..
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*
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*  Purpose
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*  =======
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*
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*  ZTPSV  solves one of the systems of equations
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*
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*     A*x = b,   or   A'*x = b,   or   conjg( A' )*x = b,
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*
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*  where b and x are n element vectors and A is an n by n unit, or
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*  non-unit, upper or lower triangular matrix, supplied in packed form.
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*
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*  No test for singularity or near-singularity is included in this
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*  routine. Such tests must be performed before calling this routine.
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*
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*  Parameters
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*  ==========
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*
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*  UPLO   - CHARACTER*1.
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*           On entry, UPLO specifies whether the matrix is an upper or
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*           lower triangular matrix as follows:
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*
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*              UPLO = 'U' or 'u'   A is an upper triangular matrix.
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*
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*              UPLO = 'L' or 'l'   A is a lower triangular matrix.
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*
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*           Unchanged on exit.
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*
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*  TRANS  - CHARACTER*1.
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*           On entry, TRANS specifies the equations to be solved as
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*           follows:
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*
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*              TRANS = 'N' or 'n'   A*x = b.
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*
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*              TRANS = 'T' or 't'   A'*x = b.
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*
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*              TRANS = 'C' or 'c'   conjg( A' )*x = b.
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*
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*           Unchanged on exit.
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*
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*  DIAG   - CHARACTER*1.
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*           On entry, DIAG specifies whether or not A is unit
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*           triangular as follows:
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*
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*              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
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*
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*              DIAG = 'N' or 'n'   A is not assumed to be unit
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*                                  triangular.
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*
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*           Unchanged on exit.
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*
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*  N      - INTEGER.
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*           On entry, N specifies the order of the matrix A.
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*           N must be at least zero.
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*           Unchanged on exit.
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*
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*  AP     - COMPLEX*16       array of DIMENSION at least
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*           ( ( n*( n + 1 ) )/2 ).
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*           Before entry with  UPLO = 'U' or 'u', the array AP must
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*           contain the upper triangular matrix packed sequentially,
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*           column by column, so that AP( 1 ) contains a( 1, 1 ),
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*           AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
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*           respectively, and so on.
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*           Before entry with UPLO = 'L' or 'l', the array AP must
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*           contain the lower triangular matrix packed sequentially,
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*           column by column, so that AP( 1 ) contains a( 1, 1 ),
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*           AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
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*           respectively, and so on.
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*           Note that when  DIAG = 'U' or 'u', the diagonal elements of
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*           A are not referenced, but are assumed to be unity.
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*           Unchanged on exit.
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*
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*  X      - COMPLEX*16       array of dimension at least
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*           ( 1 + ( n - 1 )*abs( INCX ) ).
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*           Before entry, the incremented array X must contain the n
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*           element right-hand side vector b. On exit, X is overwritten
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*           with the solution vector x.
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*
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*  INCX   - INTEGER.
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*           On entry, INCX specifies the increment for the elements of
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*           X. INCX must not be zero.
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*           Unchanged on exit.
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*
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*
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*  Level 2 Blas routine.
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*
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*  -- Written on 22-October-1986.
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*     Jack Dongarra, Argonne National Lab.
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*     Jeremy Du Croz, Nag Central Office.
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*     Sven Hammarling, Nag Central Office.
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*     Richard Hanson, Sandia National Labs.
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*
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*
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*     .. Parameters ..
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      COMPLEX*16         ZERO
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      PARAMETER        ( ZERO = ( 0.0D+0, 0.0D+0 ) )
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*     .. Local Scalars ..
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      COMPLEX*16         TEMP
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      INTEGER            I, INFO, IX, J, JX, K, KK, KX
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      LOGICAL            NOCONJ, NOUNIT
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*     .. External Functions ..
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      LOGICAL            LSAME
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      EXTERNAL           LSAME
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*     .. External Subroutines ..
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      EXTERNAL           XERBLA
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*     .. Intrinsic Functions ..
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      INTRINSIC          DCONJG
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*     ..
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*     .. Executable Statements ..
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*
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*     Test the input parameters.
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*
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      INFO = 0
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      IF     ( .NOT.LSAME( UPLO , 'U' ).AND.
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     $         .NOT.LSAME( UPLO , 'L' )      )THEN
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         INFO = 1
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      ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND.
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     $         .NOT.LSAME( TRANS, 'T' ).AND.
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     $         .NOT.LSAME( TRANS, 'R' ).AND.
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     $         .NOT.LSAME( TRANS, 'C' )      )THEN
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         INFO = 2
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      ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND.
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     $         .NOT.LSAME( DIAG , 'N' )      )THEN
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         INFO = 3
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      ELSE IF( N.LT.0 )THEN
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         INFO = 4
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      ELSE IF( INCX.EQ.0 )THEN
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         INFO = 7
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      END IF
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      IF( INFO.NE.0 )THEN
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         CALL XERBLA( 'ZTPSV ', INFO )
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         RETURN
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      END IF
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*
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*     Quick return if possible.
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*
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      IF( N.EQ.0 )
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     $   RETURN
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*
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      NOCONJ = LSAME( TRANS, 'N' ) .OR. LSAME( TRANS, 'T' )
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      NOUNIT = LSAME( DIAG , 'N' )
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*
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*     Set up the start point in X if the increment is not unity. This
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*     will be  ( N - 1 )*INCX  too small for descending loops.
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*
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      IF( INCX.LE.0 )THEN
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         KX = 1 - ( N - 1 )*INCX
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      ELSE IF( INCX.NE.1 )THEN
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         KX = 1
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      END IF
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*
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*     Start the operations. In this version the elements of AP are
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*     accessed sequentially with one pass through AP.
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*
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      IF( LSAME( TRANS, 'N' ) .OR.LSAME( TRANS, 'R' ))THEN
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*
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*        Form  x := inv( A )*x.
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*
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         IF( LSAME( UPLO, 'U' ) )THEN
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            KK = ( N*( N + 1 ) )/2
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            IF( INCX.EQ.1 )THEN
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               DO 20, J = N, 1, -1
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                  IF( X( J ).NE.ZERO )THEN
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                     IF( NOCONJ )THEN
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                        IF( NOUNIT )
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     $                       X( J ) = X( J )/AP( KK )
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                     ELSE
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                        IF( NOUNIT )
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     $                       X( J ) = X( J )/DCONJG(AP( KK ))
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                     END IF
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                     TEMP = X( J )
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                     K    = KK     - 1
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                     DO 10, I = J - 1, 1, -1
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                     IF( NOCONJ )THEN
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                        X( I ) = X( I ) - TEMP*AP( K )
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                     ELSE
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                        X( I ) = X( I ) - TEMP*DCONJG(AP( K ))
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                     END IF
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                     K      = K      - 1
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   10                CONTINUE
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                  END IF
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                  KK = KK - J
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   20          CONTINUE
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            ELSE
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               JX = KX + ( N - 1 )*INCX
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               DO 40, J = N, 1, -1
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                  IF( X( JX ).NE.ZERO )THEN
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                     IF( NOCONJ )THEN
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                        IF( NOUNIT )
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     $                       X( JX ) = X( JX )/AP( KK )
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                     ELSE
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                        IF( NOUNIT )
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     $                       X( JX ) = X( JX )/DCONJG(AP( KK ))
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                     END IF
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                     TEMP = X( JX )
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                     IX   = JX
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                     DO 30, K = KK - 1, KK - J + 1, -1
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                        IX      = IX      - INCX
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                     IF( NOCONJ )THEN
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                        X( IX ) = X( IX ) - TEMP*AP( K )
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                     ELSE
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                        X( IX ) = X( IX ) - TEMP*DCONJG(AP( K ))
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                     END IF
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   30                CONTINUE
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                  END IF
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                  JX = JX - INCX
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                  KK = KK - J
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   40          CONTINUE
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            END IF
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         ELSE
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            KK = 1
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            IF( INCX.EQ.1 )THEN
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               DO 60, J = 1, N
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                  IF( X( J ).NE.ZERO )THEN
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                     IF( NOCONJ )THEN
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                        IF( NOUNIT )
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     $                       X( J ) = X( J )/AP( KK )
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                     ELSE
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                        IF( NOUNIT )
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     $                       X( J ) = X( J )/DCONJG(AP( KK ))
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                     END IF
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                     TEMP = X( J )
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                     K    = KK     + 1
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                     DO 50, I = J + 1, N
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                        IF( NOCONJ )THEN
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                           X( I ) = X( I ) - TEMP*AP( K )
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                        ELSE
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                           X( I ) = X( I ) - TEMP*DCONJG(AP( K ))
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                        END IF
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                        K      = K      + 1
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   50                CONTINUE
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                  END IF
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                  KK = KK + ( N - J + 1 )
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   60          CONTINUE
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            ELSE
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               JX = KX
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               DO 80, J = 1, N
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                  IF( X( JX ).NE.ZERO )THEN
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                     IF( NOCONJ )THEN
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                        IF( NOUNIT )
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     $                       X( JX ) = X( JX )/AP( KK )
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                     ELSE
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                        IF( NOUNIT )
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     $                       X( JX ) = X( JX )/DCONJG(AP( KK ))
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                     END IF
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                     TEMP = X( JX )
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                     IX   = JX
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                     DO 70, K = KK + 1, KK + N - J
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                        IX      = IX      + INCX
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                     IF( NOCONJ )THEN
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                        X( IX ) = X( IX ) - TEMP*AP( K )
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                     ELSE
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                        X( IX ) = X( IX ) - TEMP*DCONJG(AP( K ))
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                     END IF
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   70                CONTINUE
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                  END IF
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                  JX = JX + INCX
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                  KK = KK + ( N - J + 1 )
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   80          CONTINUE
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            END IF
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         END IF
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      ELSE
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*
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*        Form  x := inv( A' )*x  or  x := inv( conjg( A' ) )*x.
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*
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         IF( LSAME( UPLO, 'U' ) )THEN
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            KK = 1
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            IF( INCX.EQ.1 )THEN
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               DO 110, J = 1, N
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                  TEMP = X( J )
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                  K    = KK
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                  IF( NOCONJ )THEN
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                     DO 90, I = 1, J - 1
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                        TEMP = TEMP - AP( K )*X( I )
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                        K    = K    + 1
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   90                CONTINUE
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                     IF( NOUNIT )
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     $                  TEMP = TEMP/AP( KK + J - 1 )
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                  ELSE
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                     DO 100, I = 1, J - 1
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                        TEMP = TEMP - DCONJG( AP( K ) )*X( I )
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                        K    = K    + 1
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  100                CONTINUE
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                     IF( NOUNIT )
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     $                  TEMP = TEMP/DCONJG( AP( KK + J - 1 ) )
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                  END IF
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                  X( J ) = TEMP
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                  KK     = KK   + J
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  110          CONTINUE
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            ELSE
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               JX = KX
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               DO 140, J = 1, N
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                  TEMP = X( JX )
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                  IX   = KX
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                  IF( NOCONJ )THEN
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                     DO 120, K = KK, KK + J - 2
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                        TEMP = TEMP - AP( K )*X( IX )
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                        IX   = IX   + INCX
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  120                CONTINUE
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                     IF( NOUNIT )
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     $                  TEMP = TEMP/AP( KK + J - 1 )
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                  ELSE
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                     DO 130, K = KK, KK + J - 2
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                        TEMP = TEMP - DCONJG( AP( K ) )*X( IX )
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                        IX   = IX   + INCX
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  130                CONTINUE
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                     IF( NOUNIT )
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     $                  TEMP = TEMP/DCONJG( AP( KK + J - 1 ) )
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                  END IF
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                  X( JX ) = TEMP
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                  JX      = JX   + INCX
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                  KK      = KK   + J
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  140          CONTINUE
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            END IF
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         ELSE
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            KK = ( N*( N + 1 ) )/2
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            IF( INCX.EQ.1 )THEN
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               DO 170, J = N, 1, -1
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                  TEMP = X( J )
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                  K    = KK
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                  IF( NOCONJ )THEN
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                     DO 150, I = N, J + 1, -1
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                        TEMP = TEMP - AP( K )*X( I )
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                        K    = K    - 1
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  150                CONTINUE
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                     IF( NOUNIT )
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     $                  TEMP = TEMP/AP( KK - N + J )
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                  ELSE
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                     DO 160, I = N, J + 1, -1
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                        TEMP = TEMP - DCONJG( AP( K ) )*X( I )
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                        K    = K    - 1
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  160                CONTINUE
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                     IF( NOUNIT )
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     $                  TEMP = TEMP/DCONJG( AP( KK - N + J ) )
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                  END IF
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                  X( J ) = TEMP
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                  KK     = KK   - ( N - J + 1 )
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  170          CONTINUE
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            ELSE
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               KX = KX + ( N - 1 )*INCX
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               JX = KX
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               DO 200, J = N, 1, -1
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                  TEMP = X( JX )
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                  IX   = KX
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                  IF( NOCONJ )THEN
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                     DO 180, K = KK, KK - ( N - ( J + 1 ) ), -1
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                        TEMP = TEMP - AP( K )*X( IX )
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                        IX   = IX   - INCX
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  180                CONTINUE
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                     IF( NOUNIT )
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     $                  TEMP = TEMP/AP( KK - N + J )
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                  ELSE
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                     DO 190, K = KK, KK - ( N - ( J + 1 ) ), -1
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                        TEMP = TEMP - DCONJG( AP( K ) )*X( IX )
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                        IX   = IX   - INCX
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  190                CONTINUE
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                     IF( NOUNIT )
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     $                  TEMP = TEMP/DCONJG( AP( KK - N + J ) )
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                  END IF
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                  X( JX ) = TEMP
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                  JX      = JX   - INCX
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                  KK      = KK   - ( N - J + 1 )
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  200          CONTINUE
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            END IF
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         END IF
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      END IF
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*
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      RETURN
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*
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*     End of ZTPSV .
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*
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      END