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199 lines
5.1 KiB
199 lines
5.1 KiB
2 years ago
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*> \brief \b SPPT02
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SPPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
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* RESID )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER LDB, LDX, N, NRHS
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* REAL RESID
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* ..
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* .. Array Arguments ..
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* REAL A( * ), B( LDB, * ), RWORK( * ), X( LDX, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SPPT02 computes the residual in the solution of a symmetric system
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*> of linear equations A*x = b when packed storage is used for the
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*> coefficient matrix. The ratio computed is
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*>
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*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS),
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*>
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*> where EPS is the machine precision.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> Specifies whether the upper or lower triangular part of the
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*> symmetric matrix A is stored:
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*> = 'U': Upper triangular
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*> = 'L': Lower triangular
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of rows and columns of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] NRHS
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*> \verbatim
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*> NRHS is INTEGER
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*> The number of columns of B, the matrix of right hand sides.
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*> NRHS >= 0.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is REAL array, dimension (N*(N+1)/2)
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*> The original symmetric matrix A, stored as a packed
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*> triangular matrix.
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*> \endverbatim
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*>
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*> \param[in] X
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*> \verbatim
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*> X is REAL array, dimension (LDX,NRHS)
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*> The computed solution vectors for the system of linear
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*> equations.
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*> \endverbatim
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*>
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*> \param[in] LDX
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*> \verbatim
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*> LDX is INTEGER
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*> The leading dimension of the array X. LDX >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in,out] B
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*> \verbatim
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*> B is REAL array, dimension (LDB,NRHS)
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*> On entry, the right hand side vectors for the system of
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*> linear equations.
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*> On exit, B is overwritten with the difference B - A*X.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> The leading dimension of the array B. LDB >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is REAL array, dimension (N)
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*> \endverbatim
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*>
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*> \param[out] RESID
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*> \verbatim
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*> RESID is REAL
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*> The maximum over the number of right hand sides of
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*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup single_lin
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*
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* =====================================================================
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SUBROUTINE SPPT02( UPLO, N, NRHS, A, X, LDX, B, LDB, RWORK,
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$ RESID )
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*
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* -- LAPACK test routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER LDB, LDX, N, NRHS
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REAL RESID
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* ..
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* .. Array Arguments ..
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REAL A( * ), B( LDB, * ), RWORK( * ), X( LDX, * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER J
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REAL ANORM, BNORM, EPS, XNORM
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* ..
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* .. External Functions ..
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REAL SASUM, SLAMCH, SLANSP
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EXTERNAL SASUM, SLAMCH, SLANSP
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* ..
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* .. External Subroutines ..
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EXTERNAL SSPMV
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Executable Statements ..
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*
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* Quick exit if N = 0 or NRHS = 0.
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*
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IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
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RESID = ZERO
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RETURN
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END IF
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*
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* Exit with RESID = 1/EPS if ANORM = 0.
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*
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EPS = SLAMCH( 'Epsilon' )
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ANORM = SLANSP( '1', UPLO, N, A, RWORK )
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IF( ANORM.LE.ZERO ) THEN
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RESID = ONE / EPS
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RETURN
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END IF
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*
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* Compute B - A*X for the matrix of right hand sides B.
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*
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DO 10 J = 1, NRHS
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CALL SSPMV( UPLO, N, -ONE, A, X( 1, J ), 1, ONE, B( 1, J ), 1 )
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10 CONTINUE
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*
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* Compute the maximum over the number of right hand sides of
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* norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) .
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*
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RESID = ZERO
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DO 20 J = 1, NRHS
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BNORM = SASUM( N, B( 1, J ), 1 )
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XNORM = SASUM( N, X( 1, J ), 1 )
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IF( XNORM.LE.ZERO ) THEN
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RESID = ONE / EPS
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ELSE
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RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
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END IF
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20 CONTINUE
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*
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RETURN
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*
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* End of SPPT02
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*
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END
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