391 lines
12 KiB
Fortran
391 lines
12 KiB
Fortran
*> \brief \b ZTPSV
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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 ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
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*
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* .. Scalar Arguments ..
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* INTEGER INCX,N
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* CHARACTER DIAG,TRANS,UPLO
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* ..
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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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*
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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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*> ZTPSV solves one of the systems of equations
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*>
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*> A*x = b, or A**T*x = b, or A**H*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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*> \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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*> 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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*> \endverbatim
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*>
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*> \param[in] TRANS
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*> \verbatim
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*> TRANS is 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**T*x = b.
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*>
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*> TRANS = 'C' or 'c' A**H*x = b.
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*> \endverbatim
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*>
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*> \param[in] DIAG
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*> \verbatim
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*> DIAG is 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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*> \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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*> On entry, N specifies the order of the matrix A.
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*> N must be at least zero.
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*> \endverbatim
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*>
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*> \param[in] AP
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*> \verbatim
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*> AP is 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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*> \endverbatim
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*>
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*> \param[in,out] X
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*> \verbatim
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*> X is 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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*> \endverbatim
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*>
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*> \param[in] INCX
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*> \verbatim
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*> INCX is 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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*> \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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*> \date November 2011
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*
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*> \ingroup complex16_blas_level2
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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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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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
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*
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* -- Reference BLAS level2 routine (version 3.4.0) --
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* -- Reference BLAS 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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* November 2011
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*
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* .. Scalar Arguments ..
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INTEGER INCX,N
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CHARACTER DIAG,TRANS,UPLO
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* ..
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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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* =====================================================================
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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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* ..
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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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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DCONJG
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* ..
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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. .NOT.LSAME(UPLO,'L')) THEN
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INFO = 1
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ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .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. .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) RETURN
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*
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NOCONJ = 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')) 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 (NOUNIT) X(J) = X(J)/AP(KK)
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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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X(I) = X(I) - TEMP*AP(K)
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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 (NOUNIT) X(JX) = X(JX)/AP(KK)
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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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X(IX) = X(IX) - TEMP*AP(K)
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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 (NOUNIT) X(J) = X(J)/AP(KK)
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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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X(I) = X(I) - TEMP*AP(K)
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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 (NOUNIT) X(JX) = X(JX)/AP(KK)
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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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X(IX) = X(IX) - TEMP*AP(K)
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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**T )*x or x := inv( A**H )*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) 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) 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) 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) 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) 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) 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) 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) 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
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