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208 lines
5.8 KiB
208 lines
5.8 KiB
2 years ago
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*> \brief \b SLARRA computes the splitting points with the specified threshold.
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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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*> \htmlonly
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*> Download SLARRA + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slarra.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slarra.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slarra.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SLARRA( N, D, E, E2, SPLTOL, TNRM,
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* NSPLIT, ISPLIT, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, N, NSPLIT
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* REAL SPLTOL, TNRM
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* ..
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* .. Array Arguments ..
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* INTEGER ISPLIT( * )
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* REAL D( * ), E( * ), E2( * )
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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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*> Compute the splitting points with threshold SPLTOL.
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*> SLARRA sets any "small" off-diagonal elements to zero.
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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] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix. N > 0.
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*> \endverbatim
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*>
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*> \param[in] D
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*> \verbatim
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*> D is REAL array, dimension (N)
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*> On entry, the N diagonal elements of the tridiagonal
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*> matrix T.
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*> \endverbatim
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*>
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*> \param[in,out] E
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*> \verbatim
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*> E is REAL array, dimension (N)
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*> On entry, the first (N-1) entries contain the subdiagonal
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*> elements of the tridiagonal matrix T; E(N) need not be set.
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*> On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT,
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*> are set to zero, the other entries of E are untouched.
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*> \endverbatim
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*>
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*> \param[in,out] E2
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*> \verbatim
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*> E2 is REAL array, dimension (N)
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*> On entry, the first (N-1) entries contain the SQUARES of the
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*> subdiagonal elements of the tridiagonal matrix T;
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*> E2(N) need not be set.
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*> On exit, the entries E2( ISPLIT( I ) ),
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*> 1 <= I <= NSPLIT, have been set to zero
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*> \endverbatim
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*>
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*> \param[in] SPLTOL
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*> \verbatim
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*> SPLTOL is REAL
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*> The threshold for splitting. Two criteria can be used:
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*> SPLTOL<0 : criterion based on absolute off-diagonal value
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*> SPLTOL>0 : criterion that preserves relative accuracy
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*> \endverbatim
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*>
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*> \param[in] TNRM
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*> \verbatim
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*> TNRM is REAL
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*> The norm of the matrix.
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*> \endverbatim
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*>
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*> \param[out] NSPLIT
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*> \verbatim
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*> NSPLIT is INTEGER
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*> The number of blocks T splits into. 1 <= NSPLIT <= N.
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*> \endverbatim
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*>
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*> \param[out] ISPLIT
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*> \verbatim
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*> ISPLIT is INTEGER array, dimension (N)
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*> The splitting points, at which T breaks up into blocks.
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*> The first block consists of rows/columns 1 to ISPLIT(1),
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*> the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
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*> etc., and the NSPLIT-th consists of rows/columns
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*> ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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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 OTHERauxiliary
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*
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*> \par Contributors:
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* ==================
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*>
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*> Beresford Parlett, University of California, Berkeley, USA \n
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*> Jim Demmel, University of California, Berkeley, USA \n
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*> Inderjit Dhillon, University of Texas, Austin, USA \n
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*> Osni Marques, LBNL/NERSC, USA \n
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*> Christof Voemel, University of California, Berkeley, USA
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*
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* =====================================================================
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SUBROUTINE SLARRA( N, D, E, E2, SPLTOL, TNRM,
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$ NSPLIT, ISPLIT, INFO )
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*
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* -- LAPACK auxiliary 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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INTEGER INFO, N, NSPLIT
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REAL SPLTOL, TNRM
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* ..
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* .. Array Arguments ..
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INTEGER ISPLIT( * )
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REAL D( * ), E( * ), E2( * )
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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
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PARAMETER ( ZERO = 0.0E0 )
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* ..
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* .. Local Scalars ..
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INTEGER I
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REAL EABS, TMP1
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS
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* ..
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* .. Executable Statements ..
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*
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INFO = 0
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NSPLIT = 1
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*
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* Quick return if possible
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*
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IF( N.LE.0 ) THEN
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RETURN
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END IF
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*
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* Compute splitting points
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IF(SPLTOL.LT.ZERO) THEN
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* Criterion based on absolute off-diagonal value
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TMP1 = ABS(SPLTOL)* TNRM
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DO 9 I = 1, N-1
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EABS = ABS( E(I) )
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IF( EABS .LE. TMP1) THEN
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E(I) = ZERO
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E2(I) = ZERO
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ISPLIT( NSPLIT ) = I
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NSPLIT = NSPLIT + 1
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END IF
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9 CONTINUE
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ELSE
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* Criterion that guarantees relative accuracy
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DO 10 I = 1, N-1
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EABS = ABS( E(I) )
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IF( EABS .LE. SPLTOL * SQRT(ABS(D(I)))*SQRT(ABS(D(I+1))) )
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$ THEN
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E(I) = ZERO
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E2(I) = ZERO
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ISPLIT( NSPLIT ) = I
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NSPLIT = NSPLIT + 1
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END IF
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10 CONTINUE
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ENDIF
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ISPLIT( NSPLIT ) = N
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RETURN
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*
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* End of SLARRA
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*
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END
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