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226 lines
5.8 KiB
226 lines
5.8 KiB
2 years ago
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*> \brief \b ZPTTRF
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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 ZPTTRF + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpttrf.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/zpttrf.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/zpttrf.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 ZPTTRF( N, D, E, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, N
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION D( * )
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* COMPLEX*16 E( * )
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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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*> ZPTTRF computes the L*D*L**H factorization of a complex Hermitian
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*> positive definite tridiagonal matrix A. The factorization may also
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*> be regarded as having the form A = U**H *D*U.
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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 A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] D
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*> \verbatim
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*> D is DOUBLE PRECISION array, dimension (N)
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*> On entry, the n diagonal elements of the tridiagonal matrix
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*> A. On exit, the n diagonal elements of the diagonal matrix
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*> D from the L*D*L**H factorization of A.
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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 COMPLEX*16 array, dimension (N-1)
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*> On entry, the (n-1) subdiagonal elements of the tridiagonal
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*> matrix A. On exit, the (n-1) subdiagonal elements of the
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*> unit bidiagonal factor L from the L*D*L**H factorization of A.
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*> E can also be regarded as the superdiagonal of the unit
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*> bidiagonal factor U from the U**H *D*U factorization of A.
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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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*> < 0: if INFO = -k, the k-th argument had an illegal value
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*> > 0: if INFO = k, the leading principal minor of order k
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*> is not positive; if k < N, the factorization could not
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*> be completed, while if k = N, the factorization was
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*> completed, but D(N) <= 0.
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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 complex16PTcomputational
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*
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* =====================================================================
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SUBROUTINE ZPTTRF( N, D, E, INFO )
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*
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* -- LAPACK computational 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
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION D( * )
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COMPLEX*16 E( * )
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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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DOUBLE PRECISION ZERO
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PARAMETER ( ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, I4
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DOUBLE PRECISION EII, EIR, F, G
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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 DBLE, DCMPLX, DIMAG, MOD
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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( N.LT.0 ) THEN
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INFO = -1
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CALL XERBLA( 'ZPTTRF', -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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* Compute the L*D*L**H (or U**H *D*U) factorization of A.
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*
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I4 = MOD( N-1, 4 )
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DO 10 I = 1, I4
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IF( D( I ).LE.ZERO ) THEN
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INFO = I
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GO TO 30
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END IF
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EIR = DBLE( E( I ) )
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EII = DIMAG( E( I ) )
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F = EIR / D( I )
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G = EII / D( I )
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E( I ) = DCMPLX( F, G )
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D( I+1 ) = D( I+1 ) - F*EIR - G*EII
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10 CONTINUE
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*
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DO 20 I = I4 + 1, N - 4, 4
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*
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* Drop out of the loop if d(i) <= 0: the matrix is not positive
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* definite.
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*
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IF( D( I ).LE.ZERO ) THEN
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INFO = I
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GO TO 30
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END IF
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*
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* Solve for e(i) and d(i+1).
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*
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EIR = DBLE( E( I ) )
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EII = DIMAG( E( I ) )
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F = EIR / D( I )
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G = EII / D( I )
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E( I ) = DCMPLX( F, G )
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D( I+1 ) = D( I+1 ) - F*EIR - G*EII
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*
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IF( D( I+1 ).LE.ZERO ) THEN
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INFO = I + 1
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GO TO 30
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END IF
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*
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* Solve for e(i+1) and d(i+2).
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*
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EIR = DBLE( E( I+1 ) )
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EII = DIMAG( E( I+1 ) )
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F = EIR / D( I+1 )
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G = EII / D( I+1 )
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E( I+1 ) = DCMPLX( F, G )
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D( I+2 ) = D( I+2 ) - F*EIR - G*EII
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*
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IF( D( I+2 ).LE.ZERO ) THEN
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INFO = I + 2
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GO TO 30
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END IF
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*
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* Solve for e(i+2) and d(i+3).
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*
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EIR = DBLE( E( I+2 ) )
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EII = DIMAG( E( I+2 ) )
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F = EIR / D( I+2 )
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G = EII / D( I+2 )
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E( I+2 ) = DCMPLX( F, G )
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D( I+3 ) = D( I+3 ) - F*EIR - G*EII
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*
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IF( D( I+3 ).LE.ZERO ) THEN
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INFO = I + 3
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GO TO 30
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END IF
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*
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* Solve for e(i+3) and d(i+4).
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*
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EIR = DBLE( E( I+3 ) )
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EII = DIMAG( E( I+3 ) )
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F = EIR / D( I+3 )
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G = EII / D( I+3 )
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E( I+3 ) = DCMPLX( F, G )
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D( I+4 ) = D( I+4 ) - F*EIR - G*EII
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20 CONTINUE
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*
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* Check d(n) for positive definiteness.
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*
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IF( D( N ).LE.ZERO )
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$ INFO = N
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*
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30 CONTINUE
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RETURN
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*
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* End of ZPTTRF
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*
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END
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