246 lines
6.8 KiB
Fortran
246 lines
6.8 KiB
Fortran
*> \brief \b ZPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.
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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 ZPTTS2 + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zptts2.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/zptts2.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/zptts2.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 ZPTTS2( IUPLO, N, NRHS, D, E, B, LDB )
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*
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* .. Scalar Arguments ..
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* INTEGER IUPLO, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION D( * )
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* COMPLEX*16 B( LDB, * ), 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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*> ZPTTS2 solves a tridiagonal system of the form
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*> A * X = B
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*> using the factorization A = U**H *D*U or A = L*D*L**H computed by ZPTTRF.
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*> D is a diagonal matrix specified in the vector D, U (or L) is a unit
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*> bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
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*> the vector E, and X and B are N by NRHS matrices.
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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] IUPLO
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*> \verbatim
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*> IUPLO is INTEGER
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*> Specifies the form of the factorization and whether the
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*> vector E is the superdiagonal of the upper bidiagonal factor
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*> U or the subdiagonal of the lower bidiagonal factor L.
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*> = 1: A = U**H *D*U, E is the superdiagonal of U
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*> = 0: A = L*D*L**H, E is the subdiagonal of L
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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 order of the tridiagonal 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 right hand sides, i.e., the number of columns
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*> of the matrix B. NRHS >= 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 DOUBLE PRECISION array, dimension (N)
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*> The n diagonal elements of the diagonal matrix D from the
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*> factorization A = U**H *D*U or A = L*D*L**H.
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*> \endverbatim
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*>
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*> \param[in] E
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*> \verbatim
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*> E is COMPLEX*16 array, dimension (N-1)
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*> If IUPLO = 1, the (n-1) superdiagonal elements of the unit
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*> bidiagonal factor U from the factorization A = U**H*D*U.
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*> If IUPLO = 0, the (n-1) subdiagonal elements of the unit
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*> bidiagonal factor L from the factorization A = L*D*L**H.
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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 COMPLEX*16 array, dimension (LDB,NRHS)
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*> On entry, the right hand side vectors B for the system of
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*> linear equations.
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*> On exit, the solution vectors, 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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* 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 June 2016
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*
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*> \ingroup complex16PTcomputational
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*
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* =====================================================================
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SUBROUTINE ZPTTS2( IUPLO, N, NRHS, D, E, B, LDB )
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*
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* -- LAPACK computational routine (version 3.7.0) --
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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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* June 2016
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*
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* .. Scalar Arguments ..
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INTEGER IUPLO, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION D( * )
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COMPLEX*16 B( LDB, * ), E( * )
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* ..
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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INTEGER I, J
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* ..
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* .. External Subroutines ..
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EXTERNAL ZDSCAL
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* ..
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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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* Quick return if possible
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*
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IF( N.LE.1 ) THEN
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IF( N.EQ.1 )
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$ CALL ZDSCAL( NRHS, 1.D0 / D( 1 ), B, LDB )
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RETURN
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END IF
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*
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IF( IUPLO.EQ.1 ) THEN
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*
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* Solve A * X = B using the factorization A = U**H *D*U,
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* overwriting each right hand side vector with its solution.
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*
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IF( NRHS.LE.2 ) THEN
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J = 1
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10 CONTINUE
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*
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* Solve U**H * x = b.
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*
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DO 20 I = 2, N
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B( I, J ) = B( I, J ) - B( I-1, J )*DCONJG( E( I-1 ) )
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20 CONTINUE
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*
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* Solve D * U * x = b.
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*
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DO 30 I = 1, N
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B( I, J ) = B( I, J ) / D( I )
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30 CONTINUE
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DO 40 I = N - 1, 1, -1
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B( I, J ) = B( I, J ) - B( I+1, J )*E( I )
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40 CONTINUE
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IF( J.LT.NRHS ) THEN
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J = J + 1
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GO TO 10
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END IF
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ELSE
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DO 70 J = 1, NRHS
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*
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* Solve U**H * x = b.
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*
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DO 50 I = 2, N
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B( I, J ) = B( I, J ) - B( I-1, J )*DCONJG( E( I-1 ) )
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50 CONTINUE
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*
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* Solve D * U * x = b.
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*
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B( N, J ) = B( N, J ) / D( N )
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DO 60 I = N - 1, 1, -1
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B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I )
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60 CONTINUE
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70 CONTINUE
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END IF
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ELSE
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*
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* Solve A * X = B using the factorization A = L*D*L**H,
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* overwriting each right hand side vector with its solution.
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*
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IF( NRHS.LE.2 ) THEN
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J = 1
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80 CONTINUE
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*
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* Solve L * x = b.
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*
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DO 90 I = 2, N
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B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
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90 CONTINUE
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*
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* Solve D * L**H * x = b.
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*
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DO 100 I = 1, N
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B( I, J ) = B( I, J ) / D( I )
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100 CONTINUE
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DO 110 I = N - 1, 1, -1
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B( I, J ) = B( I, J ) - B( I+1, J )*DCONJG( E( I ) )
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110 CONTINUE
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IF( J.LT.NRHS ) THEN
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J = J + 1
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GO TO 80
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END IF
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ELSE
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DO 140 J = 1, NRHS
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*
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* Solve L * x = b.
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*
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DO 120 I = 2, N
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B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
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120 CONTINUE
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*
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* Solve D * L**H * x = b.
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*
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B( N, J ) = B( N, J ) / D( N )
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DO 130 I = N - 1, 1, -1
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B( I, J ) = B( I, J ) / D( I ) -
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$ B( I+1, J )*DCONJG( E( I ) )
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130 CONTINUE
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140 CONTINUE
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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 ZPTTS2
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*
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END
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