168 lines
4.7 KiB
Fortran
168 lines
4.7 KiB
Fortran
*> \brief <b> SPTSV computes the solution to system of linear equations A * X = B for PT matrices</b>
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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 SPTSV + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sptsv.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/sptsv.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/sptsv.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 SPTSV( N, NRHS, D, E, B, LDB, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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* REAL B( LDB, * ), D( * ), 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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*> SPTSV computes the solution to a real system of linear equations
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*> A*X = B, where A is an N-by-N symmetric positive definite tridiagonal
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*> matrix, and X and B are N-by-NRHS matrices.
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*>
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*> A is factored as A = L*D*L**T, and the factored form of A is then
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*> used to solve the system of equations.
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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] 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,out] 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 matrix
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*> A. On exit, the n diagonal elements of the diagonal matrix
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*> D from the factorization A = L*D*L**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-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**T factorization of
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*> A. (E can also be regarded as the superdiagonal of the unit
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*> bidiagonal factor U from the U**T*D*U factorization of A.)
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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 N-by-NRHS right hand side matrix B.
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*> On exit, if INFO = 0, the N-by-NRHS solution matrix 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] 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 = -i, the i-th argument had an illegal value
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*> > 0: if INFO = i, the leading minor of order i is not
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*> positive definite, and the solution has not been
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*> computed. The factorization has not been completed
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*> unless i = 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 December 2016
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*
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*> \ingroup realPTsolve
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*
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* =====================================================================
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SUBROUTINE SPTSV( N, NRHS, D, E, B, LDB, INFO )
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*
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* -- LAPACK driver 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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* December 2016
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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REAL B( LDB, * ), D( * ), E( * )
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* ..
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*
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* =====================================================================
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*
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* .. External Subroutines ..
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EXTERNAL SPTTRF, SPTTRS, XERBLA
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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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* 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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ELSE IF( NRHS.LT.0 ) THEN
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INFO = -2
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -6
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SPTSV ', -INFO )
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RETURN
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END IF
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*
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* Compute the L*D*L**T (or U**T*D*U) factorization of A.
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*
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CALL SPTTRF( N, D, E, INFO )
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IF( INFO.EQ.0 ) THEN
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*
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* Solve the system A*X = B, overwriting B with X.
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*
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CALL SPTTRS( N, NRHS, D, E, B, LDB, INFO )
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END IF
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RETURN
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*
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* End of SPTSV
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*
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END
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