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*> \brief \b SPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download SPTTS2 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sptts2.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sptts2.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sptts2.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE SPTTS2( N, NRHS, D, E, B, LDB )
*
* .. Scalar Arguments ..
* INTEGER LDB, N, NRHS
* ..
* .. Array Arguments ..
* REAL B( LDB, * ), D( * ), E( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SPTTS2 solves a tridiagonal system of the form
*> A * X = B
*> using the L*D*L**T factorization of A computed by SPTTRF. D is a
*> diagonal matrix specified in the vector D, L is a unit bidiagonal
*> matrix whose subdiagonal is specified in the vector E, and X and B
*> are N by NRHS matrices.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the tridiagonal matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of right hand sides, i.e., the number of columns
*> of the matrix B. NRHS >= 0.
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*> D is REAL array, dimension (N)
*> The n diagonal elements of the diagonal matrix D from the
*> L*D*L**T factorization of A.
*> \endverbatim
*>
*> \param[in] E
*> \verbatim
*> E is REAL array, dimension (N-1)
*> The (n-1) subdiagonal elements of the unit bidiagonal factor
*> L from the L*D*L**T factorization of A. E can also be regarded
*> as the superdiagonal of the unit bidiagonal factor U from the
*> factorization A = U**T*D*U.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is REAL array, dimension (LDB,NRHS)
*> On entry, the right hand side vectors B for the system of
*> linear equations.
*> On exit, the solution vectors, X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup realPTcomputational
*
* =====================================================================
SUBROUTINE SPTTS2( N, NRHS, D, E, B, LDB )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
INTEGER LDB, N, NRHS
* ..
* .. Array Arguments ..
REAL B( LDB, * ), D( * ), E( * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I, J
* ..
* .. External Subroutines ..
EXTERNAL SSCAL
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( N.LE.1 ) THEN
IF( N.EQ.1 )
$ CALL SSCAL( NRHS, 1. / D( 1 ), B, LDB )
RETURN
END IF
*
* Solve A * X = B using the factorization A = L*D*L**T,
* overwriting each right hand side vector with its solution.
*
DO 30 J = 1, NRHS
*
* Solve L * x = b.
*
DO 10 I = 2, N
B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
10 CONTINUE
*
* Solve D * L**T * x = b.
*
B( N, J ) = B( N, J ) / D( N )
DO 20 I = N - 1, 1, -1
B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I )
20 CONTINUE
30 CONTINUE
*
RETURN
*
* End of SPTTS2
*
END
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