*> \brief \b DPTTS2 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 DPTTS2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DPTTS2( N, NRHS, D, E, B, LDB ) * * .. Scalar Arguments .. * INTEGER LDB, N, NRHS * .. * .. Array Arguments .. * DOUBLE PRECISION B( LDB, * ), D( * ), E( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DPTTS2 solves a tridiagonal system of the form *> A * X = B *> using the L*D*L**T factorization of A computed by DPTTRF. 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 doublePTcomputational * * ===================================================================== SUBROUTINE DPTTS2( 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 .. DOUBLE PRECISION B( LDB, * ), D( * ), E( * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER I, J * .. * .. External Subroutines .. EXTERNAL DSCAL * .. * .. Executable Statements .. * * Quick return if possible * IF( N.LE.1 ) THEN IF( N.EQ.1 ) \$ CALL DSCAL( NRHS, 1.D0 / 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 DPTTS2 * END