version 1.4, 2010/08/06 15:32:33
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version 1.16, 2017/06/17 10:54:02
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*> \brief \b DPTTS2 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 DPTTS2 + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dptts2.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/dptts2.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/dptts2.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 DPTTS2( N, NRHS, D, E, B, LDB ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER LDB, N, NRHS |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION 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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*> DPTTS2 solves a tridiagonal system of the form |
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*> A * X = B |
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*> using the L*D*L**T factorization of A computed by DPTTRF. D is a |
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*> diagonal matrix specified in the vector D, L is a unit bidiagonal |
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*> matrix whose subdiagonal is specified in the vector E, and X and B |
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*> 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] 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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*> L*D*L**T factorization of A. |
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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 DOUBLE PRECISION array, dimension (N-1) |
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*> The (n-1) subdiagonal elements of the unit bidiagonal factor |
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*> L from the L*D*L**T factorization of A. E can also be regarded |
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*> as the superdiagonal of the unit bidiagonal factor U from the |
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*> factorization A = U**T*D*U. |
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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 DOUBLE PRECISION 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 December 2016 |
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* |
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*> \ingroup doublePTcomputational |
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* |
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* ===================================================================== |
SUBROUTINE DPTTS2( N, NRHS, D, E, B, LDB ) |
SUBROUTINE DPTTS2( N, NRHS, D, E, B, LDB ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine (version 3.7.0) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* December 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER LDB, N, NRHS |
INTEGER LDB, N, NRHS |
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DOUBLE PRECISION B( LDB, * ), D( * ), E( * ) |
DOUBLE PRECISION B( LDB, * ), D( * ), E( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DPTTS2 solves a tridiagonal system of the form |
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* A * X = B |
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* using the L*D*L' factorization of A computed by DPTTRF. D is a |
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* diagonal matrix specified in the vector D, L is a unit bidiagonal |
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* matrix whose subdiagonal is specified in the vector E, and X and B |
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* are N by NRHS matrices. |
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* |
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* Arguments |
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* ========= |
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* |
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* N (input) INTEGER |
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* The order of the tridiagonal matrix A. N >= 0. |
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* |
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* NRHS (input) 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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* |
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* D (input) DOUBLE PRECISION array, dimension (N) |
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* The n diagonal elements of the diagonal matrix D from the |
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* L*D*L' factorization of A. |
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* |
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* E (input) DOUBLE PRECISION array, dimension (N-1) |
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* The (n-1) subdiagonal elements of the unit bidiagonal factor |
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* L from the L*D*L' factorization of A. E can also be regarded |
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* as the superdiagonal of the unit bidiagonal factor U from the |
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* factorization A = U'*D*U. |
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* |
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* B (input/output) DOUBLE PRECISION 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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* |
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* LDB (input) INTEGER |
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* The leading dimension of the array B. LDB >= max(1,N). |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Local Scalars .. |
* .. Local Scalars .. |
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RETURN |
RETURN |
END IF |
END IF |
* |
* |
* Solve A * X = B using the factorization A = L*D*L', |
* Solve A * X = B using the factorization A = L*D*L**T, |
* overwriting each right hand side vector with its solution. |
* overwriting each right hand side vector with its solution. |
* |
* |
DO 30 J = 1, NRHS |
DO 30 J = 1, NRHS |
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B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 ) |
B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 ) |
10 CONTINUE |
10 CONTINUE |
* |
* |
* Solve D * L' * x = b. |
* Solve D * L**T * x = b. |
* |
* |
B( N, J ) = B( N, J ) / D( N ) |
B( N, J ) = B( N, J ) / D( N ) |
DO 20 I = N - 1, 1, -1 |
DO 20 I = N - 1, 1, -1 |