version 1.5, 2010/08/07 13:22:17
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version 1.12, 2012/12/14 12:30:22
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*> \brief \b DLAGTS solves the system of equations (T-λI)x = y or (T-λI)Tx = y,where T is a general tridiagonal matrix and λ a scalar, using the LU factorization computed by slagtf. |
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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 DLAGTS + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlagts.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/dlagts.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/dlagts.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 DLAGTS( JOB, N, A, B, C, D, IN, Y, TOL, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER INFO, JOB, N |
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* DOUBLE PRECISION TOL |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IN( * ) |
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* DOUBLE PRECISION A( * ), B( * ), C( * ), D( * ), Y( * ) |
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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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*> DLAGTS may be used to solve one of the systems of equations |
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*> |
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*> (T - lambda*I)*x = y or (T - lambda*I)**T*x = y, |
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*> |
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*> where T is an n by n tridiagonal matrix, for x, following the |
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*> factorization of (T - lambda*I) as |
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*> |
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*> (T - lambda*I) = P*L*U , |
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*> |
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*> by routine DLAGTF. The choice of equation to be solved is |
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*> controlled by the argument JOB, and in each case there is an option |
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*> to perturb zero or very small diagonal elements of U, this option |
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*> being intended for use in applications such as inverse iteration. |
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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] JOB |
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*> \verbatim |
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*> JOB is INTEGER |
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*> Specifies the job to be performed by DLAGTS as follows: |
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*> = 1: The equations (T - lambda*I)x = y are to be solved, |
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*> but diagonal elements of U are not to be perturbed. |
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*> = -1: The equations (T - lambda*I)x = y are to be solved |
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*> and, if overflow would otherwise occur, the diagonal |
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*> elements of U are to be perturbed. See argument TOL |
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*> below. |
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*> = 2: The equations (T - lambda*I)**Tx = y are to be solved, |
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*> but diagonal elements of U are not to be perturbed. |
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*> = -2: The equations (T - lambda*I)**Tx = y are to be solved |
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*> and, if overflow would otherwise occur, the diagonal |
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*> elements of U are to be perturbed. See argument TOL |
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*> below. |
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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 matrix T. |
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*> \endverbatim |
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*> |
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*> \param[in] A |
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*> \verbatim |
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*> A is DOUBLE PRECISION array, dimension (N) |
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*> On entry, A must contain the diagonal elements of U as |
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*> returned from DLAGTF. |
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*> \endverbatim |
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*> |
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*> \param[in] B |
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*> \verbatim |
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*> B is DOUBLE PRECISION array, dimension (N-1) |
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*> On entry, B must contain the first super-diagonal elements of |
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*> U as returned from DLAGTF. |
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*> \endverbatim |
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*> |
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*> \param[in] C |
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*> \verbatim |
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*> C is DOUBLE PRECISION array, dimension (N-1) |
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*> On entry, C must contain the sub-diagonal elements of L as |
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*> returned from DLAGTF. |
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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-2) |
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*> On entry, D must contain the second super-diagonal elements |
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*> of U as returned from DLAGTF. |
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*> \endverbatim |
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*> |
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*> \param[in] IN |
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*> \verbatim |
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*> IN is INTEGER array, dimension (N) |
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*> On entry, IN must contain details of the matrix P as returned |
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*> from DLAGTF. |
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*> \endverbatim |
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*> |
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*> \param[in,out] Y |
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*> \verbatim |
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*> Y is DOUBLE PRECISION array, dimension (N) |
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*> On entry, the right hand side vector y. |
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*> On exit, Y is overwritten by the solution vector x. |
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*> \endverbatim |
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*> |
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*> \param[in,out] TOL |
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*> \verbatim |
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*> TOL is DOUBLE PRECISION |
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*> On entry, with JOB .lt. 0, TOL should be the minimum |
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*> perturbation to be made to very small diagonal elements of U. |
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*> TOL should normally be chosen as about eps*norm(U), where eps |
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*> is the relative machine precision, but if TOL is supplied as |
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*> non-positive, then it is reset to eps*max( abs( u(i,j) ) ). |
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*> If JOB .gt. 0 then TOL is not referenced. |
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*> |
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*> On exit, TOL is changed as described above, only if TOL is |
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*> non-positive on entry. Otherwise TOL is unchanged. |
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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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*> .lt. 0: if INFO = -i, the i-th argument had an illegal value |
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*> .gt. 0: overflow would occur when computing the INFO(th) |
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*> element of the solution vector x. This can only occur |
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*> when JOB is supplied as positive and either means |
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*> that a diagonal element of U is very small, or that |
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*> the elements of the right-hand side vector y are very |
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*> large. |
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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 September 2012 |
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* |
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*> \ingroup auxOTHERauxiliary |
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* |
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* ===================================================================== |
SUBROUTINE DLAGTS( JOB, N, A, B, C, D, IN, Y, TOL, INFO ) |
SUBROUTINE DLAGTS( JOB, N, A, B, C, D, IN, Y, TOL, INFO ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.2) -- |
* -- LAPACK auxiliary routine (version 3.4.2) -- |
* -- 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 |
* September 2012 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INFO, JOB, N |
INTEGER INFO, JOB, N |
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DOUBLE PRECISION A( * ), B( * ), C( * ), D( * ), Y( * ) |
DOUBLE PRECISION A( * ), B( * ), C( * ), D( * ), Y( * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* DLAGTS may be used to solve one of the systems of equations |
|
* |
|
* (T - lambda*I)*x = y or (T - lambda*I)'*x = y, |
|
* |
|
* where T is an n by n tridiagonal matrix, for x, following the |
|
* factorization of (T - lambda*I) as |
|
* |
|
* (T - lambda*I) = P*L*U , |
|
* |
|
* by routine DLAGTF. The choice of equation to be solved is |
|
* controlled by the argument JOB, and in each case there is an option |
|
* to perturb zero or very small diagonal elements of U, this option |
|
* being intended for use in applications such as inverse iteration. |
|
* |
|
* Arguments |
|
* ========= |
|
* |
|
* JOB (input) INTEGER |
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* Specifies the job to be performed by DLAGTS as follows: |
|
* = 1: The equations (T - lambda*I)x = y are to be solved, |
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* but diagonal elements of U are not to be perturbed. |
|
* = -1: The equations (T - lambda*I)x = y are to be solved |
|
* and, if overflow would otherwise occur, the diagonal |
|
* elements of U are to be perturbed. See argument TOL |
|
* below. |
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* = 2: The equations (T - lambda*I)'x = y are to be solved, |
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* but diagonal elements of U are not to be perturbed. |
|
* = -2: The equations (T - lambda*I)'x = y are to be solved |
|
* and, if overflow would otherwise occur, the diagonal |
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* elements of U are to be perturbed. See argument TOL |
|
* below. |
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* |
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* N (input) INTEGER |
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* The order of the matrix T. |
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* |
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* A (input) DOUBLE PRECISION array, dimension (N) |
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* On entry, A must contain the diagonal elements of U as |
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* returned from DLAGTF. |
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* |
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* B (input) DOUBLE PRECISION array, dimension (N-1) |
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* On entry, B must contain the first super-diagonal elements of |
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* U as returned from DLAGTF. |
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* |
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* C (input) DOUBLE PRECISION array, dimension (N-1) |
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* On entry, C must contain the sub-diagonal elements of L as |
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* returned from DLAGTF. |
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* |
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* D (input) DOUBLE PRECISION array, dimension (N-2) |
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* On entry, D must contain the second super-diagonal elements |
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* of U as returned from DLAGTF. |
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* |
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* IN (input) INTEGER array, dimension (N) |
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* On entry, IN must contain details of the matrix P as returned |
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* from DLAGTF. |
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* |
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* Y (input/output) DOUBLE PRECISION array, dimension (N) |
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* On entry, the right hand side vector y. |
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* On exit, Y is overwritten by the solution vector x. |
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* |
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* TOL (input/output) DOUBLE PRECISION |
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* On entry, with JOB .lt. 0, TOL should be the minimum |
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* perturbation to be made to very small diagonal elements of U. |
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* TOL should normally be chosen as about eps*norm(U), where eps |
|
* is the relative machine precision, but if TOL is supplied as |
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* non-positive, then it is reset to eps*max( abs( u(i,j) ) ). |
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* If JOB .gt. 0 then TOL is not referenced. |
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* |
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* On exit, TOL is changed as described above, only if TOL is |
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* non-positive on entry. Otherwise TOL is unchanged. |
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* |
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* INFO (output) INTEGER |
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* = 0 : successful exit |
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* .lt. 0: if INFO = -i, the i-th argument had an illegal value |
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* .gt. 0: overflow would occur when computing the INFO(th) |
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* element of the solution vector x. This can only occur |
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* when JOB is supplied as positive and either means |
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* that a diagonal element of U is very small, or that |
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* the elements of the right-hand side vector y are very |
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* large. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |