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@shBang #!/usr/bin/env python3
@*
RichardsonFixedStep.tmpl
Created by Sean Wild on 2013-10-10.
Copyright (c) 2007-2013, Graham Dennis
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*@
@extends xpdeint.Segments.Integrators._RichardsonFixedStep
@def description: segment $segmentNumber ($stepper.name fixed-step, fixed-order integrator with Richardson Extrapolation)
@attr $extrapolations = 4
@attr $supportsConstantIPOperators = False
@attr $maxIntegrationStepsVar = '_max_integration_steps'
@def localInitialise
@#
@super
@#
@for $vector in $integrationVectors
${vector.type}* _T0_${vector.id}[$extrapolations];
${vector.type}* _T1_${vector.id}[$extrapolations];
@for $i in range(0, $extrapolations)
_T0_${vector.id}[$i] = _rerow_T0_${i}_${vector.id};
_T1_${vector.id}[$i] = _rerow_T1_${i}_${vector.id};
@end for
${vector.type}** _Tprev_${vector.id} = _T0_${vector.id};
${vector.type}** _Tcurr_${vector.id} = _T1_${vector.id};
${vector.type}* _result_${vector.id};
@end for
${copyVectors($integrationVectors, '_re_reset')}@slurp
@end def
@*
Function prototypes
*@
@def functionPrototypes
@#
@super
@#
@for $vector in $integrationVectors
void _segment${segmentNumber}_${vector.id}_reset(${vector.type}* _reset_to);
@end for
@#
@end def
@def segmentFunctionBody($function) @* Overrides segmentFunctionBody of FixedStep *@
@#
${createStepVariable}@slurp
@#
@set $featureOrderingOuter = ['Stochastic']
${insertCodeForFeatures('integrateFixedStepBegin', featureOrderingOuter)}@slurp
${allocate}@slurp
${initialise}@slurp
${localInitialise}@slurp
for (long _istep = 0; _istep < ${stepCount}; _istep++) {
@# Insert code for features
@set $featureOrderingInner = ['Output', 'ErrorCheck', 'Stochastic']
@#
@set $dict = {'extraIndent': 0}
${insertCodeForFeatures('integrateFixedStepInnerLoopBegin', featureOrderingInner, dict), autoIndent=True}@slurp
@set $extraIndent = $dict.extraIndent
${preSingleStep, autoIndent=True, extraIndent=extraIndent}@slurp
${richardsonExtrapolate(function), autoIndent=True, extraIndent=extraIndent}@slurp
${postSingleStep, autoIndent=True, extraIndent=extraIndent}@slurp
@if $cross
@# If we are cross-integrating, then we now need to copy our result back
@# into the original arrays for the integration vectors
${copyResultIntoIntegrationArrays, autoIndent=True, extraIndent=extraIndent}@slurp
@end if
@#
${insertCodeForFeaturesInReverseOrder('integrateFixedStepInnerLoopEnd', featureOrderingInner, dict), autoIndent=True}@slurp
}
${localFinalise}@slurp
${finalise}@slurp
${free}@slurp
${insertCodeForFeaturesInReverseOrder('integrateFixedStepEnd', featureOrderingOuter)}@slurp
@#
@end def
@def richardsonExtrapolate($function)
@#
long _k = 0;
long _max_integration_steps = 0;
long _istep_temp = _istep;
real _step_temp = _step;
real _${propagationDimension}_temp = ${propagationDimension};
for (_k = 0; _k < $extrapolations; _k++)
{
// Swap active rows
{
@for $vector in $integrationVectors
${vector.type}** _temp_${vector.id} = _Tprev_${vector.id};
_Tprev_${vector.id} = _Tcurr_${vector.id};
_Tcurr_${vector.id} = _temp_${vector.id};
@end for
}
long _nk = 2 * (_k + 1);
_max_integration_steps = _nk;
_step = _step_temp / _nk;
${propagationDimension} = _${propagationDimension}_temp;
for (_istep = 0; _istep < _nk; _istep++) {
${stepper.singleIntegrationStep(function), autoIndent=True}@slurp
}
_istep = _istep_temp;
_step = _step_temp;
@for $vector in $integrationVectors
_result_${vector.id} = _Tcurr_${vector.id}[0];
@end for
${copyVectors($integrationVectors, '_result', '_active'), autoIndent=True}@slurp
for (long _j = 0; _j < _k; _j++)
{
real _nksubj = 2 * (_k - _j);
real _denominator = pow(((real)_nk) / _nksubj, 2) - 1.0;
@for $vector in $integrationVectors
${vector.type}* const _TcurrJPlusOne_${vector.id} = _Tcurr_${vector.id}[_j+1];
${vector.type}* const _TcurrJ_${vector.id} = _Tcurr_${vector.id}[_j];
${vector.type}* const _TprevJ_${vector.id} = _Tprev_${vector.id}[_j];
@end for
${loopOverVectorsWithInnerContentTemplate($integrationVectors,
"""_TcurrJPlusOne_${vector.id}[$index] = _TcurrJ_${vector.id}[$index] + (_TcurrJ_${vector.id}[$index] - _TprevJ_${vector.id}[$index]) / _denominator;
""", basis = $homeBasis), autoIndent=True}@slurp
}
// Reset
${copyVectors($integrationVectors, '_active', '_re_reset'), autoIndent=True}@slurp
}
@for $vector in $integrationVectors
_result_${vector.id} = _Tcurr_${vector.id}[_k-1];
@end for
${copyVectors($integrationVectors, '_active', '_result')}@slurp
${copyVectors($integrationVectors, '_re_reset', '_active')}@slurp
${propagationDimension} = _${propagationDimension}_temp + _step;
@#
@end def
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