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* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
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package org.apache.commons.math3.ode.nonstiff;
import java.util.Arrays;
import org.apache.commons.math3.RealFieldElement;
import org.apache.commons.math3.linear.Array2DRowFieldMatrix;
import org.apache.commons.math3.ode.FieldEquationsMapper;
import org.apache.commons.math3.ode.FieldODEStateAndDerivative;
import org.apache.commons.math3.ode.sampling.AbstractFieldStepInterpolator;
import org.apache.commons.math3.util.MathArrays;
/**
* This class implements an interpolator for Adams integrators using Nordsieck representation.
*
* <p>This interpolator computes dense output around the current point.
* The interpolation equation is based on Taylor series formulas.
*
* @see AdamsBashforthFieldIntegrator
* @see AdamsMoultonFieldIntegrator
* @param <T> the type of the field elements
* @since 3.6
*/
class AdamsFieldStepInterpolator<T extends RealFieldElement<T>> extends AbstractFieldStepInterpolator<T> {
/** Step size used in the first scaled derivative and Nordsieck vector. */
private T scalingH;
/** Reference state.
* <p>Sometimes, the reference state is the same as globalPreviousState,
* sometimes it is the same as globalCurrentState, so we use a separate
* field to avoid any confusion.
* </p>
*/
private final FieldODEStateAndDerivative<T> reference;
/** First scaled derivative. */
private final T[] scaled;
/** Nordsieck vector. */
private final Array2DRowFieldMatrix<T> nordsieck;
/** Simple constructor.
* @param stepSize step size used in the scaled and Nordsieck arrays
* @param reference reference state from which Taylor expansion are estimated
* @param scaled first scaled derivative
* @param nordsieck Nordsieck vector
* @param isForward integration direction indicator
* @param globalPreviousState start of the global step
* @param globalCurrentState end of the global step
* @param equationsMapper mapper for ODE equations primary and secondary components
*/
AdamsFieldStepInterpolator(final T stepSize, final FieldODEStateAndDerivative<T> reference,
final T[] scaled, final Array2DRowFieldMatrix<T> nordsieck,
final boolean isForward,
final FieldODEStateAndDerivative<T> globalPreviousState,
final FieldODEStateAndDerivative<T> globalCurrentState,
final FieldEquationsMapper<T> equationsMapper) {
this(stepSize, reference, scaled, nordsieck,
isForward, globalPreviousState, globalCurrentState,
globalPreviousState, globalCurrentState, equationsMapper);
}
/** Simple constructor.
* @param stepSize step size used in the scaled and Nordsieck arrays
* @param reference reference state from which Taylor expansion are estimated
* @param scaled first scaled derivative
* @param nordsieck Nordsieck vector
* @param isForward integration direction indicator
* @param globalPreviousState start of the global step
* @param globalCurrentState end of the global step
* @param softPreviousState start of the restricted step
* @param softCurrentState end of the restricted step
* @param equationsMapper mapper for ODE equations primary and secondary components
*/
private AdamsFieldStepInterpolator(final T stepSize, final FieldODEStateAndDerivative<T> reference,
final T[] scaled, final Array2DRowFieldMatrix<T> nordsieck,
final boolean isForward,
final FieldODEStateAndDerivative<T> globalPreviousState,
final FieldODEStateAndDerivative<T> globalCurrentState,
final FieldODEStateAndDerivative<T> softPreviousState,
final FieldODEStateAndDerivative<T> softCurrentState,
final FieldEquationsMapper<T> equationsMapper) {
super(isForward, globalPreviousState, globalCurrentState,
softPreviousState, softCurrentState, equationsMapper);
this.scalingH = stepSize;
this.reference = reference;
this.scaled = scaled.clone();
this.nordsieck = new Array2DRowFieldMatrix<T>(nordsieck.getData(), false);
}
/** Create a new instance.
* @param newForward integration direction indicator
* @param newGlobalPreviousState start of the global step
* @param newGlobalCurrentState end of the global step
* @param newSoftPreviousState start of the restricted step
* @param newSoftCurrentState end of the restricted step
* @param newMapper equations mapper for the all equations
* @return a new instance
*/
@Override
protected AdamsFieldStepInterpolator<T> create(boolean newForward,
FieldODEStateAndDerivative<T> newGlobalPreviousState,
FieldODEStateAndDerivative<T> newGlobalCurrentState,
FieldODEStateAndDerivative<T> newSoftPreviousState,
FieldODEStateAndDerivative<T> newSoftCurrentState,
FieldEquationsMapper<T> newMapper) {
return new AdamsFieldStepInterpolator<T>(scalingH, reference, scaled, nordsieck,
newForward,
newGlobalPreviousState, newGlobalCurrentState,
newSoftPreviousState, newSoftCurrentState,
newMapper);
}
/** {@inheritDoc} */
@Override
protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> equationsMapper,
final T time, final T theta,
final T thetaH, final T oneMinusThetaH) {
return taylor(reference, time, scalingH, scaled, nordsieck);
}
/** Estimate state by applying Taylor formula.
* @param reference reference state
* @param time time at which state must be estimated
* @param stepSize step size used in the scaled and Nordsieck arrays
* @param scaled first scaled derivative
* @param nordsieck Nordsieck vector
* @return estimated state
* @param <S> the type of the field elements
*/
public static <S extends RealFieldElement<S>> FieldODEStateAndDerivative<S> taylor(final FieldODEStateAndDerivative<S> reference,
final S time, final S stepSize,
final S[] scaled,
final Array2DRowFieldMatrix<S> nordsieck) {
final S x = time.subtract(reference.getTime());
final S normalizedAbscissa = x.divide(stepSize);
S[] stateVariation = MathArrays.buildArray(time.getField(), scaled.length);
Arrays.fill(stateVariation, time.getField().getZero());
S[] estimatedDerivatives = MathArrays.buildArray(time.getField(), scaled.length);
Arrays.fill(estimatedDerivatives, time.getField().getZero());
// apply Taylor formula from high order to low order,
// for the sake of numerical accuracy
final S[][] nData = nordsieck.getDataRef();
for (int i = nData.length - 1; i >= 0; --i) {
final int order = i + 2;
final S[] nDataI = nData[i];
final S power = normalizedAbscissa.pow(order);
for (int j = 0; j < nDataI.length; ++j) {
final S d = nDataI[j].multiply(power);
stateVariation[j] = stateVariation[j].add(d);
estimatedDerivatives[j] = estimatedDerivatives[j].add(d.multiply(order));
}
}
S[] estimatedState = reference.getState();
for (int j = 0; j < stateVariation.length; ++j) {
stateVariation[j] = stateVariation[j].add(scaled[j].multiply(normalizedAbscissa));
estimatedState[j] = estimatedState[j].add(stateVariation[j]);
estimatedDerivatives[j] =
estimatedDerivatives[j].add(scaled[j].multiply(normalizedAbscissa)).divide(x);
}
return new FieldODEStateAndDerivative<S>(time, estimatedState, estimatedDerivatives);
}
}