RungeKuttaFieldIntegrator.java
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* 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
*
* https://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
* limitations under the License.
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/*
* This is not the original file distributed by the Apache Software Foundation
* It has been modified by the Hipparchus project
*/
package org.hipparchus.ode.nonstiff;
import org.hipparchus.CalculusFieldElement;
import org.hipparchus.Field;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.exception.MathIllegalStateException;
import org.hipparchus.ode.AbstractFieldIntegrator;
import org.hipparchus.ode.FieldEquationsMapper;
import org.hipparchus.ode.FieldExpandableODE;
import org.hipparchus.ode.FieldODEState;
import org.hipparchus.ode.FieldODEStateAndDerivative;
import org.hipparchus.util.MathArrays;
/**
* This class implements the common part of all fixed step Runge-Kutta
* integrators for Ordinary Differential Equations.
*
* <p>These methods are explicit Runge-Kutta methods, their Butcher
* arrays are as follows :</p>
* <pre>
* 0 |
* c2 | a21
* c3 | a31 a32
* ... | ...
* cs | as1 as2 ... ass-1
* |--------------------------
* | b1 b2 ... bs-1 bs
* </pre>
*
* @see EulerFieldIntegrator
* @see ClassicalRungeKuttaFieldIntegrator
* @see GillFieldIntegrator
* @see MidpointFieldIntegrator
* @param <T> the type of the field elements
*/
public abstract class RungeKuttaFieldIntegrator<T extends CalculusFieldElement<T>>
extends AbstractFieldIntegrator<T> implements FieldExplicitRungeKuttaIntegrator<T> {
/** Time steps from Butcher array (without the first zero). */
private final T[] c;
/** Internal weights from Butcher array (without the first empty row). */
private final T[][] a;
/** External weights for the high order method from Butcher array. */
private final T[] b;
/** Time steps from Butcher array (without the first zero). */
private double[] realC = new double[0];
/** Internal weights from Butcher array (without the first empty row). Real version, optional. */
private double[][] realA = new double[0][];
/** External weights for the high order method from Butcher array. Real version, optional. */
private double[] realB = new double[0];
/** Integration step. */
private final T step;
/** Flag setting whether coefficients in Butcher array are interpreted as Field or real numbers. */
private boolean usingFieldCoefficients;
/** Simple constructor.
* Build a Runge-Kutta integrator with the given
* step. The default step handler does nothing.
* @param field field to which the time and state vector elements belong
* @param name name of the method
* @param step integration step
*/
protected RungeKuttaFieldIntegrator(final Field<T> field, final String name, final T step) {
super(field, name);
this.c = getC();
this.a = getA();
this.b = getB();
this.step = step.abs();
this.usingFieldCoefficients = false;
}
/** Getter for the default, positive step-size assigned at constructor level.
* @return step
*/
public T getDefaultStep() {
return this.step;
}
/**
* Setter for the flag between real or Field coefficients in the Butcher array.
*
* @param usingFieldCoefficients new value for flag
*/
public void setUsingFieldCoefficients(boolean usingFieldCoefficients) {
this.usingFieldCoefficients = usingFieldCoefficients;
}
/** {@inheritDoc} */
@Override
public boolean isUsingFieldCoefficients() {
return usingFieldCoefficients;
}
/** {@inheritDoc} */
@Override
public int getNumberOfStages() {
return b.length;
}
/** Create an interpolator.
* @param forward integration direction indicator
* @param yDotK slopes at the intermediate points
* @param globalPreviousState start of the global step
* @param globalCurrentState end of the global step
* @param mapper equations mapper for the all equations
* @return external weights for the high order method from Butcher array
*/
protected abstract RungeKuttaFieldStateInterpolator<T> createInterpolator(boolean forward, T[][] yDotK,
FieldODEStateAndDerivative<T> globalPreviousState,
FieldODEStateAndDerivative<T> globalCurrentState,
FieldEquationsMapper<T> mapper);
/** {@inheritDoc} */
@Override
protected FieldODEStateAndDerivative<T> initIntegration(FieldExpandableODE<T> eqn, FieldODEState<T> s0, T t) {
if (!isUsingFieldCoefficients()) {
realA = getRealA();
realB = getRealB();
realC = getRealC();
}
return super.initIntegration(eqn, s0, t);
}
/** {@inheritDoc} */
@Override
public FieldODEStateAndDerivative<T> integrate(final FieldExpandableODE<T> equations,
final FieldODEState<T> initialState, final T finalTime)
throws MathIllegalArgumentException, MathIllegalStateException {
sanityChecks(initialState, finalTime);
setStepStart(initIntegration(equations, initialState, finalTime));
final boolean forward = finalTime.subtract(initialState.getTime()).getReal() > 0;
// create some internal working arrays
final int stages = getNumberOfStages();
final T[][] yDotK = MathArrays.buildArray(getField(), stages, -1);
MathArrays.buildArray(getField(), equations.getMapper().getTotalDimension());
// set up integration control objects
if (forward) {
if (getStepStart().getTime().add(step).subtract(finalTime).getReal() >= 0) {
setStepSize(finalTime.subtract(getStepStart().getTime()));
} else {
setStepSize(step);
}
} else {
if (getStepStart().getTime().subtract(step).subtract(finalTime).getReal() <= 0) {
setStepSize(finalTime.subtract(getStepStart().getTime()));
} else {
setStepSize(step.negate());
}
}
// main integration loop
setIsLastStep(false);
do {
// first stage
final T[] y = getStepStart().getCompleteState();
yDotK[0] = getStepStart().getCompleteDerivative();
// next stages
final T[] yTmp;
if (isUsingFieldCoefficients()) {
FieldExplicitRungeKuttaIntegrator.applyInternalButcherWeights(getEquations(), getStepStart().getTime(),
y, getStepSize(), a, c, yDotK);
yTmp = FieldExplicitRungeKuttaIntegrator.applyExternalButcherWeights(y, yDotK, getStepSize(), b);
} else {
FieldExplicitRungeKuttaIntegrator.applyInternalButcherWeights(getEquations(), getStepStart().getTime(),
y, getStepSize(), realA, realC, yDotK);
yTmp = FieldExplicitRungeKuttaIntegrator.applyExternalButcherWeights(y, yDotK, getStepSize(), realB);
}
incrementEvaluations(stages - 1);
final T stepEnd = getStepStart().getTime().add(getStepSize());
final T[] yDotTmp = computeDerivatives(stepEnd, yTmp);
final FieldODEStateAndDerivative<T> stateTmp = equations.getMapper().mapStateAndDerivative(stepEnd, yTmp, yDotTmp);
// discrete events handling
setStepStart(acceptStep(createInterpolator(forward, yDotK, getStepStart(), stateTmp, equations.getMapper()),
finalTime));
if (!isLastStep()) {
// stepsize control for next step
final T nextT = getStepStart().getTime().add(getStepSize());
final boolean nextIsLast = forward ?
(nextT.subtract(finalTime).getReal() >= 0) :
(nextT.subtract(finalTime).getReal() <= 0);
if (nextIsLast) {
setStepSize(finalTime.subtract(getStepStart().getTime()));
}
}
} while (!isLastStep());
final FieldODEStateAndDerivative<T> finalState = getStepStart();
setStepStart(null);
setStepSize(null);
return finalState;
}
}