DormandPrince54FieldIntegrator.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,
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* See the License for the specific language governing permissions and
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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.ode.FieldEquationsMapper;
import org.hipparchus.ode.FieldODEStateAndDerivative;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathArrays;
/**
* This class implements the 5(4) Dormand-Prince integrator for Ordinary
* Differential Equations.
* <p>This integrator is an embedded Runge-Kutta integrator
* of order 5(4) used in local extrapolation mode (i.e. the solution
* is computed using the high order formula) with stepsize control
* (and automatic step initialization) and continuous output. This
* method uses 7 functions evaluations per step. However, since this
* is an <i>fsal</i>, the last evaluation of one step is the same as
* the first evaluation of the next step and hence can be avoided. So
* the cost is really 6 functions evaluations per step.</p>
*
* <p>This method has been published (whithout the continuous output
* that was added by Shampine in 1986) in the following article :</p>
* <pre>
* A family of embedded Runge-Kutta formulae
* J. R. Dormand and P. J. Prince
* Journal of Computational and Applied Mathematics
* volume 6, no 1, 1980, pp. 19-26
* </pre>
*
* @param <T> the type of the field elements
*/
public class DormandPrince54FieldIntegrator<T extends CalculusFieldElement<T>>
extends EmbeddedRungeKuttaFieldIntegrator<T> {
/** Name of integration scheme. */
public static final String METHOD_NAME = DormandPrince54Integrator.METHOD_NAME;
/** Simple constructor.
* Build a fifth order Dormand-Prince integrator with the given step bounds
* @param field field to which the time and state vector elements belong
* @param minStep minimal step (sign is irrelevant, regardless of
* integration direction, forward or backward), the last step can
* be smaller than this
* @param maxStep maximal step (sign is irrelevant, regardless of
* integration direction, forward or backward), the last step can
* be smaller than this
* @param scalAbsoluteTolerance allowed absolute error
* @param scalRelativeTolerance allowed relative error
*/
public DormandPrince54FieldIntegrator(final Field<T> field,
final double minStep, final double maxStep,
final double scalAbsoluteTolerance,
final double scalRelativeTolerance) {
super(field, METHOD_NAME, 6,
minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
}
/** Simple constructor.
* Build a fifth order Dormand-Prince integrator with the given step bounds
* @param field field to which the time and state vector elements belong
* @param minStep minimal step (sign is irrelevant, regardless of
* integration direction, forward or backward), the last step can
* be smaller than this
* @param maxStep maximal step (sign is irrelevant, regardless of
* integration direction, forward or backward), the last step can
* be smaller than this
* @param vecAbsoluteTolerance allowed absolute error
* @param vecRelativeTolerance allowed relative error
*/
public DormandPrince54FieldIntegrator(final Field<T> field,
final double minStep, final double maxStep,
final double[] vecAbsoluteTolerance,
final double[] vecRelativeTolerance) {
super(field, DormandPrince54Integrator.METHOD_NAME, 6,
minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
}
/** {@inheritDoc} */
@Override
public T[] getC() {
final T[] c = MathArrays.buildArray(getField(), 6);
c[0] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 1, 5);
c[1] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 3, 10);
c[2] = FieldExplicitRungeKuttaIntegrator.fraction(getField(),4, 5);
c[3] = FieldExplicitRungeKuttaIntegrator.fraction(getField(),8, 9);
c[4] = getField().getOne();
c[5] = getField().getOne();
return c;
}
/** {@inheritDoc} */
@Override
public T[][] getA() {
final T[][] a = MathArrays.buildArray(getField(), 6, -1);
for (int i = 0; i < a.length; ++i) {
a[i] = MathArrays.buildArray(getField(), i + 1);
}
a[0][0] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 1, 5);
a[1][0] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 3, 40);
a[1][1] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 9, 40);
a[2][0] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 44, 45);
a[2][1] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), -56, 15);
a[2][2] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 32, 9);
a[3][0] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 19372, 6561);
a[3][1] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), -25360, 2187);
a[3][2] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 64448, 6561);
a[3][3] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), -212, 729);
a[4][0] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 9017, 3168);
a[4][1] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), -355, 33);
a[4][2] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 46732, 5247);
a[4][3] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 49, 176);
a[4][4] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), -5103, 18656);
a[5][0] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 35, 384);
a[5][1] = getField().getZero();
a[5][2] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 500, 1113);
a[5][3] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 125, 192);
a[5][4] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), -2187, 6784);
a[5][5] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 11, 84);
return a;
}
/** {@inheritDoc} */
@Override
public T[] getB() {
final T[] b = MathArrays.buildArray(getField(), 7);
b[0] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 35, 384);
b[1] = getField().getZero();
b[2] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 500, 1113);
b[3] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 125, 192);
b[4] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), -2187, 6784);
b[5] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 11, 84);
b[6] = getField().getZero();
return b;
}
/** {@inheritDoc} */
@Override
protected DormandPrince54FieldStateInterpolator<T>
createInterpolator(final boolean forward, T[][] yDotK,
final FieldODEStateAndDerivative<T> globalPreviousState,
final FieldODEStateAndDerivative<T> globalCurrentState, final FieldEquationsMapper<T> mapper) {
return new DormandPrince54FieldStateInterpolator<T>(getField(), forward, yDotK,
globalPreviousState, globalCurrentState,
globalPreviousState, globalCurrentState,
mapper);
}
/** {@inheritDoc} */
@Override
public int getOrder() {
return 5;
}
/** {@inheritDoc} */
@Override
protected double estimateError(final T[][] yDotK, final T[] y0, final T[] y1, final T h) {
final StepsizeHelper helper = getStepSizeHelper();
double error = 0;
for (int j = 0; j < helper.getMainSetDimension(); ++j) {
final double errSum = DormandPrince54Integrator.E1 * yDotK[0][j].getReal() + DormandPrince54Integrator.E3 * yDotK[2][j].getReal() +
DormandPrince54Integrator.E4 * yDotK[3][j].getReal() + DormandPrince54Integrator.E5 * yDotK[4][j].getReal() +
DormandPrince54Integrator.E6 * yDotK[5][j].getReal() + DormandPrince54Integrator.E7 * yDotK[6][j].getReal();
final double tol = helper.getTolerance(j, FastMath.max(FastMath.abs(y0[j].getReal()), FastMath.abs(y1[j].getReal())));
final double ratio = h.getReal() * errSum / tol;
error += ratio * ratio;
}
return FastMath.sqrt(error / helper.getMainSetDimension());
}
}