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Java example source code file (DormandPrince54FieldIntegrator.java)

This example Java source code file (DormandPrince54FieldIntegrator.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

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Java - Java tags/keywords

dormand-prince, dormandprince54fieldintegrator, dormandprince54fieldstepinterpolator, embeddedrungekuttafieldintegrator, fieldequationsmapper, fieldodestateandderivative, method_name, override, realfieldelement, string

The DormandPrince54FieldIntegrator.java Java example source code

/*
 * 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
 *
 *      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
 * limitations under the License.
 */

package org.apache.commons.math3.ode.nonstiff;

import org.apache.commons.math3.Field;
import org.apache.commons.math3.RealFieldElement;
import org.apache.commons.math3.ode.FieldEquationsMapper;
import org.apache.commons.math3.ode.FieldODEStateAndDerivative;
import org.apache.commons.math3.util.MathArrays;
import org.apache.commons.math3.util.MathUtils;


/**
 * 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, 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 :
 * <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 * @since 3.6 */ public class DormandPrince54FieldIntegrator<T extends RealFieldElement extends EmbeddedRungeKuttaFieldIntegrator<T> { /** Integrator method name. */ private static final String METHOD_NAME = "Dormand-Prince 5(4)"; /** Error array, element 1. */ private final T e1; // element 2 is zero, so it is neither stored nor used /** Error array, element 3. */ private final T e3; /** Error array, element 4. */ private final T e4; /** Error array, element 5. */ private final T e5; /** Error array, element 6. */ private final T e6; /** Error array, element 7. */ private final T e7; /** 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); e1 = fraction( 71, 57600); e3 = fraction( -71, 16695); e4 = fraction( 71, 1920); e5 = fraction(-17253, 339200); e6 = fraction( 22, 525); e7 = fraction( -1, 40); } /** 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, METHOD_NAME, 6, minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance); e1 = fraction( 71, 57600); e3 = fraction( -71, 16695); e4 = fraction( 71, 1920); e5 = fraction(-17253, 339200); e6 = fraction( 22, 525); e7 = fraction( -1, 40); } /** {@inheritDoc} */ public T[] getC() { final T[] c = MathArrays.buildArray(getField(), 6); c[0] = fraction(1, 5); c[1] = fraction(3, 10); c[2] = fraction(4, 5); c[3] = fraction(8, 9); c[4] = getField().getOne(); c[5] = getField().getOne(); return c; } /** {@inheritDoc} */ 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] = fraction( 1, 5); a[1][0] = fraction( 3, 40); a[1][1] = fraction( 9, 40); a[2][0] = fraction( 44, 45); a[2][1] = fraction( -56, 15); a[2][2] = fraction( 32, 9); a[3][0] = fraction( 19372, 6561); a[3][1] = fraction(-25360, 2187); a[3][2] = fraction( 64448, 6561); a[3][3] = fraction( -212, 729); a[4][0] = fraction( 9017, 3168); a[4][1] = fraction( -355, 33); a[4][2] = fraction( 46732, 5247); a[4][3] = fraction( 49, 176); a[4][4] = fraction( -5103, 18656); a[5][0] = fraction( 35, 384); a[5][1] = getField().getZero(); a[5][2] = fraction( 500, 1113); a[5][3] = fraction( 125, 192); a[5][4] = fraction( -2187, 6784); a[5][5] = fraction( 11, 84); return a; } /** {@inheritDoc} */ public T[] getB() { final T[] b = MathArrays.buildArray(getField(), 7); b[0] = fraction( 35, 384); b[1] = getField().getZero(); b[2] = fraction( 500, 1113); b[3] = fraction( 125, 192); b[4] = fraction(-2187, 6784); b[5] = fraction( 11, 84); b[6] = getField().getZero(); return b; } /** {@inheritDoc} */ @Override protected DormandPrince54FieldStepInterpolator<T> createInterpolator(final boolean forward, T[][] yDotK, final FieldODEStateAndDerivative<T> globalPreviousState, final FieldODEStateAndDerivative<T> globalCurrentState, final FieldEquationsMapper mapper) { return new DormandPrince54FieldStepInterpolator<T>(getField(), forward, yDotK, globalPreviousState, globalCurrentState, globalPreviousState, globalCurrentState, mapper); } /** {@inheritDoc} */ @Override public int getOrder() { return 5; } /** {@inheritDoc} */ @Override protected T estimateError(final T[][] yDotK, final T[] y0, final T[] y1, final T h) { T error = getField().getZero(); for (int j = 0; j < mainSetDimension; ++j) { final T errSum = yDotK[0][j].multiply(e1). add(yDotK[2][j].multiply(e3)). add(yDotK[3][j].multiply(e4)). add(yDotK[4][j].multiply(e5)). add(yDotK[5][j].multiply(e6)). add(yDotK[6][j].multiply(e7)); final T yScale = MathUtils.max(y0[j].abs(), y1[j].abs()); final T tol = (vecAbsoluteTolerance == null) ? yScale.multiply(scalRelativeTolerance).add(scalAbsoluteTolerance) : yScale.multiply(vecRelativeTolerance[j]).add(vecAbsoluteTolerance[j]); final T ratio = h.multiply(errSum).divide(tol); error = error.add(ratio.multiply(ratio)); } return error.divide(mainSetDimension).sqrt(); } }

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