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
- *
- * 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.math4.legacy.ode.nonstiff;
- import org.apache.commons.math4.legacy.core.Field;
- import org.apache.commons.math4.legacy.core.RealFieldElement;
- import org.apache.commons.math4.legacy.ode.FieldEquationsMapper;
- import org.apache.commons.math4.legacy.ode.FieldODEStateAndDerivative;
- import org.apache.commons.math4.legacy.core.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 :
- * <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<T>>
- 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} */
- @Override
- 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} */
- @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] = 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} */
- @Override
- 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<T> mapper) {
- return new DormandPrince54FieldStepInterpolator<>(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 = RealFieldElement.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();
- }
- }