Field-based version of midpoint method for solving ODE.
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Luc Maisonobe
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/*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with
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* this work for additional information regarding copyright ownership.
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* The ASF licenses this file to You under the Apache License, Version 2.0
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* (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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package org.apache.commons.math4.ode.nonstiff;
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import org.apache.commons.math4.Field;
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import org.apache.commons.math4.RealFieldElement;
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/**
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* This class implements a second order Runge-Kutta integrator for
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* Ordinary Differential Equations.
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*
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* <p>This method is an explicit Runge-Kutta method, its Butcher-array
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* is the following one :
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* <pre>
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* 0 | 0 0
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* 1/2 | 1/2 0
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* |----------
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* | 0 1
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* </pre>
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* </p>
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*
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* @see EulerFieldIntegrator
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* @see ClassicalRungeKuttaFieldIntegrator
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* @see GillFieldIntegrator
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* @see ThreeEighthesFieldIntegrator
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* @see LutherFieldIntegrator
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*
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* @param <T> the type of the field elements
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* @since 3.6
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*/
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public class MidpointFieldIntegrator<T extends RealFieldElement<T>> extends RungeKuttaFieldIntegrator<T> {
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/** Time steps Butcher array. */
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private static final double[] STATIC_C = {
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1.0 / 2.0
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};
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/** Internal weights Butcher array. */
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private static final double[][] STATIC_A = {
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{ 1.0 / 2.0 }
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};
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/** Propagation weights Butcher array. */
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private static final double[] STATIC_B = {
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0.0, 1.0
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};
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/** Simple constructor.
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* Build a midpoint integrator with the given step.
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* @param field field to which the time and state vector elements belong
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* @param step integration step
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*/
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public MidpointFieldIntegrator(final Field<T> field, final T step) {
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super(field, "midpoint", STATIC_C, STATIC_A, STATIC_B, new MidpointFieldStepInterpolator<T>(), step);
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}
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}
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@ -0,0 +1,119 @@
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/*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with
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* this work for additional information regarding copyright ownership.
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* The ASF licenses this file to You under the Apache License, Version 2.0
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* (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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package org.apache.commons.math4.ode.nonstiff;
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import org.apache.commons.math4.RealFieldElement;
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import org.apache.commons.math4.ode.FieldEquationsMapper;
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import org.apache.commons.math4.ode.FieldODEStateAndDerivative;
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import org.apache.commons.math4.util.MathArrays;
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/**
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* This class implements a step interpolator for second order
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* Runge-Kutta integrator.
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*
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* <p>This interpolator computes dense output inside the last
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* step computed. The interpolation equation is consistent with the
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* integration scheme :
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* <ul>
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* <li>Using reference point at step start:<br>
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* y(t<sub>n</sub> + θ h) = y (t<sub>n</sub>) + θ h [(1 - θ) y'<sub>1</sub> + θ y'<sub>2</sub>]
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* </li>
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* <li>Using reference point at step end:<br>
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* y(t<sub>n</sub> + θ h) = y (t<sub>n</sub> + h) + (1-θ) h [θ y'<sub>1</sub> - (1+θ) y'<sub>2</sub>]
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* </li>
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* </ul>
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* </p>
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*
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* where θ belongs to [0 ; 1] and where y'<sub>1</sub> and y'<sub>2</sub> are the two
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* evaluations of the derivatives already computed during the
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* step.</p>
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*
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* @see MidpointFieldIntegrator
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* @param <T> the type of the field elements
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* @since 3.6
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*/
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class MidpointFieldStepInterpolator<T extends RealFieldElement<T>>
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extends RungeKuttaFieldStepInterpolator<T> {
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/** Simple constructor.
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* This constructor builds an instance that is not usable yet, the
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* {@link
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* org.apache.commons.math4.ode.sampling.AbstractStepInterpolator#reinitialize}
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* method should be called before using the instance in order to
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* initialize the internal arrays. This constructor is used only
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* in order to delay the initialization in some cases. The {@link
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* RungeKuttaFieldIntegrator} class uses the prototyping design pattern
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* to create the step interpolators by cloning an uninitialized model
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* and later initializing the copy.
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*/
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MidpointFieldStepInterpolator() {
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}
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/** Copy constructor.
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* @param interpolator interpolator to copy from. The copy is a deep
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* copy: its arrays are separated from the original arrays of the
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* instance
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*/
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MidpointFieldStepInterpolator(final MidpointFieldStepInterpolator<T> interpolator) {
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super(interpolator);
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}
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/** {@inheritDoc} */
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@Override
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protected MidpointFieldStepInterpolator<T> doCopy() {
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return new MidpointFieldStepInterpolator<T>(this);
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}
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/** {@inheritDoc} */
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@Override
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protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> mapper,
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final T time, final T theta,
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final T oneMinusThetaH) {
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final T coeffDot2 = theta.multiply(2);
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final T coeffDot1 = time.getField().getOne().subtract(coeffDot2);
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final T[] interpolatedState = MathArrays.buildArray(theta.getField(), previousState.length);
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final T[] interpolatedDerivatives = MathArrays.buildArray(theta.getField(), previousState.length);
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if ((previousState != null) && (theta.getReal() <= 0.5)) {
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final T coeff1 = theta.multiply(oneMinusThetaH);
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final T coeff2 = theta.multiply(theta).multiply(h);
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for (int i = 0; i < previousState.length; ++i) {
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final T yDot1 = yDotK[0][i];
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final T yDot2 = yDotK[1][i];
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interpolatedState[i] = previousState[i].add(coeff1.multiply(yDot1)).add(coeff2.multiply(yDot2));
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interpolatedDerivatives[i] = coeffDot1.multiply(yDot1).add(coeffDot2.multiply(yDot2));
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}
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} else {
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final T coeff1 = oneMinusThetaH.multiply(theta);
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final T coeff2 = oneMinusThetaH.multiply(theta.add(1));
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for (int i = 0; i < previousState.length; ++i) {
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final T yDot1 = yDotK[0][i];
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final T yDot2 = yDotK[1][i];
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interpolatedState[i] = currentState[i].add(coeff1.multiply(yDot1)).subtract(coeff2.multiply(yDot2));
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interpolatedDerivatives[i] = coeffDot1.multiply(yDot1).add(coeffDot2.multiply(yDot2));
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}
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}
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return new FieldODEStateAndDerivative<T>(time, interpolatedState, yDotK[0]);
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}
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}
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