/*
* 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.ode.sampling.StepInterpolator;
/**
* This class implements a step interpolator for second order
* Runge-Kutta integrator.
*
* <p>This interpolator computes dense output inside the last
* step computed. The interpolation equation is consistent with the
* integration scheme :
* <ul>
* <li>Using reference point at step start:<br>
* 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>]
* </li>
* <li>Using reference point at step end:<br>
* 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>]
* </li>
* </ul>
* </p>
*
* where θ belongs to [0 ; 1] and where y'<sub>1</sub> and y'<sub>2</sub> are the two
* evaluations of the derivatives already computed during the
* step.</p>
*
* @see MidpointIntegrator
* @since 1.2
*/
class MidpointStepInterpolator
extends RungeKuttaStepInterpolator {
/** Serializable version identifier */
private static final long serialVersionUID = 20111120L;
/** Simple constructor.
* This constructor builds an instance that is not usable yet, the
* {@link
* org.apache.commons.math3.ode.sampling.AbstractStepInterpolator#reinitialize}
* method should be called before using the instance in order to
* initialize the internal arrays. This constructor is used only
* in order to delay the initialization in some cases. The {@link
* RungeKuttaIntegrator} class uses the prototyping design pattern
* to create the step interpolators by cloning an uninitialized model
* and later initializing the copy.
*/
public MidpointStepInterpolator() {
}
/** Copy constructor.
* @param interpolator interpolator to copy from. The copy is a deep
* copy: its arrays are separated from the original arrays of the
* instance
*/
public MidpointStepInterpolator(final MidpointStepInterpolator interpolator) {
super(interpolator);
}
/** {@inheritDoc} */
@Override
protected StepInterpolator doCopy() {
return new MidpointStepInterpolator(this);
}
/** {@inheritDoc} */
@Override
protected void computeInterpolatedStateAndDerivatives(final double theta,
final double oneMinusThetaH) {
final double coeffDot2 = 2 * theta;
final double coeffDot1 = 1 - coeffDot2;
if ((previousState != null) && (theta <= 0.5)) {
final double coeff1 = theta * oneMinusThetaH;
final double coeff2 = theta * theta * h;
for (int i = 0; i < interpolatedState.length; ++i) {
final double yDot1 = yDotK[0][i];
final double yDot2 = yDotK[1][i];
interpolatedState[i] = previousState[i] + coeff1 * yDot1 + coeff2 * yDot2;
interpolatedDerivatives[i] = coeffDot1 * yDot1 + coeffDot2 * yDot2;
}
} else {
final double coeff1 = oneMinusThetaH * theta;
final double coeff2 = oneMinusThetaH * (1.0 + theta);
for (int i = 0; i < interpolatedState.length; ++i) {
final double yDot1 = yDotK[0][i];
final double yDot2 = yDotK[1][i];
interpolatedState[i] = currentState[i] + coeff1 * yDot1 - coeff2 * yDot2;
interpolatedDerivatives[i] = coeffDot1 * yDot1 + coeffDot2 * yDot2;
}
}
}
}