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/*
* 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.math.ode.nonstiff;
import org.apache.commons.math.ode.DerivativeException;
import org.apache.commons.math.ode.sampling.StepInterpolator;
import org.apache.commons.math.util.FastMath;
/**
* This class implements a step interpolator for the Gill fourth
* order Runge-Kutta integrator.
*
* <p>This interpolator allows to compute dense output inside the last
* step computed. The interpolation equation is consistent with the
* integration scheme :
*
* <pre>
* y(t_n + theta h) = y (t_n + h)
* - (1 - theta) (h/6) [ (1 - theta) (1 - 4 theta) y'_1
* + (1 - theta) (1 + 2 theta) ((2-q) y'_2 + (2+q) y'_3)
* + (1 + theta + 4 theta^2) y'_4
* ]
* </pre>
* where theta belongs to [0 ; 1], q = sqrt(2) and where y'_1 to y'_4
* are the four evaluations of the derivatives already computed during
* the step.</p>
*
* @see GillIntegrator
* @version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $
* @since 1.2
*/
class GillStepInterpolator
extends RungeKuttaStepInterpolator {
/** First Gill coefficient. */
private static final double TWO_MINUS_SQRT_2 = 2 - FastMath.sqrt(2.0);
/** Second Gill coefficient. */
private static final double TWO_PLUS_SQRT_2 = 2 + FastMath.sqrt(2.0);
/** Serializable version identifier */
private static final long serialVersionUID = -107804074496313322L;
/** Simple constructor.
* This constructor builds an instance that is not usable yet, the
* {@link
* org.apache.commons.math.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 GillStepInterpolator() {
}
/** 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 GillStepInterpolator(final GillStepInterpolator interpolator) {
super(interpolator);
}
/** {@inheritDoc} */
@Override
protected StepInterpolator doCopy() {
return new GillStepInterpolator(this);
}
/** {@inheritDoc} */
@Override
protected void computeInterpolatedStateAndDerivatives(final double theta,
final double oneMinusThetaH)
throws DerivativeException {
final double twoTheta = 2 * theta;
final double fourTheta = 4 * theta;
final double s = oneMinusThetaH / 6.0;
final double oMt = 1 - theta;
final double soMt = s * oMt;
final double c23 = soMt * (1 + twoTheta);
final double coeff1 = soMt * (1 - fourTheta);
final double coeff2 = c23 * TWO_MINUS_SQRT_2;
final double coeff3 = c23 * TWO_PLUS_SQRT_2;
final double coeff4 = s * (1 + theta * (1 + fourTheta));
final double coeffDot1 = theta * (twoTheta - 3) + 1;
final double cDot23 = theta * oMt;
final double coeffDot2 = cDot23 * TWO_MINUS_SQRT_2;
final double coeffDot3 = cDot23 * TWO_PLUS_SQRT_2;
final double coeffDot4 = theta * (twoTheta - 1);
for (int i = 0; i < interpolatedState.length; ++i) {
final double yDot1 = yDotK[0][i];
final double yDot2 = yDotK[1][i];
final double yDot3 = yDotK[2][i];
final double yDot4 = yDotK[3][i];
interpolatedState[i] =
currentState[i] - coeff1 * yDot1 - coeff2 * yDot2 - coeff3 * yDot3 - coeff4 * yDot4;
interpolatedDerivatives[i] =
coeffDot1 * yDot1 + coeffDot2 * yDot2 + coeffDot3 * yDot3 + coeffDot4 * yDot4;
}
}
}
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