/*
* 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 represents an interpolator over the last step during an
* ODE integration for the 5(4) Higham and Hall integrator.
*
* @see HighamHall54Integrator
*
* @since 1.2
*/
class HighamHall54StepInterpolator
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
* EmbeddedRungeKuttaIntegrator} uses the prototyping design pattern
* to create the step interpolators by cloning an uninitialized model
* and later initializing the copy.
*/
public HighamHall54StepInterpolator() {
super();
}
/** 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 HighamHall54StepInterpolator(final HighamHall54StepInterpolator interpolator) {
super(interpolator);
}
/** {@inheritDoc} */
@Override
protected StepInterpolator doCopy() {
return new HighamHall54StepInterpolator(this);
}
/** {@inheritDoc} */
@Override
protected void computeInterpolatedStateAndDerivatives(final double theta,
final double oneMinusThetaH) {
final double bDot0 = 1 + theta * (-15.0/2.0 + theta * (16.0 - 10.0 * theta));
final double bDot2 = theta * (459.0/16.0 + theta * (-729.0/8.0 + 135.0/2.0 * theta));
final double bDot3 = theta * (-44.0 + theta * (152.0 - 120.0 * theta));
final double bDot4 = theta * (375.0/16.0 + theta * (-625.0/8.0 + 125.0/2.0 * theta));
final double bDot5 = theta * 5.0/8.0 * (2 * theta - 1);
if ((previousState != null) && (theta <= 0.5)) {
final double hTheta = h * theta;
final double b0 = hTheta * (1.0 + theta * (-15.0/4.0 + theta * (16.0/3.0 - 5.0/2.0 * theta)));
final double b2 = hTheta * ( theta * (459.0/32.0 + theta * (-243.0/8.0 + theta * 135.0/8.0)));
final double b3 = hTheta * ( theta * (-22.0 + theta * (152.0/3.0 + theta * -30.0)));
final double b4 = hTheta * ( theta * (375.0/32.0 + theta * (-625.0/24.0 + theta * 125.0/8.0)));
final double b5 = hTheta * ( theta * (-5.0/16.0 + theta * 5.0/12.0));
for (int i = 0; i < interpolatedState.length; ++i) {
final double yDot0 = yDotK[0][i];
final double yDot2 = yDotK[2][i];
final double yDot3 = yDotK[3][i];
final double yDot4 = yDotK[4][i];
final double yDot5 = yDotK[5][i];
interpolatedState[i] =
previousState[i] + b0 * yDot0 + b2 * yDot2 + b3 * yDot3 + b4 * yDot4 + b5 * yDot5;
interpolatedDerivatives[i] =
bDot0 * yDot0 + bDot2 * yDot2 + bDot3 * yDot3 + bDot4 * yDot4 + bDot5 * yDot5;
}
} else {
final double theta2 = theta * theta;
final double b0 = h * (-1.0/12.0 + theta * (1.0 + theta * (-15.0/4.0 + theta * (16.0/3.0 + theta * -5.0/2.0))));
final double b2 = h * (-27.0/32.0 + theta2 * (459.0/32.0 + theta * (-243.0/8.0 + theta * 135.0/8.0)));
final double b3 = h * (4.0/3.0 + theta2 * (-22.0 + theta * (152.0/3.0 + theta * -30.0)));
final double b4 = h * (-125.0/96.0 + theta2 * (375.0/32.0 + theta * (-625.0/24.0 + theta * 125.0/8.0)));
final double b5 = h * (-5.0/48.0 + theta2 * (-5.0/16.0 + theta * 5.0/12.0));
for (int i = 0; i < interpolatedState.length; ++i) {
final double yDot0 = yDotK[0][i];
final double yDot2 = yDotK[2][i];
final double yDot3 = yDotK[3][i];
final double yDot4 = yDotK[4][i];
final double yDot5 = yDotK[5][i];
interpolatedState[i] =
currentState[i] + b0 * yDot0 + b2 * yDot2 + b3 * yDot3 + b4 * yDot4 + b5 * yDot5;
interpolatedDerivatives[i] =
bDot0 * yDot0 + bDot2 * yDot2 + bDot3 * yDot3 + bDot4 * yDot4 + bDot5 * yDot5;
}
}
}
}