/*
* 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;
import org.apache.commons.math3.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 :
* <ul>
* <li>Using reference point at step start:<br>
* y(t<sub>n</sub> + θ h) = y (t<sub>n</sub>)
* + θ (h/6) [ (6 - 9 θ + 4 θ<sup>2</sup>) y'<sub>1</sub>
* + ( 6 θ - 4 θ<sup>2</sup>) ((1-1/√2) y'<sub>2</sub> + (1+1/√2)) y'<sub>3</sub>)
* + ( - 3 θ + 4 θ<sup>2</sup>) y'<sub>4</sub>
* ]
* </li>
* <li>Using reference point at step start:<br>
* y(t<sub>n</sub> + θ h) = y (t<sub>n</sub> + h)
* - (1 - θ) (h/6) [ (1 - 5 θ + 4 θ<sup>2</sup>) y'<sub>1</sub>
* + (2 + 2 θ - 4 θ<sup>2</sup>) ((1-1/√2) y'<sub>2</sub> + (1+1/√2)) y'<sub>3</sub>)
* + (1 + θ + 4 θ<sup>2</sup>) y'<sub>4</sub>
* ]
* </li>
* </ul>
* </p>
* where θ belongs to [0 ; 1] and where y'<sub>1</sub> to y'<sub>4</sub>
* are the four evaluations of the derivatives already computed during
* the step.</p>
*
* @see GillIntegrator
* @since 1.2
*/
class GillStepInterpolator
extends RungeKuttaStepInterpolator {
/** First Gill coefficient. */
private static final double ONE_MINUS_INV_SQRT_2 = 1 - FastMath.sqrt(0.5);
/** Second Gill coefficient. */
private static final double ONE_PLUS_INV_SQRT_2 = 1 + FastMath.sqrt(0.5);
/** 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 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) {
final double twoTheta = 2 * theta;
final double fourTheta2 = twoTheta * twoTheta;
final double coeffDot1 = theta * (twoTheta - 3) + 1;
final double cDot23 = twoTheta * (1 - theta);
final double coeffDot2 = cDot23 * ONE_MINUS_INV_SQRT_2;
final double coeffDot3 = cDot23 * ONE_PLUS_INV_SQRT_2;
final double coeffDot4 = theta * (twoTheta - 1);
if ((previousState != null) && (theta <= 0.5)) {
final double s = theta * h / 6.0;
final double c23 = s * (6 * theta - fourTheta2);
final double coeff1 = s * (6 - 9 * theta + fourTheta2);
final double coeff2 = c23 * ONE_MINUS_INV_SQRT_2;
final double coeff3 = c23 * ONE_PLUS_INV_SQRT_2;
final double coeff4 = s * (-3 * theta + fourTheta2);
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] =
previousState[i] + coeff1 * yDot1 + coeff2 * yDot2 + coeff3 * yDot3 + coeff4 * yDot4;
interpolatedDerivatives[i] =
coeffDot1 * yDot1 + coeffDot2 * yDot2 + coeffDot3 * yDot3 + coeffDot4 * yDot4;
}
} else {
final double s = oneMinusThetaH / 6.0;
final double c23 = s * (2 + twoTheta - fourTheta2);
final double coeff1 = s * (1 - 5 * theta + fourTheta2);
final double coeff2 = c23 * ONE_MINUS_INV_SQRT_2;
final double coeff3 = c23 * ONE_PLUS_INV_SQRT_2;
final double coeff4 = s * (1 + theta + fourTheta2);
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;
}
}
}
}