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* 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,
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* See the License for the specific language governing permissions and
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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.
This interpolator allows to compute dense output inside the last
step computed. The interpolation equation is consistent with the
integration scheme :
- Using reference point at step start:
y(tn + θ h) = y (tn)
+ θ (h/6) [ (6 - 9 θ + 4 θ2) y'1
+ ( 6 θ - 4 θ2) ((1-1/√2) y'2 + (1+1/√2)) y'3)
+ ( - 3 θ + 4 θ2) y'4
]
- Using reference point at step start:
y(tn + θ h) = y (tn + h)
- (1 - θ) (h/6) [ (1 - 5 θ + 4 θ2) y'1
+ (2 + 2 θ - 4 θ2) ((1-1/√2) y'2 + (1+1/√2)) y'3)
+ (1 + θ + 4 θ2) y'4
]
where θ belongs to [0 ; 1] and where y'1 to y'4
are the four evaluations of the derivatives already computed during
the step.
See Also: - GillIntegrator
Since: 1.2
/**
* 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. /** First Gill coefficient. */
private static final double ONE_MINUS_INV_SQRT_2 = 1 - FastMath.sqrt(0.5);
Second Gill coefficient. /** Second Gill coefficient. */
private static final double ONE_PLUS_INV_SQRT_2 = 1 + FastMath.sqrt(0.5);
Serializable version identifier. /** Serializable version identifier. */
private static final long serialVersionUID = 20111120L;
Simple constructor. This constructor builds an instance that is not usable yet, the 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 RungeKuttaIntegrator class uses the prototyping design pattern to create the step interpolators by cloning an uninitialized model and later initializing the copy. /** 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.
*/
// CHECKSTYLE: stop RedundantModifier
// the public modifier here is needed for serialization
public GillStepInterpolator() {
}
// CHECKSTYLE: resume RedundantModifier
Copy constructor.
Params: - interpolator – interpolator to copy from. The copy is a deep
copy: its arrays are separated from the original arrays of the
instance
/** 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
*/
GillStepInterpolator(final GillStepInterpolator interpolator) {
super(interpolator);
}
{@inheritDoc} /** {@inheritDoc} */
@Override
protected StepInterpolator doCopy() {
return new GillStepInterpolator(this);
}
{@inheritDoc} /** {@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;
}
}
}
}