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Field-based version of Gill method for solving ODE.

This commit is contained in:
Luc Maisonobe 2016-01-06 12:24:18 +01:00
parent d67f7e2af9
commit 58e713233d
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src/main/java/org/apache/commons/math4/ode/nonstiff/GillFieldIntegrator.java Normal file
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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.math4.ode.nonstiff;
import org.apache.commons.math4.Field;
import org.apache.commons.math4.RealFieldElement;
import org.apache.commons.math4.util.FastMath;
/**
* This class implements the Gill fourth order Runge-Kutta
* integrator for Ordinary Differential Equations .
* <p>This method is an explicit Runge-Kutta method, its Butcher-array
* is the following one :
* <pre>
* 0 | 0 0 0 0
* 1/2 | 1/2 0 0 0
* 1/2 | (q-1)/2 (2-q)/2 0 0
* 1 | 0 -q/2 (2+q)/2 0
* |-------------------------------
* | 1/6 (2-q)/6 (2+q)/6 1/6
* </pre>
* where q = sqrt(2)</p>
*
* @see EulerFieldIntegrator
* @see ClassicalRungeKuttaFieldIntegrator
* @see MidpointFieldIntegrator
* @see ThreeEighthesFieldIntegrator
* @see LutherFieldIntegrator
* @param <T> the type of the field elements
* @since 3.6
*/
public class GillFieldIntegrator<T extends RealFieldElement<T>>
extends RungeKuttaFieldIntegrator<T> {
/** Time steps Butcher array. */
private static final double[] STATIC_C = {
1.0 / 2.0, 1.0 / 2.0, 1.0
};
/** Internal weights Butcher array. */
private static final double[][] STATIC_A = {
{ 1.0 / 2.0 },
{ (FastMath.sqrt(2.0) - 1.0) / 2.0, (2.0 - FastMath.sqrt(2.0)) / 2.0 },
{ 0.0, -FastMath.sqrt(2.0) / 2.0, (2.0 + FastMath.sqrt(2.0)) / 2.0 }
};
/** Propagation weights Butcher array. */
private static final double[] STATIC_B = {
1.0 / 6.0, (2.0 - FastMath.sqrt(2.0)) / 6.0, (2.0 + FastMath.sqrt(2.0)) / 6.0, 1.0 / 6.0
};
/** Simple constructor.
* Build a fourth-order Gill integrator with the given step.
* @param field field to which the time and state vector elements belong
* @param step integration step
*/
public GillFieldIntegrator(final Field<T> field, final T step) {
super(field, "Gill", STATIC_C, STATIC_A, STATIC_B, new GillFieldStepInterpolator<T>(), step);
}
}

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src/main/java/org/apache/commons/math4/ode/nonstiff/GillFieldStepInterpolator.java Normal file
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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.math4.ode.nonstiff;
import org.apache.commons.math4.RealFieldElement;
import org.apache.commons.math4.ode.FieldEquationsMapper;
import org.apache.commons.math4.ode.FieldODEStateAndDerivative;
import org.apache.commons.math4.util.FastMath;
import org.apache.commons.math4.util.MathArrays;
/**
* 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> + &theta; h) = y (t<sub>n</sub>)
* + &theta; (h/6) [ (6 - 9 &theta; + 4 &theta;<sup>2</sup>) y'<sub>1</sub>
* + ( 6 &theta; - 4 &theta;<sup>2</sup>) ((1-1/&radic;2) y'<sub>2</sub> + (1+1/&radic;2)) y'<sub>3</sub>)
* + ( - 3 &theta; + 4 &theta;<sup>2</sup>) y'<sub>4</sub>
* ]
* </li>
* <li>Using reference point at step start:<br>
* y(t<sub>n</sub> + &theta; h) = y (t<sub>n</sub> + h)
* - (1 - &theta;) (h/6) [ (1 - 5 &theta; + 4 &theta;<sup>2</sup>) y'<sub>1</sub>
* + (2 + 2 &theta; - 4 &theta;<sup>2</sup>) ((1-1/&radic;2) y'<sub>2</sub> + (1+1/&radic;2)) y'<sub>3</sub>)
* + (1 + &theta; + 4 &theta;<sup>2</sup>) y'<sub>4</sub>
* ]
* </li>
* </ul>
* </p>
* where &theta; 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 GillFieldIntegrator
* @param <T> the type of the field elements
* @since 3.6
*/
class GillFieldStepInterpolator<T extends RealFieldElement<T>>
extends RungeKuttaFieldStepInterpolator<T> {
/** 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);
/** Simple constructor.
* This constructor builds an instance that is not usable yet, the
* {@link
* org.apache.commons.math4.ode.sampling.AbstractFieldStepInterpolator#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
* RungeKuttaFieldIntegrator} class uses the prototyping design pattern
* to create the step interpolators by cloning an uninitialized model
* and later initializing the copy.
*/
GillFieldStepInterpolator() {
}
/** 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
*/
GillFieldStepInterpolator(final GillFieldStepInterpolator<T> interpolator) {
super(interpolator);
}
/** {@inheritDoc} */
@Override
protected GillFieldStepInterpolator<T> doCopy() {
return new GillFieldStepInterpolator<T>(this);
}
/** {@inheritDoc} */
@Override
protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> mapper,
final T time, final T theta,
final T oneMinusThetaH) {
final T one = time.getField().getOne();
final T twoTheta = theta.multiply(2);
final T fourTheta2 = twoTheta.multiply(twoTheta);
final T coeffDot1 = theta.multiply(twoTheta.subtract(3)).add(1);
final T cDot23 = twoTheta.multiply(one.subtract(theta));
final T coeffDot2 = cDot23.multiply(ONE_MINUS_INV_SQRT_2);
final T coeffDot3 = cDot23.multiply(ONE_PLUS_INV_SQRT_2);
final T coeffDot4 = theta.multiply(twoTheta.subtract(1));
final T[] interpolatedState = MathArrays.buildArray(theta.getField(), previousState.length);
final T[] interpolatedDerivatives = MathArrays.buildArray(theta.getField(), previousState.length);
if ((previousState != null) && (theta.getReal() <= 0.5)) {
final T s = theta.multiply(h).divide(6.0);
final T c23 = s.multiply(theta.multiply(6).subtract(fourTheta2));
final T coeff1 = s.multiply(fourTheta2.subtract(theta.multiply(6)).add(6));
final T coeff2 = c23.multiply(ONE_MINUS_INV_SQRT_2);
final T coeff3 = c23.multiply(ONE_PLUS_INV_SQRT_2);
final T coeff4 = s.multiply(fourTheta2.subtract(theta.multiply(3)));
for (int i = 0; i < interpolatedState.length; ++i) {
final T yDot1 = yDotK[0][i];
final T yDot2 = yDotK[1][i];
final T yDot3 = yDotK[2][i];
final T yDot4 = yDotK[3][i];
interpolatedState[i] = previousState[i].
add(coeff1.multiply(yDot1)).add(coeff2.multiply(yDot2)).
add(coeff3.multiply(yDot3)).add(coeff4.multiply(yDot4));
interpolatedDerivatives[i] = coeffDot1.multiply(yDot1).add(coeffDot2.multiply(yDot2)).
add(coeffDot3.multiply(yDot3)).add(coeffDot4.multiply(yDot4));
}
} else {
final T s = oneMinusThetaH.divide(6.0);
final T c23 = s .multiply(twoTheta.add(2).subtract(fourTheta2));
final T coeff1 = s.multiply(fourTheta2.subtract(theta.multiply(5)).add(1));
final T coeff2 = c23.multiply(ONE_MINUS_INV_SQRT_2);
final T coeff3 = c23.multiply(ONE_PLUS_INV_SQRT_2);
final T coeff4 = s.multiply(fourTheta2.add(theta).add(1));
for (int i = 0; i < interpolatedState.length; ++i) {
final T yDot1 = yDotK[0][i];
final T yDot2 = yDotK[1][i];
final T yDot3 = yDotK[2][i];
final T yDot4 = yDotK[3][i];
interpolatedState[i] = currentState[i].
subtract(coeff1.multiply(yDot1)).subtract(coeff2.multiply(yDot2)).
subtract(coeff3.multiply(yDot3)).subtract(coeff4.multiply(yDot4));
interpolatedDerivatives[i] = coeffDot1.multiply(yDot1).add(coeffDot2.multiply(yDot2)).
add(coeffDot3.multiply(yDot3)).add(coeffDot4.multiply(yDot4));
}
}
return new FieldODEStateAndDerivative<T>(time, interpolatedState, yDotK[0]);
}
}