GillStateInterpolator.java
/*
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* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The Hipparchus project 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
*
* https://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.hipparchus.ode.nonstiff;
import org.hipparchus.ode.EquationsMapper;
import org.hipparchus.ode.ODEStateAndDerivative;
import org.hipparchus.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 :</p>
* <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
*/
class GillStateInterpolator
extends RungeKuttaStateInterpolator {
/** 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 = 20160328L;
/** Simple constructor.
* @param forward integration direction indicator
* @param yDotK slopes at the intermediate points
* @param globalPreviousState start of the global step
* @param globalCurrentState end of the global step
* @param softPreviousState start of the restricted step
* @param softCurrentState end of the restricted step
* @param mapper equations mapper for the all equations
*/
GillStateInterpolator(final boolean forward,
final double[][] yDotK,
final ODEStateAndDerivative globalPreviousState,
final ODEStateAndDerivative globalCurrentState,
final ODEStateAndDerivative softPreviousState,
final ODEStateAndDerivative softCurrentState,
final EquationsMapper mapper) {
super(forward, yDotK,
globalPreviousState, globalCurrentState, softPreviousState, softCurrentState,
mapper);
}
/** {@inheritDoc} */
@Override
protected GillStateInterpolator create(final boolean newForward, final double[][] newYDotK,
final ODEStateAndDerivative newGlobalPreviousState,
final ODEStateAndDerivative newGlobalCurrentState,
final ODEStateAndDerivative newSoftPreviousState,
final ODEStateAndDerivative newSoftCurrentState,
final EquationsMapper newMapper) {
return new GillStateInterpolator(newForward, newYDotK,
newGlobalPreviousState, newGlobalCurrentState,
newSoftPreviousState, newSoftCurrentState,
newMapper);
}
/** {@inheritDoc} */
@Override
protected ODEStateAndDerivative computeInterpolatedStateAndDerivatives(final EquationsMapper mapper,
final double time, final double theta,
final double thetaH, 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);
final double[] interpolatedState;
final double[] interpolatedDerivatives;
if (getGlobalPreviousState() != null && theta <= 0.5) {
final double s = thetaH / 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);
interpolatedState = previousStateLinearCombination(coeff1, coeff2, coeff3, coeff4);
interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3 , coeffDot4);
} 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);
interpolatedState = currentStateLinearCombination(coeff1, coeff2, coeff3, coeff4);
interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3 , coeffDot4);
}
return mapper.mapStateAndDerivative(time, interpolatedState, interpolatedDerivatives);
}
}