ThreeEighthesStateInterpolator.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;
/**
* This class implements a step interpolator for the 3/8 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/8) [ (8 - 15 θ + 8 θ<sup>2</sup>) y'<sub>1</sub>
* + 3 * (15 θ - 12 θ<sup>2</sup>) y'<sub>2</sub>
* + 3 θ y'<sub>3</sub>
* + (-3 θ + 4 θ<sup>2</sup>) y'<sub>4</sub>
* ]
* </li>
* <li>Using reference point at step end:<br>
* y(t<sub>n</sub> + θ h) = y (t<sub>n</sub> + h)
* - (1 - θ) (h/8) [(1 - 7 θ + 8 θ<sup>2</sup>) y'<sub>1</sub>
* + 3 (1 + θ - 4 θ<sup>2</sup>) y'<sub>2</sub>
* + 3 (1 + θ) 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 ThreeEighthesIntegrator
*/
class ThreeEighthesStateInterpolator
extends RungeKuttaStateInterpolator {
/** 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
*/
ThreeEighthesStateInterpolator(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 ThreeEighthesStateInterpolator create(final boolean newForward, final double[][] newYDotK,
final ODEStateAndDerivative newGlobalPreviousState,
final ODEStateAndDerivative newGlobalCurrentState,
final ODEStateAndDerivative newSoftPreviousState,
final ODEStateAndDerivative newSoftCurrentState,
final EquationsMapper newMapper) {
return new ThreeEighthesStateInterpolator(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 coeffDot3 = 0.75 * theta;
final double coeffDot1 = coeffDot3 * (4 * theta - 5) + 1;
final double coeffDot2 = coeffDot3 * (5 - 6 * theta);
final double coeffDot4 = coeffDot3 * (2 * theta - 1);
final double[] interpolatedState;
final double[] interpolatedDerivatives;
if (getGlobalPreviousState() != null && theta <= 0.5) {
final double s = thetaH / 8.0;
final double fourTheta2 = 4 * theta * theta;
final double coeff1 = s * (8 - 15 * theta + 2 * fourTheta2);
final double coeff2 = 3 * s * (5 * theta - fourTheta2);
final double coeff3 = 3 * s * theta;
final double coeff4 = s * (-3 * theta + fourTheta2);
interpolatedState = previousStateLinearCombination(coeff1, coeff2, coeff3, coeff4);
interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3, coeffDot4);
} else {
final double s = oneMinusThetaH / -8.0;
final double fourTheta2 = 4 * theta * theta;
final double coeff1 = s * (1 - 7 * theta + 2 * fourTheta2);
final double coeff2 = 3 * s * (1 + theta - fourTheta2);
final double coeff3 = 3 * s * (1 + theta);
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);
}
}