ClassicalRungeKuttaStateInterpolator.java
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* The Hipparchus project licenses this file to You under the Apache License, Version 2.0
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*
* https://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
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package org.hipparchus.ode.nonstiff;
import org.hipparchus.ode.EquationsMapper;
import org.hipparchus.ode.ODEStateAndDerivative;
/**
* This class implements a step interpolator for the classical 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>) (y'<sub>2</sub> + 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/6) [ (-4 θ^2 + 5 θ - 1) y'<sub>1</sub>
* +(4 θ^2 - 2 θ - 2) (y'<sub>2</sub> + y'<sub>3</sub>)
* -(4 θ^2 + θ + 1) 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 ClassicalRungeKuttaIntegrator
*/
class ClassicalRungeKuttaStateInterpolator
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
*/
ClassicalRungeKuttaStateInterpolator(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 ClassicalRungeKuttaStateInterpolator create(final boolean newForward, final double[][] newYDotK,
final ODEStateAndDerivative newGlobalPreviousState,
final ODEStateAndDerivative newGlobalCurrentState,
final ODEStateAndDerivative newSoftPreviousState,
final ODEStateAndDerivative newSoftCurrentState,
final EquationsMapper newMapper) {
return new ClassicalRungeKuttaStateInterpolator(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 oneMinusTheta = 1.0 - theta;
final double oneMinus2Theta = 1.0 - theta * 2.0;
final double coeffDot1 = oneMinusTheta * oneMinus2Theta;
final double coeffDot23 = theta * oneMinusTheta * 2;
final double coeffDot4 = -theta * oneMinus2Theta;
final double[] interpolatedState;
final double[] interpolatedDerivatives;
if (getGlobalPreviousState() != null && theta <= 0.5) {
final double fourTheta2 = theta * theta * 4;
final double s = thetaH / 6.0;
final double coeff1 = s * (fourTheta2 - theta * 9 + 6);
final double coeff23 = s * (theta * 6 - fourTheta2);
final double coeff4 = s * (fourTheta2 - theta * 3);
interpolatedState = previousStateLinearCombination(coeff1, coeff23, coeff23, coeff4);
interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot23, coeffDot23, coeffDot4);
} else {
final double fourTheta = theta * 4;
final double s = oneMinusThetaH / 6.0;
final double coeff1 = s * (theta * (-fourTheta + 5) - 1);
final double coeff23 = s * (theta * ( fourTheta - 2) - 2);
final double coeff4 = s * (theta * (-fourTheta - 1) - 1);
interpolatedState = currentStateLinearCombination(coeff1, coeff23, coeff23, coeff4);
interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot23, coeffDot23, coeffDot4);
}
return mapper.mapStateAndDerivative(time, interpolatedState, interpolatedDerivatives);
}
}