The ClassicalRungeKuttaFieldStepInterpolator.java Java example source code
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package org.apache.commons.math3.ode.nonstiff;
import org.apache.commons.math3.Field;
import org.apache.commons.math3.RealFieldElement;
import org.apache.commons.math3.ode.FieldEquationsMapper;
import org.apache.commons.math3.ode.FieldODEStateAndDerivative;
/**
* 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 :
* <ul>
* <li>Using reference point at step start:
* y(t<sub>n + ? h) = y (tn)
* + ? (h/6) [ (6 - 9 ? + 4 ?<sup>2) y'1
* + ( 6 ? - 4 ?<sup>2) (y'2 + y'3)
* + ( -3 ? + 4 ?<sup>2) y'4
* ]
* </li>
* <li>Using reference point at step end:
* y(t<sub>n + ? h) = y (tn + h)
* + (1 - ?) (h/6) [ (-4 ?^2 + 5 ? - 1) y'<sub>1
* +(4 ?^2 - 2 ? - 2) (y'<sub>2 + y'3)
* -(4 ?^2 + ? + 1) y'<sub>4
* ]
* </li>
* </ul>
* </p>
*
* where ? belongs to [0 ; 1] and where y'<sub>1 to y'4 are the four
* evaluations of the derivatives already computed during the
* step.</p>
*
* @see ClassicalRungeKuttaFieldIntegrator
* @param <T> the type of the field elements
* @since 3.6
*/
class ClassicalRungeKuttaFieldStepInterpolator<T extends RealFieldElement
extends RungeKuttaFieldStepInterpolator<T> {
/** Simple constructor.
* @param field field to which the time and state vector elements belong
* @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
*/
ClassicalRungeKuttaFieldStepInterpolator(final Field<T> field, final boolean forward,
final T[][] yDotK,
final FieldODEStateAndDerivative<T> globalPreviousState,
final FieldODEStateAndDerivative<T> globalCurrentState,
final FieldODEStateAndDerivative<T> softPreviousState,
final FieldODEStateAndDerivative<T> softCurrentState,
final FieldEquationsMapper<T> mapper) {
super(field, forward, yDotK,
globalPreviousState, globalCurrentState, softPreviousState, softCurrentState,
mapper);
}
/** {@inheritDoc} */
@Override
protected ClassicalRungeKuttaFieldStepInterpolator<T> create(final Field newField, final boolean newForward, final T[][] newYDotK,
final FieldODEStateAndDerivative<T> newGlobalPreviousState,
final FieldODEStateAndDerivative<T> newGlobalCurrentState,
final FieldODEStateAndDerivative<T> newSoftPreviousState,
final FieldODEStateAndDerivative<T> newSoftCurrentState,
final FieldEquationsMapper<T> newMapper) {
return new ClassicalRungeKuttaFieldStepInterpolator<T>(newField, newForward, newYDotK,
newGlobalPreviousState, newGlobalCurrentState,
newSoftPreviousState, newSoftCurrentState,
newMapper);
}
/** {@inheritDoc} */
@SuppressWarnings("unchecked")
@Override
protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper mapper,
final T time, final T theta,
final T thetaH, final T oneMinusThetaH) {
final T one = time.getField().getOne();
final T oneMinusTheta = one.subtract(theta);
final T oneMinus2Theta = one.subtract(theta.multiply(2));
final T coeffDot1 = oneMinusTheta.multiply(oneMinus2Theta);
final T coeffDot23 = theta.multiply(oneMinusTheta).multiply(2);
final T coeffDot4 = theta.multiply(oneMinus2Theta).negate();
final T[] interpolatedState;
final T[] interpolatedDerivatives;
if (getGlobalPreviousState() != null && theta.getReal() <= 0.5) {
final T fourTheta2 = theta.multiply(theta).multiply(4);
final T s = thetaH.divide(6.0);
final T coeff1 = s.multiply(fourTheta2.subtract(theta.multiply(9)).add(6));
final T coeff23 = s.multiply(theta.multiply(6).subtract(fourTheta2));
final T coeff4 = s.multiply(fourTheta2.subtract(theta.multiply(3)));
interpolatedState = previousStateLinearCombination(coeff1, coeff23, coeff23, coeff4);
interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot23, coeffDot23, coeffDot4);
} else {
final T fourTheta = theta.multiply(4);
final T s = oneMinusThetaH.divide(6);
final T coeff1 = s.multiply(theta.multiply(fourTheta.negate().add(5)).subtract(1));
final T coeff23 = s.multiply(theta.multiply(fourTheta.subtract(2)).subtract(2));
final T coeff4 = s.multiply(theta.multiply(fourTheta.negate().subtract(1)).subtract(1));
interpolatedState = currentStateLinearCombination(coeff1, coeff23, coeff23, coeff4);
interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot23, coeffDot23, coeffDot4);
}
return new FieldODEStateAndDerivative<T>(time, interpolatedState, interpolatedDerivatives);
}
}
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