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With inspiration from other libraries
/*
* 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.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 Gill fourth
* order Runge-Kutta integrator.
*
* This interpolator allows to compute dense output inside the last
* step computed. The interpolation equation is consistent with the
* integration scheme :
*
* - Using reference point at step start:
* y(tn + θ h) = y (tn)
* + θ (h/6) [ (6 - 9 θ + 4 θ2) y'1
* + ( 6 θ - 4 θ2) ((1-1/√2) y'2 + (1+1/√2)) y'3)
* + ( - 3 θ + 4 θ2) y'4
* ]
*
* - Using reference point at step start:
* y(tn + θ h) = y (tn + h)
* - (1 - θ) (h/6) [ (1 - 5 θ + 4 θ2) y'1
* + (2 + 2 θ - 4 θ2) ((1-1/√2) y'2 + (1+1/√2)) y'3)
* + (1 + θ + 4 θ2) y'4
* ]
*
*
*
* where θ belongs to [0 ; 1] and where y'1 to y'4
* are the four evaluations of the derivatives already computed during
* the step.
*
* @see GillFieldIntegrator
* @param the type of the field elements
* @since 3.6
*/
class GillFieldStepInterpolator>
extends RungeKuttaFieldStepInterpolator {
/** First Gill coefficient. */
private final T one_minus_inv_sqrt_2;
/** Second Gill coefficient. */
private final T one_plus_inv_sqrt_2;
/** 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
*/
GillFieldStepInterpolator(final Field field, final boolean forward,
final T[][] yDotK,
final FieldODEStateAndDerivative globalPreviousState,
final FieldODEStateAndDerivative globalCurrentState,
final FieldODEStateAndDerivative softPreviousState,
final FieldODEStateAndDerivative softCurrentState,
final FieldEquationsMapper mapper) {
super(field, forward, yDotK,
globalPreviousState, globalCurrentState, softPreviousState, softCurrentState,
mapper);
final T sqrt = field.getZero().add(0.5).sqrt();
one_minus_inv_sqrt_2 = field.getOne().subtract(sqrt);
one_plus_inv_sqrt_2 = field.getOne().add(sqrt);
}
/** {@inheritDoc} */
@Override
protected GillFieldStepInterpolator create(final Field newField, final boolean newForward, final T[][] newYDotK,
final FieldODEStateAndDerivative newGlobalPreviousState,
final FieldODEStateAndDerivative newGlobalCurrentState,
final FieldODEStateAndDerivative newSoftPreviousState,
final FieldODEStateAndDerivative newSoftCurrentState,
final FieldEquationsMapper newMapper) {
return new GillFieldStepInterpolator(newField, newForward, newYDotK,
newGlobalPreviousState, newGlobalCurrentState,
newSoftPreviousState, newSoftCurrentState,
newMapper);
}
/** {@inheritDoc} */
@SuppressWarnings("unchecked")
@Override
protected FieldODEStateAndDerivative computeInterpolatedStateAndDerivatives(final FieldEquationsMapper mapper,
final T time, final T theta,
final T thetaH, 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;
final T[] interpolatedDerivatives;
if (getGlobalPreviousState() != null && theta.getReal() <= 0.5) {
final T s = thetaH.divide(6.0);
final T c23 = s.multiply(theta.multiply(6).subtract(fourTheta2));
final T coeff1 = s.multiply(fourTheta2.subtract(theta.multiply(9)).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)));
interpolatedState = previousStateLinearCombination(coeff1, coeff2, coeff3, coeff4);
interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3, coeffDot4);
} 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));
interpolatedState = currentStateLinearCombination(coeff1, coeff2, coeff3, coeff4);
interpolatedDerivatives = derivativeLinearCombination(coeffDot1, coeffDot2, coeffDot3, coeffDot4);
}
return new FieldODEStateAndDerivative(time, interpolatedState, interpolatedDerivatives);
}
}