| /* |
| * 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.math4.legacy.ode.nonstiff; |
| |
| import org.apache.commons.math4.legacy.core.Field; |
| import org.apache.commons.math4.legacy.core.RealFieldElement; |
| import org.apache.commons.math4.legacy.ode.FieldEquationsMapper; |
| import org.apache.commons.math4.legacy.ode.FieldODEStateAndDerivative; |
| |
| /** |
| * 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 : |
| * <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> |
| * 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 GillFieldIntegrator |
| * @param <T> the type of the field elements |
| * @since 3.6 |
| */ |
| |
| class GillFieldStepInterpolator<T extends RealFieldElement<T>> |
| extends RungeKuttaFieldStepInterpolator<T> { |
| |
| /** 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<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); |
| 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<T> create(final Field<T> 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 GillFieldStepInterpolator<>(newField, newForward, newYDotK, |
| newGlobalPreviousState, newGlobalCurrentState, |
| newSoftPreviousState, newSoftCurrentState, |
| newMapper); |
| } |
| |
| /** {@inheritDoc} */ |
| @SuppressWarnings("unchecked") |
| @Override |
| protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(final FieldEquationsMapper<T> 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); |
| |
| } |
| |
| } |
