| /* |
| * 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; |
| import org.apache.commons.math4.legacy.core.MathArrays; |
| |
| |
| /** |
| * This class implements the Gill fourth order Runge-Kutta |
| * integrator for Ordinary Differential Equations . |
| |
| * <p>This method is an explicit Runge-Kutta method, its Butcher-array |
| * is the following one : |
| * <pre> |
| * 0 | 0 0 0 0 |
| * 1/2 | 1/2 0 0 0 |
| * 1/2 | (q-1)/2 (2-q)/2 0 0 |
| * 1 | 0 -q/2 (2+q)/2 0 |
| * |------------------------------- |
| * | 1/6 (2-q)/6 (2+q)/6 1/6 |
| * </pre> |
| * where q = sqrt(2) |
| * |
| * @see EulerFieldIntegrator |
| * @see ClassicalRungeKuttaFieldIntegrator |
| * @see MidpointFieldIntegrator |
| * @see ThreeEighthesFieldIntegrator |
| * @see LutherFieldIntegrator |
| * @param <T> the type of the field elements |
| * @since 3.6 |
| */ |
| |
| public class GillFieldIntegrator<T extends RealFieldElement<T>> |
| extends RungeKuttaFieldIntegrator<T> { |
| |
| /** Simple constructor. |
| * Build a fourth-order Gill integrator with the given step. |
| * @param field field to which the time and state vector elements belong |
| * @param step integration step |
| */ |
| public GillFieldIntegrator(final Field<T> field, final T step) { |
| super(field, "Gill", step); |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public T[] getC() { |
| final T[] c = MathArrays.buildArray(getField(), 3); |
| c[0] = fraction(1, 2); |
| c[1] = c[0]; |
| c[2] = getField().getOne(); |
| return c; |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public T[][] getA() { |
| |
| final T two = getField().getZero().add(2); |
| final T sqrtTwo = two.sqrt(); |
| |
| final T[][] a = MathArrays.buildArray(getField(), 3, -1); |
| for (int i = 0; i < a.length; ++i) { |
| a[i] = MathArrays.buildArray(getField(), i + 1); |
| } |
| a[0][0] = fraction(1, 2); |
| a[1][0] = sqrtTwo.subtract(1).multiply(0.5); |
| a[1][1] = sqrtTwo.subtract(2).multiply(-0.5); |
| a[2][0] = getField().getZero(); |
| a[2][1] = sqrtTwo.multiply(-0.5); |
| a[2][2] = sqrtTwo.add(2).multiply(0.5); |
| return a; |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public T[] getB() { |
| |
| final T two = getField().getZero().add(2); |
| final T sqrtTwo = two.sqrt(); |
| |
| final T[] b = MathArrays.buildArray(getField(), 4); |
| b[0] = fraction(1, 6); |
| b[1] = sqrtTwo.subtract(2).divide(-6); |
| b[2] = sqrtTwo.add(2).divide(6); |
| b[3] = b[0]; |
| |
| return b; |
| |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| protected GillFieldStepInterpolator<T> |
| createInterpolator(final boolean forward, T[][] yDotK, |
| final FieldODEStateAndDerivative<T> globalPreviousState, |
| final FieldODEStateAndDerivative<T> globalCurrentState, |
| final FieldEquationsMapper<T> mapper) { |
| return new GillFieldStepInterpolator<>(getField(), forward, yDotK, |
| globalPreviousState, globalCurrentState, |
| globalPreviousState, globalCurrentState, |
| mapper); |
| } |
| |
| } |