001/* 002 * Licensed to the Apache Software Foundation (ASF) under one or more 003 * contributor license agreements. See the NOTICE file distributed with 004 * this work for additional information regarding copyright ownership. 005 * The ASF licenses this file to You under the Apache License, Version 2.0 006 * (the "License"); you may not use this file except in compliance with 007 * the License. You may obtain a copy of the License at 008 * 009 * http://www.apache.org/licenses/LICENSE-2.0 010 * 011 * Unless required by applicable law or agreed to in writing, software 012 * distributed under the License is distributed on an "AS IS" BASIS, 013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 014 * See the License for the specific language governing permissions and 015 * limitations under the License. 016 */ 017 018package org.apache.commons.math3.ode.nonstiff; 019 020import org.apache.commons.math3.Field; 021import org.apache.commons.math3.RealFieldElement; 022import org.apache.commons.math3.ode.FieldEquationsMapper; 023import org.apache.commons.math3.ode.FieldODEStateAndDerivative; 024import org.apache.commons.math3.util.MathArrays; 025 026 027/** 028 * This class implements the Gill fourth order Runge-Kutta 029 * integrator for Ordinary Differential Equations . 030 031 * <p>This method is an explicit Runge-Kutta method, its Butcher-array 032 * is the following one : 033 * <pre> 034 * 0 | 0 0 0 0 035 * 1/2 | 1/2 0 0 0 036 * 1/2 | (q-1)/2 (2-q)/2 0 0 037 * 1 | 0 -q/2 (2+q)/2 0 038 * |------------------------------- 039 * | 1/6 (2-q)/6 (2+q)/6 1/6 040 * </pre> 041 * where q = sqrt(2)</p> 042 * 043 * @see EulerFieldIntegrator 044 * @see ClassicalRungeKuttaFieldIntegrator 045 * @see MidpointFieldIntegrator 046 * @see ThreeEighthesFieldIntegrator 047 * @see LutherFieldIntegrator 048 * @param <T> the type of the field elements 049 * @since 3.6 050 */ 051 052public class GillFieldIntegrator<T extends RealFieldElement<T>> 053 extends RungeKuttaFieldIntegrator<T> { 054 055 /** Simple constructor. 056 * Build a fourth-order Gill integrator with the given step. 057 * @param field field to which the time and state vector elements belong 058 * @param step integration step 059 */ 060 public GillFieldIntegrator(final Field<T> field, final T step) { 061 super(field, "Gill", step); 062 } 063 064 /** {@inheritDoc} */ 065 public T[] getC() { 066 final T[] c = MathArrays.buildArray(getField(), 3); 067 c[0] = fraction(1, 2); 068 c[1] = c[0]; 069 c[2] = getField().getOne(); 070 return c; 071 } 072 073 /** {@inheritDoc} */ 074 public T[][] getA() { 075 076 final T two = getField().getZero().add(2); 077 final T sqrtTwo = two.sqrt(); 078 079 final T[][] a = MathArrays.buildArray(getField(), 3, -1); 080 for (int i = 0; i < a.length; ++i) { 081 a[i] = MathArrays.buildArray(getField(), i + 1); 082 } 083 a[0][0] = fraction(1, 2); 084 a[1][0] = sqrtTwo.subtract(1).multiply(0.5); 085 a[1][1] = sqrtTwo.subtract(2).multiply(-0.5); 086 a[2][0] = getField().getZero(); 087 a[2][1] = sqrtTwo.multiply(-0.5); 088 a[2][2] = sqrtTwo.add(2).multiply(0.5); 089 return a; 090 } 091 092 /** {@inheritDoc} */ 093 public T[] getB() { 094 095 final T two = getField().getZero().add(2); 096 final T sqrtTwo = two.sqrt(); 097 098 final T[] b = MathArrays.buildArray(getField(), 4); 099 b[0] = fraction(1, 6); 100 b[1] = sqrtTwo.subtract(2).divide(-6); 101 b[2] = sqrtTwo.add(2).divide(6); 102 b[3] = b[0]; 103 104 return b; 105 106 } 107 108 /** {@inheritDoc} */ 109 @Override 110 protected GillFieldStepInterpolator<T> 111 createInterpolator(final boolean forward, T[][] yDotK, 112 final FieldODEStateAndDerivative<T> globalPreviousState, 113 final FieldODEStateAndDerivative<T> globalCurrentState, 114 final FieldEquationsMapper<T> mapper) { 115 return new GillFieldStepInterpolator<T>(getField(), forward, yDotK, 116 globalPreviousState, globalCurrentState, 117 globalPreviousState, globalCurrentState, 118 mapper); 119 } 120 121}