| /* |
| * 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 Luther sixth order Runge-Kutta |
| * integrator for Ordinary Differential Equations. |
| |
| * <p> |
| * This method is described in H. A. Luther 1968 paper <a |
| * href="http://www.ams.org/journals/mcom/1968-22-102/S0025-5718-68-99876-1/S0025-5718-68-99876-1.pdf"> |
| * An explicit Sixth-Order Runge-Kutta Formula</a>. |
| * </p> |
| |
| * <p>This method is an explicit Runge-Kutta method, its Butcher-array |
| * is the following one : |
| * <pre> |
| * 0 | 0 0 0 0 0 0 |
| * 1 | 1 0 0 0 0 0 |
| * 1/2 | 3/8 1/8 0 0 0 0 |
| * 2/3 | 8/27 2/27 8/27 0 0 0 |
| * (7-q)/14 | ( -21 + 9q)/392 ( -56 + 8q)/392 ( 336 - 48q)/392 ( -63 + 3q)/392 0 0 |
| * (7+q)/14 | (-1155 - 255q)/1960 ( -280 - 40q)/1960 ( 0 - 320q)/1960 ( 63 + 363q)/1960 ( 2352 + 392q)/1960 0 |
| * 1 | ( 330 + 105q)/180 ( 120 + 0q)/180 ( -200 + 280q)/180 ( 126 - 189q)/180 ( -686 - 126q)/180 ( 490 - 70q)/180 |
| * |-------------------------------------------------------------------------------------------------------------------------------------------------- |
| * | 1/20 0 16/45 0 49/180 49/180 1/20 |
| * </pre> |
| * where q = √21 |
| * |
| * @see EulerFieldIntegrator |
| * @see ClassicalRungeKuttaFieldIntegrator |
| * @see GillFieldIntegrator |
| * @see MidpointFieldIntegrator |
| * @see ThreeEighthesFieldIntegrator |
| * @param <T> the type of the field elements |
| * @since 3.6 |
| */ |
| |
| public class LutherFieldIntegrator<T extends RealFieldElement<T>> |
| extends RungeKuttaFieldIntegrator<T> { |
| |
| /** Simple constructor. |
| * Build a fourth-order Luther integrator with the given step. |
| * @param field field to which the time and state vector elements belong |
| * @param step integration step |
| */ |
| public LutherFieldIntegrator(final Field<T> field, final T step) { |
| super(field, "Luther", step); |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public T[] getC() { |
| final T q = getField().getZero().add(21).sqrt(); |
| final T[] c = MathArrays.buildArray(getField(), 6); |
| c[0] = getField().getOne(); |
| c[1] = fraction(1, 2); |
| c[2] = fraction(2, 3); |
| c[3] = q.subtract(7).divide(-14); |
| c[4] = q.add(7).divide(14); |
| c[5] = getField().getOne(); |
| return c; |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public T[][] getA() { |
| final T q = getField().getZero().add(21).sqrt(); |
| final T[][] a = MathArrays.buildArray(getField(), 6, -1); |
| for (int i = 0; i < a.length; ++i) { |
| a[i] = MathArrays.buildArray(getField(), i + 1); |
| } |
| a[0][0] = getField().getOne(); |
| a[1][0] = fraction(3, 8); |
| a[1][1] = fraction(1, 8); |
| a[2][0] = fraction(8, 27); |
| a[2][1] = fraction(2, 27); |
| a[2][2] = a[2][0]; |
| a[3][0] = q.multiply( 9).add( -21).divide( 392); |
| a[3][1] = q.multiply( 8).add( -56).divide( 392); |
| a[3][2] = q.multiply( -48).add( 336).divide( 392); |
| a[3][3] = q.multiply( 3).add( -63).divide( 392); |
| a[4][0] = q.multiply(-255).add(-1155).divide(1960); |
| a[4][1] = q.multiply( -40).add( -280).divide(1960); |
| a[4][2] = q.multiply(-320) .divide(1960); |
| a[4][3] = q.multiply( 363).add( 63).divide(1960); |
| a[4][4] = q.multiply( 392).add( 2352).divide(1960); |
| a[5][0] = q.multiply( 105).add( 330).divide( 180); |
| a[5][1] = fraction(2, 3); |
| a[5][2] = q.multiply( 280).add( -200).divide( 180); |
| a[5][3] = q.multiply(-189).add( 126).divide( 180); |
| a[5][4] = q.multiply(-126).add( -686).divide( 180); |
| a[5][5] = q.multiply( -70).add( 490).divide( 180); |
| return a; |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| public T[] getB() { |
| |
| final T[] b = MathArrays.buildArray(getField(), 7); |
| b[0] = fraction( 1, 20); |
| b[1] = getField().getZero(); |
| b[2] = fraction(16, 45); |
| b[3] = getField().getZero(); |
| b[4] = fraction(49, 180); |
| b[5] = b[4]; |
| b[6] = b[0]; |
| |
| return b; |
| |
| } |
| |
| /** {@inheritDoc} */ |
| @Override |
| protected LutherFieldStepInterpolator<T> |
| createInterpolator(final boolean forward, T[][] yDotK, |
| final FieldODEStateAndDerivative<T> globalPreviousState, |
| final FieldODEStateAndDerivative<T> globalCurrentState, |
| final FieldEquationsMapper<T> mapper) { |
| return new LutherFieldStepInterpolator<>(getField(), forward, yDotK, |
| globalPreviousState, globalCurrentState, |
| globalPreviousState, globalCurrentState, |
| mapper); |
| } |
| |
| } |
