/*
* 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;
import org.apache.commons.math3.util.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</p>
*
* @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} */
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} */
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} */
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<T>(getField(), forward, yDotK,
globalPreviousState, globalCurrentState,
globalPreviousState, globalCurrentState,
mapper);
}
}