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 * 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
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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 Gill fourth order Runge-Kutta
integrator for Ordinary Differential Equations .
This method is an explicit Runge-Kutta method, its Butcher-array
is the following one :
   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

where q = sqrt(2)

Type parameters:
<T> – the type of the field elements
See Also:
EulerFieldIntegrator
ClassicalRungeKuttaFieldIntegrator
MidpointFieldIntegrator
ThreeEighthesFieldIntegrator
LutherFieldIntegrator
Since:
3.6/**
 * 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)</p>
 *
 * @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.
Params:
field – field to which the time and state vector elements belong
step – integration step/** 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} /** {@inheritDoc} */
    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} /** {@inheritDoc} */
    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} /** {@inheritDoc} */
    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} /** {@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<T>(getField(), forward, yDotK,
                                                globalPreviousState, globalCurrentState,
                                                globalPreviousState, globalCurrentState,
                                                mapper);
    }

}