1 /*
2 * Licensed to the Apache Software Foundation (ASF) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The ASF licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * https://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17
18 /*
19 * This is not the original file distributed by the Apache Software Foundation
20 * It has been modified by the Hipparchus project
21 */
22
23 package org.hipparchus.ode.nonstiff;
24
25 import org.hipparchus.CalculusFieldElement;
26 import org.hipparchus.Field;
27 import org.hipparchus.ode.FieldEquationsMapper;
28 import org.hipparchus.ode.FieldODEStateAndDerivative;
29 import org.hipparchus.util.MathArrays;
30
31
32 /**
33 * This class implements the Gill fourth order Runge-Kutta
34 * integrator for Ordinary Differential Equations .
35
36 * <p>This method is an explicit Runge-Kutta method, its Butcher-array
37 * is the following one :</p>
38 * <pre>
39 * 0 | 0 0 0 0
40 * 1/2 | 1/2 0 0 0
41 * 1/2 | (q-1)/2 (2-q)/2 0 0
42 * 1 | 0 -q/2 (2+q)/2 0
43 * |-------------------------------
44 * | 1/6 (2-q)/6 (2+q)/6 1/6
45 * </pre>
46 * <p>where q = sqrt(2)</p>
47 *
48 * @see EulerFieldIntegrator
49 * @see ClassicalRungeKuttaFieldIntegrator
50 * @see MidpointFieldIntegrator
51 * @see ThreeEighthesFieldIntegrator
52 * @see LutherFieldIntegrator
53 * @param <T> the type of the field elements
54 */
55
56 public class GillFieldIntegrator<T extends CalculusFieldElement<T>>
57 extends RungeKuttaFieldIntegrator<T> {
58
59 /** Name of integration scheme. */
60 public static final String METHOD_NAME = GillIntegrator.METHOD_NAME;
61
62 /** Simple constructor.
63 * Build a fourth-order Gill integrator with the given step.
64 * @param field field to which the time and state vector elements belong
65 * @param step integration step
66 */
67 public GillFieldIntegrator(final Field<T> field, final T step) {
68 super(field, METHOD_NAME, step);
69 }
70
71 /** {@inheritDoc} */
72 @Override
73 public T[] getC() {
74 final T[] c = MathArrays.buildArray(getField(), 3);
75 c[0] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 1, 2);
76 c[1] = c[0];
77 c[2] = getField().getOne();
78 return c;
79 }
80
81 /** {@inheritDoc} */
82 @Override
83 public T[][] getA() {
84
85 final T two = getField().getZero().add(2);
86 final T sqrtTwo = two.sqrt();
87
88 final T[][] a = MathArrays.buildArray(getField(), 3, -1);
89 for (int i = 0; i < a.length; ++i) {
90 a[i] = MathArrays.buildArray(getField(), i + 1);
91 }
92 a[0][0] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 1, 2);
93 a[1][0] = sqrtTwo.subtract(1).multiply(0.5);
94 a[1][1] = sqrtTwo.subtract(2).multiply(-0.5);
95 a[2][0] = getField().getZero();
96 a[2][1] = sqrtTwo.multiply(-0.5);
97 a[2][2] = sqrtTwo.add(2).multiply(0.5);
98 return a;
99 }
100
101 /** {@inheritDoc} */
102 @Override
103 public T[] getB() {
104
105 final T two = getField().getZero().add(2);
106 final T sqrtTwo = two.sqrt();
107
108 final T[] b = MathArrays.buildArray(getField(), 4);
109 b[0] = FieldExplicitRungeKuttaIntegrator.fraction(getField(), 1, 6);
110 b[1] = sqrtTwo.subtract(2).divide(-6);
111 b[2] = sqrtTwo.add(2).divide(6);
112 b[3] = b[0];
113
114 return b;
115
116 }
117
118 /** {@inheritDoc} */
119 @Override
120 protected GillFieldStateInterpolator<T>
121 createInterpolator(final boolean forward, T[][] yDotK,
122 final FieldODEStateAndDerivative<T> globalPreviousState,
123 final FieldODEStateAndDerivative<T> globalCurrentState,
124 final FieldEquationsMapper<T> mapper) {
125 return new GillFieldStateInterpolator<T>(getField(), forward, yDotK,
126 globalPreviousState, globalCurrentState,
127 globalPreviousState, globalCurrentState,
128 mapper);
129 }
130
131 }