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 * http://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 package org.apache.commons.math4.legacy.ode.nonstiff;
19
20 import org.apache.commons.math4.legacy.core.Field;
21 import org.apache.commons.math4.legacy.core.RealFieldElement;
22 import org.apache.commons.math4.legacy.ode.FieldEquationsMapper;
23 import org.apache.commons.math4.legacy.ode.FieldODEStateAndDerivative;
24 import org.apache.commons.math4.legacy.core.MathArrays;
25
26
27 /**
28 * This class implements the 5(4) Dormand-Prince integrator for Ordinary
29 * Differential Equations.
30
31 * <p>This integrator is an embedded Runge-Kutta integrator
32 * of order 5(4) used in local extrapolation mode (i.e. the solution
33 * is computed using the high order formula) with stepsize control
34 * (and automatic step initialization) and continuous output. This
35 * method uses 7 functions evaluations per step. However, since this
36 * is an <i>fsal</i>, the last evaluation of one step is the same as
37 * the first evaluation of the next step and hence can be avoided. So
38 * the cost is really 6 functions evaluations per step.</p>
39 *
40 * <p>This method has been published (whithout the continuous output
41 * that was added by Shampine in 1986) in the following article :
42 * <pre>
43 * A family of embedded Runge-Kutta formulae
44 * J. R. Dormand and P. J. Prince
45 * Journal of Computational and Applied Mathematics
46 * volume 6, no 1, 1980, pp. 19-26
47 * </pre>
48 *
49 * @param <T> the type of the field elements
50 * @since 3.6
51 */
52
53 public class DormandPrince54FieldIntegrator<T extends RealFieldElement<T>>
54 extends EmbeddedRungeKuttaFieldIntegrator<T> {
55
56 /** Integrator method name. */
57 private static final String METHOD_NAME = "Dormand-Prince 5(4)";
58
59 /** Error array, element 1. */
60 private final T e1;
61
62 // element 2 is zero, so it is neither stored nor used
63
64 /** Error array, element 3. */
65 private final T e3;
66
67 /** Error array, element 4. */
68 private final T e4;
69
70 /** Error array, element 5. */
71 private final T e5;
72
73 /** Error array, element 6. */
74 private final T e6;
75
76 /** Error array, element 7. */
77 private final T e7;
78
79 /** Simple constructor.
80 * Build a fifth order Dormand-Prince integrator with the given step bounds
81 * @param field field to which the time and state vector elements belong
82 * @param minStep minimal step (sign is irrelevant, regardless of
83 * integration direction, forward or backward), the last step can
84 * be smaller than this
85 * @param maxStep maximal step (sign is irrelevant, regardless of
86 * integration direction, forward or backward), the last step can
87 * be smaller than this
88 * @param scalAbsoluteTolerance allowed absolute error
89 * @param scalRelativeTolerance allowed relative error
90 */
91 public DormandPrince54FieldIntegrator(final Field<T> field,
92 final double minStep, final double maxStep,
93 final double scalAbsoluteTolerance,
94 final double scalRelativeTolerance) {
95 super(field, METHOD_NAME, 6,
96 minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);
97 e1 = fraction( 71, 57600);
98 e3 = fraction( -71, 16695);
99 e4 = fraction( 71, 1920);
100 e5 = fraction(-17253, 339200);
101 e6 = fraction( 22, 525);
102 e7 = fraction( -1, 40);
103 }
104
105 /** Simple constructor.
106 * Build a fifth order Dormand-Prince integrator with the given step bounds
107 * @param field field to which the time and state vector elements belong
108 * @param minStep minimal step (sign is irrelevant, regardless of
109 * integration direction, forward or backward), the last step can
110 * be smaller than this
111 * @param maxStep maximal step (sign is irrelevant, regardless of
112 * integration direction, forward or backward), the last step can
113 * be smaller than this
114 * @param vecAbsoluteTolerance allowed absolute error
115 * @param vecRelativeTolerance allowed relative error
116 */
117 public DormandPrince54FieldIntegrator(final Field<T> field,
118 final double minStep, final double maxStep,
119 final double[] vecAbsoluteTolerance,
120 final double[] vecRelativeTolerance) {
121 super(field, METHOD_NAME, 6,
122 minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
123 e1 = fraction( 71, 57600);
124 e3 = fraction( -71, 16695);
125 e4 = fraction( 71, 1920);
126 e5 = fraction(-17253, 339200);
127 e6 = fraction( 22, 525);
128 e7 = fraction( -1, 40);
129 }
130
131 /** {@inheritDoc} */
132 @Override
133 public T[] getC() {
134 final T[] c = MathArrays.buildArray(getField(), 6);
135 c[0] = fraction(1, 5);
136 c[1] = fraction(3, 10);
137 c[2] = fraction(4, 5);
138 c[3] = fraction(8, 9);
139 c[4] = getField().getOne();
140 c[5] = getField().getOne();
141 return c;
142 }
143
144 /** {@inheritDoc} */
145 @Override
146 public T[][] getA() {
147 final T[][] a = MathArrays.buildArray(getField(), 6, -1);
148 for (int i = 0; i < a.length; ++i) {
149 a[i] = MathArrays.buildArray(getField(), i + 1);
150 }
151 a[0][0] = fraction( 1, 5);
152 a[1][0] = fraction( 3, 40);
153 a[1][1] = fraction( 9, 40);
154 a[2][0] = fraction( 44, 45);
155 a[2][1] = fraction( -56, 15);
156 a[2][2] = fraction( 32, 9);
157 a[3][0] = fraction( 19372, 6561);
158 a[3][1] = fraction(-25360, 2187);
159 a[3][2] = fraction( 64448, 6561);
160 a[3][3] = fraction( -212, 729);
161 a[4][0] = fraction( 9017, 3168);
162 a[4][1] = fraction( -355, 33);
163 a[4][2] = fraction( 46732, 5247);
164 a[4][3] = fraction( 49, 176);
165 a[4][4] = fraction( -5103, 18656);
166 a[5][0] = fraction( 35, 384);
167 a[5][1] = getField().getZero();
168 a[5][2] = fraction( 500, 1113);
169 a[5][3] = fraction( 125, 192);
170 a[5][4] = fraction( -2187, 6784);
171 a[5][5] = fraction( 11, 84);
172 return a;
173 }
174
175 /** {@inheritDoc} */
176 @Override
177 public T[] getB() {
178 final T[] b = MathArrays.buildArray(getField(), 7);
179 b[0] = fraction( 35, 384);
180 b[1] = getField().getZero();
181 b[2] = fraction( 500, 1113);
182 b[3] = fraction( 125, 192);
183 b[4] = fraction(-2187, 6784);
184 b[5] = fraction( 11, 84);
185 b[6] = getField().getZero();
186 return b;
187 }
188
189 /** {@inheritDoc} */
190 @Override
191 protected DormandPrince54FieldStepInterpolator<T>
192 createInterpolator(final boolean forward, T[][] yDotK,
193 final FieldODEStateAndDerivative<T> globalPreviousState,
194 final FieldODEStateAndDerivative<T> globalCurrentState, final FieldEquationsMapper<T> mapper) {
195 return new DormandPrince54FieldStepInterpolator<>(getField(), forward, yDotK,
196 globalPreviousState, globalCurrentState,
197 globalPreviousState, globalCurrentState,
198 mapper);
199 }
200
201 /** {@inheritDoc} */
202 @Override
203 public int getOrder() {
204 return 5;
205 }
206
207 /** {@inheritDoc} */
208 @Override
209 protected T estimateError(final T[][] yDotK, final T[] y0, final T[] y1, final T h) {
210
211 T error = getField().getZero();
212
213 for (int j = 0; j < mainSetDimension; ++j) {
214 final T errSum = yDotK[0][j].multiply(e1).
215 add(yDotK[2][j].multiply(e3)).
216 add(yDotK[3][j].multiply(e4)).
217 add(yDotK[4][j].multiply(e5)).
218 add(yDotK[5][j].multiply(e6)).
219 add(yDotK[6][j].multiply(e7));
220
221 final T yScale = RealFieldElement.max(y0[j].abs(), y1[j].abs());
222 final T tol = (vecAbsoluteTolerance == null) ?
223 yScale.multiply(scalRelativeTolerance).add(scalAbsoluteTolerance) :
224 yScale.multiply(vecRelativeTolerance[j]).add(vecAbsoluteTolerance[j]);
225 final T ratio = h.multiply(errSum).divide(tol);
226 error = error.add(ratio.multiply(ratio));
227 }
228
229 return error.divide(mainSetDimension).sqrt();
230 }
231 }