1 /*
2 * Licensed to the Hipparchus project 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 Hipparchus project 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 package org.hipparchus.complex;
18
19 import java.util.function.Function;
20
21 import org.hipparchus.CalculusFieldElement;
22 import org.hipparchus.analysis.CalculusFieldUnivariateFunction;
23 import org.hipparchus.analysis.integration.FieldUnivariateIntegrator;
24
25 /**
26 * Wrapper to perform univariate complex integration using an underlying real integration algorithms.
27 * @param <T> the type of the field elements
28 * @since 2.0
29 */
30 public class FieldComplexUnivariateIntegrator<T extends CalculusFieldElement<T>> {
31
32 /** Underlying real integrator. */
33 private FieldUnivariateIntegrator<T> integrator;
34
35 /** Crate a complex integrator from a real integrator.
36 * @param integrator underlying real integrator to use
37 */
38 public FieldComplexUnivariateIntegrator(final FieldUnivariateIntegrator<T> integrator) {
39 this.integrator = integrator;
40 }
41
42 /**
43 * Integrate a function along a straight path between points.
44 *
45 * @param maxEval maximum number of evaluations (real and imaginary
46 * parts are evaluated separately, so up to twice this number may be used)
47 * @param f the integrand function
48 * @param start start point of the integration path
49 * @param end end point of the integration path
50 * @return the value of integral along the straight path
51 */
52 public FieldComplex<T> integrate(final int maxEval, final CalculusFieldUnivariateFunction<FieldComplex<T>> f,
53 final FieldComplex<T> start, final FieldComplex<T> end) {
54
55 // linear mapping from real interval [0; 1] to function value along complex straight path from start to end
56 final FieldComplex<T> rate = end.subtract(start);
57 final Function<T, FieldComplex<T>> mapped = t -> f.value(start.add(rate.multiply(t)));
58
59 final T zero = start.getRealPart().getField().getZero();
60 final T one = start.getRealPart().getField().getOne();
61
62 // integrate real and imaginary parts separately
63 final T real = integrator.integrate(maxEval, t -> mapped.apply(t).getRealPart(), zero, one);
64 final T imaginary = integrator.integrate(maxEval, t -> mapped.apply(t).getImaginaryPart(), zero, one);
65
66 // combine integrals
67 return new FieldComplex<>(real, imaginary).multiply(rate);
68
69 }
70
71 /**
72 * Integrate a function along a polyline path between any number of points.
73 *
74 * @param maxEval maximum number of evaluations (real and imaginary
75 * parts are evaluated separately and each path segments are also evaluated
76 * separately, so up to 2n times this number may be used for n segments)
77 * @param f the integrand function
78 * @param start start point of the integration path
79 * @param path successive points defining the path vertices
80 * @return the value of integral along the polyline path
81 */
82 public FieldComplex<T> integrate(final int maxEval, final CalculusFieldUnivariateFunction<FieldComplex<T>> f,
83 final FieldComplex<T> start,
84 @SuppressWarnings("unchecked") final FieldComplex<T>...path) {
85 FieldComplex<T> sum = start.newInstance(0);
86 FieldComplex<T> previous = start;
87 for (final FieldComplex<T> current : path) {
88 sum = sum.add(integrate(maxEval, f, previous, current));
89 previous = current;
90 }
91 return sum;
92 }
93
94 }