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.DoubleFunction;
20
21 import org.hipparchus.analysis.CalculusFieldUnivariateFunction;
22 import org.hipparchus.analysis.integration.UnivariateIntegrator;
23
24 /**
25 * Wrapper to perform univariate complex integration using an underlying real integration algorithms.
26 * @since 2.0
27 */
28 public class ComplexUnivariateIntegrator {
29
30 /** Underlying real integrator. */
31 private UnivariateIntegrator integrator;
32
33 /** Crate a complex integrator from a real integrator.
34 * @param integrator underlying real integrator to use
35 */
36 public ComplexUnivariateIntegrator(final UnivariateIntegrator integrator) {
37 this.integrator = integrator;
38 }
39
40 /**
41 * Integrate a function along a straight path between points.
42 *
43 * @param maxEval maximum number of evaluations (real and imaginary
44 * parts are evaluated separately, so up to twice this number may be used)
45 * @param f the integrand function
46 * @param start start point of the integration path
47 * @param end end point of the integration path
48 * @return the value of integral along the straight path
49 */
50 public Complex integrate(final int maxEval, final CalculusFieldUnivariateFunction<Complex> f,
51 final Complex start, final Complex end) {
52
53 // linear mapping from real interval [0; 1] to function value along complex straight path from start to end
54 final Complex rate = end.subtract(start);
55 final DoubleFunction<Complex> mapped = t -> f.value(start.add(rate.multiply(t)));
56
57 // integrate real and imaginary parts separately
58 final double real = integrator.integrate(maxEval, t -> mapped.apply(t).getRealPart(), 0.0, 1.0);
59 final double imaginary = integrator.integrate(maxEval, t -> mapped.apply(t).getImaginaryPart(), 0.0, 1.0);
60
61 // combine integrals
62 return new Complex(real, imaginary).multiply(rate);
63
64 }
65
66 /**
67 * Integrate a function along a polyline path between any number of points.
68 *
69 * @param maxEval maximum number of evaluations (real and imaginary
70 * parts are evaluated separately and each path segments are also evaluated
71 * separately, so up to 2n times this number may be used for n segments)
72 * @param f the integrand function
73 * @param start start point of the integration path
74 * @param path successive points defining the path vertices
75 * @return the value of integral along the polyline path
76 */
77 public Complex integrate(final int maxEval, final CalculusFieldUnivariateFunction<Complex> f,
78 final Complex start, final Complex...path) {
79 Complex sum = Complex.ZERO;
80 Complex previous = start;
81 for (final Complex current : path) {
82 sum = sum.add(integrate(maxEval, f, previous, current));
83 previous = current;
84 }
85 return sum;
86 }
87
88 }