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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  package org.hipparchus.analysis.integration;
23  
24  import org.hipparchus.CalculusFieldElement;
25  import org.hipparchus.Field;
26  import org.hipparchus.exception.LocalizedCoreFormats;
27  import org.hipparchus.exception.MathIllegalArgumentException;
28  import org.hipparchus.exception.MathIllegalStateException;
29  import org.hipparchus.util.FastMath;
30  
31  /**
32   * Implements the <a href="http://en.wikipedia.org/wiki/Midpoint_method">
33   * Midpoint Rule</a> for integration of real univariate functions. For
34   * reference, see <b>Numerical Mathematics</b>, ISBN 0387989595,
35   * chapter 9.2.
36   * <p>
37   * The function should be integrable.</p>
38   * @param <T> Type of the field elements.
39   * @since 2.0
40   */
41  public class FieldMidPointIntegrator<T extends CalculusFieldElement<T>> extends BaseAbstractFieldUnivariateIntegrator<T> {
42  
43      /** Maximum number of iterations for midpoint. */
44      public static final int MIDPOINT_MAX_ITERATIONS_COUNT = 64;
45  
46      /**
47       * Build a midpoint integrator with given accuracies and iterations counts.
48       * @param field field to which function argument and value belong
49       * @param relativeAccuracy relative accuracy of the result
50       * @param absoluteAccuracy absolute accuracy of the result
51       * @param minimalIterationCount minimum number of iterations
52       * @param maximalIterationCount maximum number of iterations
53       * (must be less than or equal to {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
54       * @exception MathIllegalArgumentException if minimal number of iterations
55       * is not strictly positive
56       * @exception MathIllegalArgumentException if maximal number of iterations
57       * is lesser than or equal to the minimal number of iterations
58       * @exception MathIllegalArgumentException if maximal number of iterations
59       * is greater than {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
60       */
61      public FieldMidPointIntegrator(final Field<T> field,
62                                     final double relativeAccuracy,
63                                     final double absoluteAccuracy,
64                                     final int minimalIterationCount,
65                                     final int maximalIterationCount)
66          throws MathIllegalArgumentException {
67          super(field, relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
68          if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) {
69              throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_LARGE_BOUND_EXCLUDED,
70                                                     maximalIterationCount, MIDPOINT_MAX_ITERATIONS_COUNT);
71          }
72      }
73  
74      /**
75       * Build a midpoint integrator with given iteration counts.
76       * @param field field to which function argument and value belong
77       * @param minimalIterationCount minimum number of iterations
78       * @param maximalIterationCount maximum number of iterations
79       * (must be less than or equal to {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
80       * @exception MathIllegalArgumentException if minimal number of iterations
81       * is not strictly positive
82       * @exception MathIllegalArgumentException if maximal number of iterations
83       * is lesser than or equal to the minimal number of iterations
84       * @exception MathIllegalArgumentException if maximal number of iterations
85       * is greater than {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
86       */
87      public FieldMidPointIntegrator(final Field<T> field,
88                                     final int minimalIterationCount,
89                                     final int maximalIterationCount)
90          throws MathIllegalArgumentException {
91          super(field, minimalIterationCount, maximalIterationCount);
92          if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) {
93              throw new MathIllegalArgumentException(LocalizedCoreFormats.NUMBER_TOO_LARGE_BOUND_EXCLUDED,
94                                                     maximalIterationCount, MIDPOINT_MAX_ITERATIONS_COUNT);
95          }
96      }
97  
98      /**
99       * Construct a midpoint integrator with default settings.
100      * @param field field to which function argument and value belong
101      * (max iteration count set to {@link #MIDPOINT_MAX_ITERATIONS_COUNT})
102      */
103     public FieldMidPointIntegrator(final Field<T> field) {
104         super(field, DEFAULT_MIN_ITERATIONS_COUNT, MIDPOINT_MAX_ITERATIONS_COUNT);
105     }
106 
107     /**
108      * Compute the n-th stage integral of midpoint rule.
109      * This function should only be called by API <code>integrate()</code> in the package.
110      * To save time it does not verify arguments - caller does.
111      * <p>
112      * The interval is divided equally into 2^n sections rather than an
113      * arbitrary m sections because this configuration can best utilize the
114      * already computed values.</p>
115      *
116      * @param n the stage of 1/2 refinement. Must be larger than 0.
117      * @param previousStageResult Result from the previous call to the
118      * {@code stage} method.
119      * @param min Lower bound of the integration interval.
120      * @param diffMaxMin Difference between the lower bound and upper bound
121      * of the integration interval.
122      * @return the value of n-th stage integral
123      * @throws MathIllegalStateException if the maximal number of evaluations
124      * is exceeded.
125      */
126     private T stage(final int n,
127                     T previousStageResult,
128                     T min,
129                     T diffMaxMin)
130         throws MathIllegalStateException {
131 
132         // number of new points in this stage
133         final long np = 1L << (n - 1);
134         T sum = getField().getZero();
135 
136         // spacing between adjacent new points
137         final T spacing = diffMaxMin.divide(np);
138 
139         // the first new point
140         T x = min.add(spacing.multiply(0.5));
141         for (long i = 0; i < np; i++) {
142             sum = sum.add(computeObjectiveValue(x));
143             x = x.add(spacing);
144         }
145         // add the new sum to previously calculated result
146         return previousStageResult.add(sum.multiply(spacing)).multiply(0.5);
147     }
148 
149 
150     /** {@inheritDoc} */
151     @Override
152     protected T doIntegrate()
153         throws MathIllegalArgumentException, MathIllegalStateException {
154 
155         final T min = getMin();
156         final T diff = getMax().subtract(min);
157         final T midPoint = min.add(diff.multiply(0.5));
158 
159         T oldt = diff.multiply(computeObjectiveValue(midPoint));
160 
161         while (true) {
162             iterations.increment();
163             final int i = iterations.getCount();
164             final T t = stage(i, oldt, min, diff);
165             if (i >= getMinimalIterationCount()) {
166                 final double delta  = FastMath.abs(t.subtract(oldt)).getReal();
167                 final double rLimit = FastMath.abs(oldt).add(FastMath.abs(t)).multiply(0.5 * getRelativeAccuracy()).getReal();
168                 if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
169                     return t;
170                 }
171             }
172             oldt = t;
173         }
174 
175     }
176 
177 }