001 /*
002 * Java Genetic Algorithm Library (jenetics-1.6.0).
003 * Copyright (c) 2007-2014 Franz Wilhelmstötter
004 *
005 * Licensed under the Apache License, Version 2.0 (the "License");
006 * you may not use this file except in compliance with the License.
007 * You may obtain a copy of the License at
008 *
009 * http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 *
017 * Author:
018 * Franz Wilhelmstötter (franz.wilhelmstoetter@gmx.at)
019 */
020 package org.jenetics.stat;
021
022 import static java.lang.String.format;
023 import static java.util.Objects.requireNonNull;
024 import static org.jenetics.internal.util.object.eq;
025
026 import java.io.Serializable;
027 import java.util.Locale;
028
029 import org.jscience.mathematics.number.Float64;
030
031 import org.jenetics.internal.util.HashBuilder;
032
033 import org.jenetics.util.Function;
034 import org.jenetics.util.Range;
035
036
037 /**
038 * <p>This distribution has the following cdf.</p>
039 * <p><img src="doc-files/LinearDistribution.png" /></p>
040 * <p>
041 * The only restriction is that the integral of the cdf must be one.
042 * </p>
043 * <p>
044 * <img src="doc-files/linear-precondition.gif"
045 * alt="\int_{x_1}^{x_2}\left(
046 * \\underset{k} {\\underbrace {\frac{y_2-y_1}{x_2-x_1}}} \cdot x +
047 * \\underset{d}{\\underbrace {y_1-\frac{y_2-y_1}{x_2-x_1}\cdot x_1}}
048 * \right)\mathrm{d}x = 1"
049 * />
050 * </p>
051 *
052 * Solving this integral leads to
053 * <p>
054 * <img src="doc-files/linear-precondition-y2.gif"
055 * alt="y_2 = -\frac{(x_2-x_1)\cdot y_1 - 2}{x_2-x_1}"
056 * />
057 * </p>
058 *
059 * for fixed values for <i>x<sub>1</sub></i>, <i>x<sub>2</sub></i> and
060 * <i>y<sub>1</sub></i>.
061 * <p>
062 * If the value of <i>y<sub>2</sub></i> < 0, the value of <i>x<sub>2</sub></i>
063 * is decreased so that the resulting triangle (<i>x<sub>1</sub></i>,0),
064 * (<i>x<sub>1</sub></i>,<i>y<sub>1</sub></i>), (<i>x<sub>2</sub></i>,0) has
065 * an area of <i>one</i>.
066 * </p>
067 *
068 * @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
069 * @since 1.0
070 * @version 1.0 — <em>$Date: 2014-03-01 $</em>
071 */
072 public class LinearDistribution<
073 N extends Number & Comparable<? super N>
074 >
075 implements Distribution<N>
076 {
077
078 /**
079 * <p>
080 * <img
081 * src="doc-files/linear-pdf.gif"
082 * alt="f(x) = \left(
083 * \frac{y_2-y_1}{x_2-x_1} \cdot x +
084 * y_1-\frac{y_2-y_1}{x_2-x_1}\cdot x_1
085 * \right)"
086 * />
087 * </p>
088 *
089 * @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
090 * @since 1.0
091 * @version 1.0 — <em>$Date: 2014-03-01 $</em>
092 */
093 static final class PDF<N extends Number & Comparable<? super N>>
094 implements
095 Function<N, Float64>,
096 Serializable
097 {
098 private static final long serialVersionUID = 1L;
099
100 private final double _min;
101 private final double _max;
102 private final double _k;
103 private final double _d;
104
105 public PDF(
106 final double x1, final double y1,
107 final double x2, final double y2
108 ) {
109 _min = x1;
110 _max = x2;
111 _k = (y2 - y1)/(x2 - x1);
112 _d = y1 - _k*x1;
113 }
114
115 @Override
116 public Float64 apply(final N value) {
117 final double x = value.doubleValue();
118
119 Float64 result = Float64.ZERO;
120 if (x >= _min && x <= _max) {
121 result = Float64.valueOf(_k*x + _d);
122 }
123
124 return result;
125 }
126
127 @Override
128 public String toString() {
129 return format(Locale.ENGLISH, "p(x) = %f·x + %f", _k, _d);
130 }
131
132 }
133
134 /**
135 * <p>
136 * <img
137 * src="doc-files/linear-cdf.gif"
138 * alt="f(x)=-\frac{(x^2-2x_2x)y_1 - (x^2 - 2x_1x)y_2}
139 * {2(x_2 - x_1)}"
140 * />
141 * </p>
142 *
143 * @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
144 * @since 1.0
145 * @version 1.0 — <em>$Date: 2014-03-01 $</em>
146 */
147 static final class CDF<N extends Number & Comparable<? super N>>
148 implements
149 Function<N, Float64>,
150 Serializable
151 {
152 private static final long serialVersionUID = 1L;
153
154 private final double _x1;
155 private final double _x2;
156
157 private final double _k;
158 private final double _d;
159
160 public CDF(
161 final double x1, final double y1,
162 final double x2, final double y2
163 ) {
164 _x1 = x1;
165 _x2 = x2;
166 _k = (y2 - y1)/(x2 - x1);
167 _d = y1 - _k*x1;
168 }
169
170 @Override
171 public Float64 apply(final N value) {
172 final double x = value.doubleValue();
173
174 Float64 result = null;
175 if (x < _x1) {
176 result = Float64.ZERO;
177 } else if (x > _x2) {
178 result = Float64.ONE;
179 } else {
180 // result = Float64.valueOf(
181 // -((x*x - 2*x*_x2)*_y1 - (x*x - 2*x*_x1)*_y2)/
182 // (2*(_x2 - _x1))
183 // );
184 result = Float64.valueOf( _k*x*x/2.0 + _d*x);
185 }
186
187 return result;
188 }
189
190 @Override
191 public String toString() {
192 return format(Locale.ENGLISH, "P(x) = %f·x² - %f·x", _k/2.0, _d);
193 }
194
195 }
196
197
198 private final Range<N> _domain;
199 private final Function<N, Float64> _cdf;
200 private final Function<N, Float64> _pdf;
201
202 private final double _x1;
203 private final double _x2;
204 private final double _y1;
205 private final double _y2;
206
207 public LinearDistribution(final Range<N> domain, final double y1) {
208 _domain = requireNonNull(domain);
209
210 _y1 = Math.max(y1, 0.0);
211 _x1 = domain.getMin().doubleValue();
212 _y2 = Math.max(y2(_x1, domain.getMax().doubleValue(), y1), 0.0);
213 if (_y2 == 0) {
214 _x2 = 2.0/_y1 + _x1;
215 } else {
216 _x2 = domain.getMax().doubleValue();
217 }
218
219 _cdf = new CDF<>(_x1, _y1, _x2, _y2);
220 _pdf = new PDF<>(_x1, _y1, _x2, _y2);
221 }
222
223 private static double y2(final double x1, final double x2, final double y1) {
224 return -((x2 - x1)*y1 - 2)/(x2 - x1);
225 }
226
227 @Override
228 public Range<N> getDomain() {
229 return _domain;
230 }
231
232 /**
233 * Return a new CDF object.
234 *
235 * <p>
236 * <img
237 * src="doc-files/linear-cdf.gif"
238 * alt="f(x)=-\frac{(x^2-2x_2x)y_1 - (x^2 - 2x_1x)y_2}
239 * {2(x_2 - x_1)}"
240 * />
241 * </p>
242 *
243 */
244 @Override
245 public Function<N, Float64> getCDF() {
246 return _cdf;
247 }
248
249 /**
250 * Return a new PDF object.
251 *
252 * <p>
253 * <img
254 * src="doc-files/linear-pdf.gif"
255 * alt="f(x) = \left(
256 * \frac{y_2-y_1}{x_2-x_1} \cdot x +
257 * y_1-\frac{y_2-y_1}{x_2-x_1}\cdot x_1
258 * \right)"
259 * />
260 * </p>
261 *
262 */
263 @Override
264 public Function<N, Float64> getPDF() {
265 return _pdf;
266 }
267
268 @Override
269 public int hashCode() {
270 return HashBuilder.of(getClass()).
271 and(_domain).
272 and(_x1).and(_x2).
273 and(_y1).and(_y2).value();
274 }
275
276 @Override
277 public boolean equals(final Object obj) {
278 if (obj == this) {
279 return true;
280 }
281 if (obj == null || getClass() != obj.getClass()) {
282 return false;
283 }
284
285 final LinearDistribution<?> dist = (LinearDistribution<?>)obj;
286 return eq(_domain, dist._domain) &&
287 eq(_x1, dist._x1) && eq(_x2, dist._x2) &&
288 eq(_y1, dist._y1) && eq(_y2, dist._y2);
289 }
290
291 @Override
292 public String toString() {
293 return format(
294 "LinearDistribution[(%f, %f), (%f, %f)]",
295 _x1, _y1, _x2, _y2
296 ) ;
297 }
298
299 }
|