001 /*
002 * Java Genetic Algorithm Library (jenetics-2.0.2).
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.math.statistics.Φ;
025 import static org.jenetics.internal.math.statistics.φ;
026 import static org.jenetics.internal.util.object.eq;
027 import static org.jenetics.internal.util.object.nonNegative;
028
029 import java.io.Serializable;
030 import java.util.Locale;
031
032 import org.jenetics.internal.util.HashBuilder;
033
034 import org.jenetics.util.Function;
035 import org.jenetics.util.Range;
036
037 /**
038 * Normal (Gaussian) distribution. With
039 *
040 * <p>
041 * <img
042 * src="doc-files/normal-pdf.gif"
043 * alt="f(x)=\frac{1}{\sqrt{2\pi \sigma^{2}}}\cdot
044 * e^{-\frac{(x-\mu)^2}{2\sigma^{2}}})"
045 * >
046 * </p>
047 * as <i>pdf</i> and
048 * <p>
049 * <img
050 * src="doc-files/normal-cdf.gif"
051 * alt="f(x)=\frac{1}{2}\cdot \left [ 1 + \textup{erf} \left(
052 * \frac{x - \mu }{\sqrt{2\sigma^{2}}} \right) \right ]"
053 * >
054 * </p>
055 * as <i>cdf</i>.
056 *
057 * @see <a href="http://en.wikipedia.org/wiki/Normal_distribution">Normal distribution</a>
058 *
059 * @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
060 * @since 1.0
061 * @version 2.0 — <em>$Date: 2014-03-28 $</em>
062 */
063 public class NormalDistribution<
064 N extends Number & Comparable<? super N>
065 >
066 implements Distribution<N>
067 {
068
069 /**
070 * <p>
071 * <img
072 * src="doc-files/normal-pdf.gif"
073 * alt="f(x)=\frac{1}{\sqrt{2\pi \sigma^{2}}}\cdot
074 * e^{-\frac{(x-\mu)^2}{2\sigma^{2}}})"
075 * >
076 * </p>
077 *
078 * @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
079 * @since 1.0
080 * @version 1.0 — <em>$Date: 2014-03-28 $</em>
081 */
082 static final class PDF<N extends Number & Comparable<? super N>>
083 implements
084 Function<N, Double>,
085 Serializable
086 {
087 private static final long serialVersionUID = 2L;
088
089 private final Range<N> _domain;
090 private final double _mean;
091 private final double _var;
092 private final double _stddev;
093
094 public PDF(final Range<N> domain, final double mean, final double var) {
095 _domain = domain;
096 _mean = mean;
097 _var = var;
098 _stddev = Math.sqrt(var);
099 }
100
101 @Override
102 public Double apply(final N value) {
103 final double x = value.doubleValue();
104
105 double result = 0.0;
106 if (_domain.contains(value)) {
107 result = φ(x, _mean, _stddev);
108 }
109
110 return result;
111 }
112
113 @Override
114 public String toString() {
115 return format(
116 Locale.ENGLISH,
117 "p(x) = N[µ=%f, σ²=%f](x)", _mean, _var
118 );
119 }
120
121 }
122
123 /**
124 * <p>
125 * <img
126 * src="doc-files/normal-cdf.gif"
127 * alt="f(x)=\frac{1}{2}\cdot \left [ 1 + \textup{erf} \left(
128 * \frac{x - \mu }{\sqrt{2\sigma^{2}}} \right) \right ]"
129 * >
130 * </p>
131 *
132 * @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
133 * @since 1.0
134 * @version 1.0 — <em>$Date: 2014-03-28 $</em>
135 */
136 static final class CDF<N extends Number & Comparable<? super N>>
137 implements
138 Function<N, Double>,
139 Serializable
140 {
141 private static final long serialVersionUID = 2L;
142
143 private final double _min;
144 private final double _max;
145 private final double _mean;
146 private final double _var;
147 private final double _stddev;
148
149 public CDF(final Range<N> domain, final double mean, final double var) {
150 _min = domain.getMin().doubleValue();
151 _max = domain.getMax().doubleValue();
152 _mean = mean;
153 _var = var;
154 _stddev = Math.sqrt(var);
155 }
156
157 @Override
158 public Double apply(final N value) {
159 final double x = value.doubleValue();
160
161 double result = 0.0;
162 if (x < _min) {
163 result = 0.0;
164 } else if (x > _max) {
165 result = 1.0;
166 } else {
167 result = Φ(x, _mean, _stddev);
168 }
169
170 return result;
171 }
172
173 @Override
174 public String toString() {
175 return format(
176 Locale.ENGLISH,
177 "P(x) = 1/2(1 + erf((x - %f)/(sqrt(2·%f))))",
178 _mean, _var
179 );
180 }
181
182 }
183
184 private final Range<N> _domain;
185 private final Function<N, Double> _cdf;
186 private final Function<N, Double> _pdf;
187 private final double _mean;
188 private final double _var;
189
190 /**
191 * Create a new normal distribution object.
192 *
193 * @param domain the domain of the distribution.
194 * @param mean the mean value of the normal distribution.
195 * @param var the variance of the normal distribution.
196 * @throws NullPointerException if the {@code domain} is {@code null}.
197 * @throws IllegalArgumentException if the variance is negative.
198 */
199 public NormalDistribution(
200 final Range<N> domain,
201 final double mean,
202 final double var
203 ) {
204 _domain = requireNonNull(domain, "Domain");
205 _mean = mean;
206 _var = nonNegative(var, "Variance");
207
208 _pdf = new PDF<>(_domain, _mean, _var);
209 _cdf = new CDF<>(_domain, _mean, _var);
210 }
211
212 @Override
213 public Range<N> getDomain() {
214 return _domain;
215 }
216
217 /**
218 * Return a new CDF object.
219 *
220 * <p>
221 * <img
222 * src="doc-files/normal-cdf.gif"
223 * alt="f(x)=\frac{1}{2}\cdot \left [ 1 + \textup{erf} \left(
224 * \frac{x - \mu }{\sqrt{2\sigma^{2}}} \right) \right ]"
225 * >
226 * </p>
227 */
228 @Override
229 public Function<N, Double> getCDF() {
230 return _cdf;
231 }
232
233 /**
234 * Return a new PDF object.
235 *
236 * <p>
237 * <img
238 * src="doc-files/normal-pdf.gif"
239 * alt="f(x)=\frac{1}{\sqrt{2\pi \sigma^{2}}}\cdot e^{-\frac{(x-\mu)^2}{2\sigma^{2}}})"
240 * >
241 * </p>
242 */
243 @Override
244 public Function<N, Double> getPDF() {
245 return _pdf;
246 }
247
248 @Override
249 public int hashCode() {
250 return HashBuilder.of(getClass()).and(_domain).and(_mean).and(_var).value();
251 }
252
253 @Override
254 public boolean equals(final Object obj) {
255 if (obj == this) {
256 return true;
257 }
258 if (obj == null || obj.getClass() != getClass()) {
259 return false;
260 }
261
262 final NormalDistribution<?> dist = (NormalDistribution<?>)obj;
263 return eq(_domain, dist._domain) &&
264 eq(_mean, dist._mean) &&
265 eq(_var, dist._var);
266 }
267
268 @Override
269 public String toString() {
270 return format("N[µ=%f, σ²=%f]", _mean, _var);
271 }
272
273 }
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