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.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.jscience.mathematics.number.Float64;
033
034 import org.jenetics.internal.util.HashBuilder;
035
036 import org.jenetics.util.Function;
037 import org.jenetics.util.Range;
038
039 /**
040 * Normal (Gaussian) distribution. With
041 *
042 * <p>
043 * <img
044 * src="doc-files/normal-pdf.gif"
045 * alt="f(x)=\frac{1}{\sqrt{2\pi \sigma^{2}}}\cdot
046 * e^{-\frac{(x-\mu)^2}{2\sigma^{2}}})"
047 * />
048 * </p>
049 * as <i>pdf</i> and
050 * <p>
051 * <img
052 * src="doc-files/normal-cdf.gif"
053 * alt="f(x)=\frac{1}{2}\cdot \left [ 1 + \textup{erf} \left(
054 * \frac{x - \mu }{\sqrt{2\sigma^{2}}} \right) \right ]"
055 * />
056 * </p>
057 * as <i>cdf</i>.
058 *
059 * @see <a href="http://en.wikipedia.org/wiki/Normal_distribution">Normal distribution</a>
060 *
061 * @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
062 * @since 1.0
063 * @version 1.0 — <em>$Date: 2014-03-01 $</em>
064 */
065 public class NormalDistribution<
066 N extends Number & Comparable<? super N>
067 >
068 implements Distribution<N>
069 {
070
071 /**
072 * <p>
073 * <img
074 * src="doc-files/normal-pdf.gif"
075 * alt="f(x)=\frac{1}{\sqrt{2\pi \sigma^{2}}}\cdot
076 * e^{-\frac{(x-\mu)^2}{2\sigma^{2}}})"
077 * />
078 * </p>
079 *
080 * @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
081 * @since 1.0
082 * @version 1.0 — <em>$Date: 2014-03-01 $</em>
083 */
084 static final class PDF<N extends Number & Comparable<? super N>>
085 implements
086 Function<N, Float64>,
087 Serializable
088 {
089 private static final long serialVersionUID = 1L;
090
091 private final Range<N> _domain;
092 private final double _mean;
093 private final double _var;
094 private final double _stddev;
095
096 public PDF(final Range<N> domain, final double mean, final double var) {
097 _domain = domain;
098 _mean = mean;
099 _var = var;
100 _stddev = Math.sqrt(var);
101 }
102
103 @Override
104 public Float64 apply(final N value) {
105 final double x = value.doubleValue();
106
107 Float64 result = Float64.ZERO;
108 if (_domain.contains(value)) {
109 result = Float64.valueOf(φ(x, _mean, _stddev));
110 }
111
112 return result;
113 }
114
115 @Override
116 public String toString() {
117 return format(
118 Locale.ENGLISH,
119 "p(x) = N[µ=%f, σ²=%f](x)", _mean, _var
120 );
121 }
122
123 }
124
125 /**
126 * <p>
127 * <img
128 * src="doc-files/normal-cdf.gif"
129 * alt="f(x)=\frac{1}{2}\cdot \left [ 1 + \textup{erf} \left(
130 * \frac{x - \mu }{\sqrt{2\sigma^{2}}} \right) \right ]"
131 * />
132 * </p>
133 *
134 * @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
135 * @since 1.0
136 * @version 1.0 — <em>$Date: 2014-03-01 $</em>
137 */
138 static final class CDF<N extends Number & Comparable<? super N>>
139 implements
140 Function<N, Float64>,
141 Serializable
142 {
143 private static final long serialVersionUID = 1L;
144
145 private final double _min;
146 private final double _max;
147 private final double _mean;
148 private final double _var;
149 private final double _stddev;
150
151 public CDF(final Range<N> domain, final double mean, final double var) {
152 _min = domain.getMin().doubleValue();
153 _max = domain.getMax().doubleValue();
154 _mean = mean;
155 _var = var;
156 _stddev = Math.sqrt(var);
157 }
158
159 @Override
160 public Float64 apply(final N value) {
161 final double x = value.doubleValue();
162
163 Float64 result = null;
164 if (x < _min) {
165 result = Float64.ZERO;
166 } else if (x > _max) {
167 result = Float64.ONE;
168 } else {
169 result = Float64.valueOf(Φ(x, _mean, _stddev));
170 }
171
172 return result;
173 }
174
175 @Override
176 public String toString() {
177 return format(
178 Locale.ENGLISH,
179 "P(x) = 1/2(1 + erf((x - %f)/(sqrt(2·%f))))",
180 _mean, _var
181 );
182 }
183
184 }
185
186 private final Range<N> _domain;
187 private final Function<N, Float64> _cdf;
188 private final Function<N, Float64> _pdf;
189 private final double _mean;
190 private final double _var;
191
192 /**
193 * Create a new normal distribution object.
194 *
195 * @param domain the domain of the distribution.
196 * @param mean the mean value of the normal distribution.
197 * @param var the variance of the normal distribution.
198 * @throws NullPointerException if the {@code domain} is {@code null}.
199 * @throws IllegalArgumentException if the variance is negative.
200 */
201 public NormalDistribution(
202 final Range<N> domain,
203 final double mean,
204 final double var
205 ) {
206 _domain = requireNonNull(domain, "Domain");
207 _mean = mean;
208 _var = nonNegative(var, "Variance");
209
210 _pdf = new PDF<>(_domain, _mean, _var);
211 _cdf = new CDF<>(_domain, _mean, _var);
212 }
213
214 @Override
215 public Range<N> getDomain() {
216 return _domain;
217 }
218
219 /**
220 * Return a new CDF object.
221 *
222 * <p>
223 * <img
224 * src="doc-files/normal-cdf.gif"
225 * alt="f(x)=\frac{1}{2}\cdot \left [ 1 + \textup{erf} \left(
226 * \frac{x - \mu }{\sqrt{2\sigma^{2}}} \right) \right ]"
227 * />
228 * </p>
229 */
230 @Override
231 public Function<N, Float64> getCDF() {
232 return _cdf;
233 }
234
235 /**
236 * Return a new PDF object.
237 *
238 * <p>
239 * <img
240 * src="doc-files/normal-pdf.gif"
241 * alt="f(x)=\frac{1}{\sqrt{2\pi \sigma^{2}}}\cdot e^{-\frac{(x-\mu)^2}{2\sigma^{2}}})"
242 * />
243 * </p>
244 */
245 @Override
246 public Function<N, Float64> getPDF() {
247 return _pdf;
248 }
249
250 @Override
251 public int hashCode() {
252 return HashBuilder.of(getClass()).and(_domain).and(_mean).and(_var).value();
253 }
254
255 @Override
256 public boolean equals(final Object obj) {
257 if (obj == this) {
258 return true;
259 }
260 if (obj == null || obj.getClass() != getClass()) {
261 return false;
262 }
263
264 final NormalDistribution<?> dist = (NormalDistribution<?>)obj;
265 return eq(_domain, dist._domain) &&
266 eq(_mean, dist._mean) &&
267 eq(_var, dist._var);
268 }
269
270 @Override
271 public String toString() {
272 return format("N[µ=%f, σ²=%f]", _mean, _var);
273 }
274
275 }
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