001 /*
002 * Java Genetic Algorithm Library (jenetics-1.5.0).
003 * Copyright (c) 2007-2013 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.util.object.eq;
027 import static org.jenetics.util.object.hashCodeOf;
028 import static org.jenetics.util.object.nonNegative;
029
030 import java.io.Serializable;
031 import java.util.Locale;
032
033 import org.jscience.mathematics.number.Float64;
034
035 import org.jenetics.util.Function;
036 import org.jenetics.util.Range;
037
038 /**
039 * Normal (Gaussian) distribution. With
040 *
041 * <p>
042 * <img
043 * src="doc-files/normal-pdf.gif"
044 * alt="f(x)=\frac{1}{\sqrt{2\pi \sigma^{2}}}\cdot
045 * e^{-\frac{(x-\mu)^2}{2\sigma^{2}}})"
046 * />
047 * </p>
048 * as <i>pdf</i> and
049 * <p>
050 * <img
051 * src="doc-files/normal-cdf.gif"
052 * alt="f(x)=\frac{1}{2}\cdot \left [ 1 + \textup{erf} \left(
053 * \frac{x - \mu }{\sqrt{2\sigma^{2}}} \right) \right ]"
054 * />
055 * </p>
056 * as <i>cdf</i>.
057 *
058 * @see <a href="http://en.wikipedia.org/wiki/Normal_distribution">Normal distribution</a>
059 *
060 * @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
061 * @since 1.0
062 * @version 1.0 — <em>$Date: 2013-09-01 $</em>
063 */
064 public class NormalDistribution<
065 N extends Number & Comparable<? super N>
066 >
067 implements Distribution<N>
068 {
069
070 /**
071 * <p>
072 * <img
073 * src="doc-files/normal-pdf.gif"
074 * alt="f(x)=\frac{1}{\sqrt{2\pi \sigma^{2}}}\cdot
075 * e^{-\frac{(x-\mu)^2}{2\sigma^{2}}})"
076 * />
077 * </p>
078 *
079 * @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
080 * @since 1.0
081 * @version 1.0 — <em>$Date: 2013-09-01 $</em>
082 */
083 static final class PDF<N extends Number & Comparable<? super N>>
084 implements
085 Function<N, Float64>,
086 Serializable
087 {
088 private static final long serialVersionUID = 1L;
089
090 private final Range<N> _domain;
091 private final double _mean;
092 private final double _var;
093 private final double _stddev;
094
095 public PDF(final Range<N> domain, final double mean, final double var) {
096 _domain = domain;
097 _mean = mean;
098 _var = var;
099 _stddev = Math.sqrt(var);
100 }
101
102 @Override
103 public Float64 apply(final N value) {
104 final double x = value.doubleValue();
105
106 Float64 result = Float64.ZERO;
107 if (_domain.contains(value)) {
108 result = Float64.valueOf(φ(x, _mean, _stddev));
109 }
110
111 return result;
112 }
113
114 @Override
115 public String toString() {
116 return format(
117 Locale.ENGLISH,
118 "p(x) = N[µ=%f, σ²=%f](x)", _mean, _var
119 );
120 }
121
122 }
123
124 /**
125 * <p>
126 * <img
127 * src="doc-files/normal-cdf.gif"
128 * alt="f(x)=\frac{1}{2}\cdot \left [ 1 + \textup{erf} \left(
129 * \frac{x - \mu }{\sqrt{2\sigma^{2}}} \right) \right ]"
130 * />
131 * </p>
132 *
133 * @author <a href="mailto:franz.wilhelmstoetter@gmx.at">Franz Wilhelmstötter</a>
134 * @since 1.0
135 * @version 1.0 — <em>$Date: 2013-09-01 $</em>
136 */
137 static final class CDF<N extends Number & Comparable<? super N>>
138 implements
139 Function<N, Float64>,
140 Serializable
141 {
142 private static final long serialVersionUID = 1L;
143
144 private final double _min;
145 private final double _max;
146 private final double _mean;
147 private final double _var;
148 private final double _stddev;
149
150 public CDF(final Range<N> domain, final double mean, final double var) {
151 _min = domain.getMin().doubleValue();
152 _max = domain.getMax().doubleValue();
153 _mean = mean;
154 _var = var;
155 _stddev = Math.sqrt(var);
156 }
157
158 @Override
159 public Float64 apply(final N value) {
160 final double x = value.doubleValue();
161
162 Float64 result = null;
163 if (x < _min) {
164 result = Float64.ZERO;
165 } else if (x > _max) {
166 result = Float64.ONE;
167 } else {
168 result = Float64.valueOf(Φ(x, _mean, _stddev));
169 }
170
171 return result;
172 }
173
174 @Override
175 public String toString() {
176 return format(
177 Locale.ENGLISH,
178 "P(x) = 1/2(1 + erf((x - %f)/(sqrt(2·%f))))",
179 _mean, _var
180 );
181 }
182
183 }
184
185 private final Range<N> _domain;
186 private final Function<N, Float64> _cdf;
187 private final Function<N, Float64> _pdf;
188 private final double _mean;
189 private final double _var;
190
191 /**
192 * Create a new normal distribution object.
193 *
194 * @param domain the domain of the distribution.
195 * @param mean the mean value of the normal distribution.
196 * @param var the variance of the normal distribution.
197 * @throws NullPointerException if the {@code domain} is {@code null}.
198 * @throws IllegalArgumentException if the variance is negative.
199 */
200 public NormalDistribution(
201 final Range<N> domain,
202 final double mean,
203 final double var
204 ) {
205 _domain = requireNonNull(domain, "Domain");
206 _mean = mean;
207 _var = nonNegative(var, "Variance");
208
209 _pdf = new PDF<>(_domain, _mean, _var);
210 _cdf = new CDF<>(_domain, _mean, _var);
211 }
212
213 @Override
214 public Range<N> getDomain() {
215 return _domain;
216 }
217
218 /**
219 * Return a new CDF object.
220 *
221 * <p>
222 * <img
223 * src="doc-files/normal-cdf.gif"
224 * alt="f(x)=\frac{1}{2}\cdot \left [ 1 + \textup{erf} \left(
225 * \frac{x - \mu }{\sqrt{2\sigma^{2}}} \right) \right ]"
226 * />
227 * </p>
228 */
229 @Override
230 public Function<N, Float64> getCDF() {
231 return _cdf;
232 }
233
234 /**
235 * Return a new PDF object.
236 *
237 * <p>
238 * <img
239 * src="doc-files/normal-pdf.gif"
240 * alt="f(x)=\frac{1}{\sqrt{2\pi \sigma^{2}}}\cdot e^{-\frac{(x-\mu)^2}{2\sigma^{2}}})"
241 * />
242 * </p>
243 */
244 @Override
245 public Function<N, Float64> getPDF() {
246 return _pdf;
247 }
248
249 @Override
250 public int hashCode() {
251 return hashCodeOf(getClass()).and(_domain).and(_mean).and(_var).value();
252 }
253
254 @Override
255 public boolean equals(final Object obj) {
256 if (obj == this) {
257 return true;
258 }
259 if (obj == null || obj.getClass() != getClass()) {
260 return false;
261 }
262
263 final NormalDistribution<?> dist = (NormalDistribution<?>)obj;
264 return eq(_domain, dist._domain) &&
265 eq(_mean, dist._mean) &&
266 eq(_var, dist._var);
267 }
268
269 @Override
270 public String toString() {
271 return format("N[µ=%f, σ²=%f]", _mean, _var);
272 }
273
274 }
275
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