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 *      http://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
18package org.apache.commons.math.distribution;
19
20import java.io.Serializable;
21
22import org.apache.commons.math.MathRuntimeException;
23import org.apache.commons.math.exception.util.LocalizedFormats;
24import org.apache.commons.math.util.FastMath;
25
26/**
27 * Default implementation of
28 * {@link org.apache.commons.math.distribution.CauchyDistribution}.
29 *
30 * @since 1.1
31 * @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $
32 */
33public class CauchyDistributionImpl extends AbstractContinuousDistribution
34        implements CauchyDistribution, Serializable {
35
36    /**
37     * Default inverse cumulative probability accuracy
38     * @since 2.1
39     */
40    public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
41
42    /** Serializable version identifier */
43    private static final long serialVersionUID = 8589540077390120676L;
44
45    /** The median of this distribution. */
46    private double median = 0;
47
48    /** The scale of this distribution. */
49    private double scale = 1;
50
51    /** Inverse cumulative probability accuracy */
52    private final double solverAbsoluteAccuracy;
53
54    /**
55     * Creates cauchy distribution with the medain equal to zero and scale
56     * equal to one.
57     */
58    public CauchyDistributionImpl(){
59        this(0.0, 1.0);
60    }
61
62    /**
63     * Create a cauchy distribution using the given median and scale.
64     * @param median median for this distribution
65     * @param s scale parameter for this distribution
66     */
67    public CauchyDistributionImpl(double median, double s){
68        this(median, s, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
69    }
70
71    /**
72     * Create a cauchy distribution using the given median and scale.
73     * @param median median for this distribution
74     * @param s scale parameter for this distribution
75     * @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates
76     * (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY})
77     * @since 2.1
78     */
79    public CauchyDistributionImpl(double median, double s, double inverseCumAccuracy) {
80        super();
81        setMedianInternal(median);
82        setScaleInternal(s);
83        solverAbsoluteAccuracy = inverseCumAccuracy;
84    }
85
86    /**
87     * For this distribution, X, this method returns P(X &lt; <code>x</code>).
88     * @param x the value at which the CDF is evaluated.
89     * @return CDF evaluated at <code>x</code>.
90     */
91    public double cumulativeProbability(double x) {
92        return 0.5 + (FastMath.atan((x - median) / scale) / FastMath.PI);
93    }
94
95    /**
96     * Access the median.
97     * @return median for this distribution
98     */
99    public double getMedian() {
100        return median;
101    }
102
103    /**
104     * Access the scale parameter.
105     * @return scale parameter for this distribution
106     */
107    public double getScale() {
108        return scale;
109    }
110
111    /**
112     * Returns the probability density for a particular point.
113     *
114     * @param x The point at which the density should be computed.
115     * @return The pdf at point x.
116     * @since 2.1
117     */
118    @Override
119    public double density(double x) {
120        final double dev = x - median;
121        return (1 / FastMath.PI) * (scale / (dev * dev + scale * scale));
122    }
123
124    /**
125     * For this distribution, X, this method returns the critical point x, such
126     * that P(X &lt; x) = <code>p</code>.
127     * <p>
128     * Returns <code>Double.NEGATIVE_INFINITY</code> for p=0 and
129     * <code>Double.POSITIVE_INFINITY</code> for p=1.</p>
130     *
131     * @param p the desired probability
132     * @return x, such that P(X &lt; x) = <code>p</code>
133     * @throws IllegalArgumentException if <code>p</code> is not a valid
134     *         probability.
135     */
136    @Override
137    public double inverseCumulativeProbability(double p) {
138        double ret;
139        if (p < 0.0 || p > 1.0) {
140            throw MathRuntimeException.createIllegalArgumentException(
141                  LocalizedFormats.OUT_OF_RANGE_SIMPLE, p, 0.0, 1.0);
142        } else if (p == 0) {
143            ret = Double.NEGATIVE_INFINITY;
144        } else  if (p == 1) {
145            ret = Double.POSITIVE_INFINITY;
146        } else {
147            ret = median + scale * FastMath.tan(FastMath.PI * (p - .5));
148        }
149        return ret;
150    }
151
152    /**
153     * Modify the median.
154     * @param median for this distribution
155     * @deprecated as of 2.1 (class will become immutable in 3.0)
156     */
157    @Deprecated
158    public void setMedian(double median) {
159        setMedianInternal(median);
160    }
161
162    /**
163     * Modify the median.
164     * @param newMedian for this distribution
165     */
166    private void setMedianInternal(double newMedian) {
167        this.median = newMedian;
168    }
169
170    /**
171     * Modify the scale parameter.
172     * @param s scale parameter for this distribution
173     * @throws IllegalArgumentException if <code>sd</code> is not positive.
174     * @deprecated as of 2.1 (class will become immutable in 3.0)
175     */
176    @Deprecated
177    public void setScale(double s) {
178        setScaleInternal(s);
179    }
180
181    /**
182     * Modify the scale parameter.
183     * @param s scale parameter for this distribution
184     * @throws IllegalArgumentException if <code>sd</code> is not positive.
185     */
186    private void setScaleInternal(double s) {
187        if (s <= 0.0) {
188            throw MathRuntimeException.createIllegalArgumentException(
189                  LocalizedFormats.NOT_POSITIVE_SCALE, s);
190        }
191        scale = s;
192    }
193
194    /**
195     * Access the domain value lower bound, based on <code>p</code>, used to
196     * bracket a CDF root.  This method is used by
197     * {@link #inverseCumulativeProbability(double)} to find critical values.
198     *
199     * @param p the desired probability for the critical value
200     * @return domain value lower bound, i.e.
201     *         P(X &lt; <i>lower bound</i>) &lt; <code>p</code>
202     */
203    @Override
204    protected double getDomainLowerBound(double p) {
205        double ret;
206
207        if (p < .5) {
208            ret = -Double.MAX_VALUE;
209        } else {
210            ret = median;
211        }
212
213        return ret;
214    }
215
216    /**
217     * Access the domain value upper bound, based on <code>p</code>, used to
218     * bracket a CDF root.  This method is used by
219     * {@link #inverseCumulativeProbability(double)} to find critical values.
220     *
221     * @param p the desired probability for the critical value
222     * @return domain value upper bound, i.e.
223     *         P(X &lt; <i>upper bound</i>) &gt; <code>p</code>
224     */
225    @Override
226    protected double getDomainUpperBound(double p) {
227        double ret;
228
229        if (p < .5) {
230            ret = median;
231        } else {
232            ret = Double.MAX_VALUE;
233        }
234
235        return ret;
236    }
237
238    /**
239     * Access the initial domain value, based on <code>p</code>, used to
240     * bracket a CDF root.  This method is used by
241     * {@link #inverseCumulativeProbability(double)} to find critical values.
242     *
243     * @param p the desired probability for the critical value
244     * @return initial domain value
245     */
246    @Override
247    protected double getInitialDomain(double p) {
248        double ret;
249
250        if (p < .5) {
251            ret = median - scale;
252        } else if (p > .5) {
253            ret = median + scale;
254        } else {
255            ret = median;
256        }
257
258        return ret;
259    }
260
261    /**
262     * Return the absolute accuracy setting of the solver used to estimate
263     * inverse cumulative probabilities.
264     *
265     * @return the solver absolute accuracy
266     * @since 2.1
267     */
268    @Override
269    protected double getSolverAbsoluteAccuracy() {
270        return solverAbsoluteAccuracy;
271    }
272
273    /**
274     * Returns the lower bound of the support for this distribution.
275     * The lower bound of the support of the Cauchy distribution is always
276     * negative infinity, regardless of the parameters.
277     *
278     * @return lower bound of the support (always Double.NEGATIVE_INFINITY)
279     * @since 2.2
280     */
281    public double getSupportLowerBound() {
282        return Double.NEGATIVE_INFINITY;
283    }
284
285    /**
286     * Returns the upper bound of the support for this distribution.
287     * The upper bound of the support of the Cauchy distribution is always
288     * positive infinity, regardless of the parameters.
289     *
290     * @return upper bound of the support (always Double.POSITIVE_INFINITY)
291     * @since 2.2
292     */
293    public double getSupportUpperBound() {
294        return Double.POSITIVE_INFINITY;
295    }
296
297    /**
298     * Returns the mean.
299     *
300     * The mean is always undefined, regardless of the parameters.
301     *
302     * @return mean (always Double.NaN)
303     * @since 2.2
304     */
305    public double getNumericalMean() {
306        return Double.NaN;
307    }
308
309    /**
310     * Returns the variance.
311     *
312     * The variance is always undefined, regardless of the parameters.
313     *
314     * @return variance (always Double.NaN)
315     * @since 2.2
316     */
317    public double getNumericalVariance() {
318        return Double.NaN;
319    }
320}
321