Raymond | dee0849 | 2015-04-02 10:43:13 -0700 | [diff] [blame] | 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 | package org.apache.commons.math.distribution; |
| 18 | |
| 19 | import java.io.Serializable; |
| 20 | |
| 21 | import org.apache.commons.math.ConvergenceException; |
| 22 | import org.apache.commons.math.MathException; |
| 23 | import org.apache.commons.math.MathRuntimeException; |
| 24 | import org.apache.commons.math.analysis.UnivariateRealFunction; |
| 25 | import org.apache.commons.math.analysis.solvers.BrentSolver; |
| 26 | import org.apache.commons.math.analysis.solvers.UnivariateRealSolverUtils; |
| 27 | import org.apache.commons.math.FunctionEvaluationException; |
| 28 | import org.apache.commons.math.exception.util.LocalizedFormats; |
| 29 | import org.apache.commons.math.random.RandomDataImpl; |
| 30 | import org.apache.commons.math.util.FastMath; |
| 31 | |
| 32 | /** |
| 33 | * Base class for continuous distributions. Default implementations are |
| 34 | * provided for some of the methods that do not vary from distribution to |
| 35 | * distribution. |
| 36 | * |
| 37 | * @version $Revision: 1073498 $ $Date: 2011-02-22 21:57:26 +0100 (mar. 22 févr. 2011) $ |
| 38 | */ |
| 39 | public abstract class AbstractContinuousDistribution |
| 40 | extends AbstractDistribution |
| 41 | implements ContinuousDistribution, Serializable { |
| 42 | |
| 43 | /** Serializable version identifier */ |
| 44 | private static final long serialVersionUID = -38038050983108802L; |
| 45 | |
| 46 | /** |
| 47 | * RandomData instance used to generate samples from the distribution |
| 48 | * @since 2.2 |
| 49 | */ |
| 50 | protected final RandomDataImpl randomData = new RandomDataImpl(); |
| 51 | |
| 52 | /** |
| 53 | * Solver absolute accuracy for inverse cumulative computation |
| 54 | * @since 2.1 |
| 55 | */ |
| 56 | private double solverAbsoluteAccuracy = BrentSolver.DEFAULT_ABSOLUTE_ACCURACY; |
| 57 | |
| 58 | /** |
| 59 | * Default constructor. |
| 60 | */ |
| 61 | protected AbstractContinuousDistribution() { |
| 62 | super(); |
| 63 | } |
| 64 | |
| 65 | /** |
| 66 | * Return the probability density for a particular point. |
| 67 | * @param x The point at which the density should be computed. |
| 68 | * @return The pdf at point x. |
| 69 | * @throws MathRuntimeException if the specialized class hasn't implemented this function |
| 70 | * @since 2.1 |
| 71 | */ |
| 72 | public double density(double x) throws MathRuntimeException { |
| 73 | throw new MathRuntimeException(new UnsupportedOperationException(), |
| 74 | LocalizedFormats.NO_DENSITY_FOR_THIS_DISTRIBUTION); |
| 75 | } |
| 76 | |
| 77 | /** |
| 78 | * For this distribution, X, this method returns the critical point x, such |
| 79 | * that P(X < x) = <code>p</code>. |
| 80 | * |
| 81 | * @param p the desired probability |
| 82 | * @return x, such that P(X < x) = <code>p</code> |
| 83 | * @throws MathException if the inverse cumulative probability can not be |
| 84 | * computed due to convergence or other numerical errors. |
| 85 | * @throws IllegalArgumentException if <code>p</code> is not a valid |
| 86 | * probability. |
| 87 | */ |
| 88 | public double inverseCumulativeProbability(final double p) |
| 89 | throws MathException { |
| 90 | if (p < 0.0 || p > 1.0) { |
| 91 | throw MathRuntimeException.createIllegalArgumentException( |
| 92 | LocalizedFormats.OUT_OF_RANGE_SIMPLE, p, 0.0, 1.0); |
| 93 | } |
| 94 | |
| 95 | // by default, do simple root finding using bracketing and default solver. |
| 96 | // subclasses can override if there is a better method. |
| 97 | UnivariateRealFunction rootFindingFunction = |
| 98 | new UnivariateRealFunction() { |
| 99 | public double value(double x) throws FunctionEvaluationException { |
| 100 | double ret = Double.NaN; |
| 101 | try { |
| 102 | ret = cumulativeProbability(x) - p; |
| 103 | } catch (MathException ex) { |
| 104 | throw new FunctionEvaluationException(x, ex.getSpecificPattern(), ex.getGeneralPattern(), ex.getArguments()); |
| 105 | } |
| 106 | if (Double.isNaN(ret)) { |
| 107 | throw new FunctionEvaluationException(x, LocalizedFormats.CUMULATIVE_PROBABILITY_RETURNED_NAN, x, p); |
| 108 | } |
| 109 | return ret; |
| 110 | } |
| 111 | }; |
| 112 | |
| 113 | // Try to bracket root, test domain endpoints if this fails |
| 114 | double lowerBound = getDomainLowerBound(p); |
| 115 | double upperBound = getDomainUpperBound(p); |
| 116 | double[] bracket = null; |
| 117 | try { |
| 118 | bracket = UnivariateRealSolverUtils.bracket( |
| 119 | rootFindingFunction, getInitialDomain(p), |
| 120 | lowerBound, upperBound); |
| 121 | } catch (ConvergenceException ex) { |
| 122 | /* |
| 123 | * Check domain endpoints to see if one gives value that is within |
| 124 | * the default solver's defaultAbsoluteAccuracy of 0 (will be the |
| 125 | * case if density has bounded support and p is 0 or 1). |
| 126 | */ |
| 127 | if (FastMath.abs(rootFindingFunction.value(lowerBound)) < getSolverAbsoluteAccuracy()) { |
| 128 | return lowerBound; |
| 129 | } |
| 130 | if (FastMath.abs(rootFindingFunction.value(upperBound)) < getSolverAbsoluteAccuracy()) { |
| 131 | return upperBound; |
| 132 | } |
| 133 | // Failed bracket convergence was not because of corner solution |
| 134 | throw new MathException(ex); |
| 135 | } |
| 136 | |
| 137 | // find root |
| 138 | double root = UnivariateRealSolverUtils.solve(rootFindingFunction, |
| 139 | // override getSolverAbsoluteAccuracy() to use a Brent solver with |
| 140 | // absolute accuracy different from BrentSolver default |
| 141 | bracket[0],bracket[1], getSolverAbsoluteAccuracy()); |
| 142 | return root; |
| 143 | } |
| 144 | |
| 145 | /** |
| 146 | * Reseeds the random generator used to generate samples. |
| 147 | * |
| 148 | * @param seed the new seed |
| 149 | * @since 2.2 |
| 150 | */ |
| 151 | public void reseedRandomGenerator(long seed) { |
| 152 | randomData.reSeed(seed); |
| 153 | } |
| 154 | |
| 155 | /** |
| 156 | * Generates a random value sampled from this distribution. The default |
| 157 | * implementation uses the |
| 158 | * <a href="http://en.wikipedia.org/wiki/Inverse_transform_sampling"> inversion method.</a> |
| 159 | * |
| 160 | * @return random value |
| 161 | * @since 2.2 |
| 162 | * @throws MathException if an error occurs generating the random value |
| 163 | */ |
| 164 | public double sample() throws MathException { |
| 165 | return randomData.nextInversionDeviate(this); |
| 166 | } |
| 167 | |
| 168 | /** |
| 169 | * Generates a random sample from the distribution. The default implementation |
| 170 | * generates the sample by calling {@link #sample()} in a loop. |
| 171 | * |
| 172 | * @param sampleSize number of random values to generate |
| 173 | * @since 2.2 |
| 174 | * @return an array representing the random sample |
| 175 | * @throws MathException if an error occurs generating the sample |
| 176 | * @throws IllegalArgumentException if sampleSize is not positive |
| 177 | */ |
| 178 | public double[] sample(int sampleSize) throws MathException { |
| 179 | if (sampleSize <= 0) { |
| 180 | MathRuntimeException.createIllegalArgumentException(LocalizedFormats.NOT_POSITIVE_SAMPLE_SIZE, sampleSize); |
| 181 | } |
| 182 | double[] out = new double[sampleSize]; |
| 183 | for (int i = 0; i < sampleSize; i++) { |
| 184 | out[i] = sample(); |
| 185 | } |
| 186 | return out; |
| 187 | } |
| 188 | |
| 189 | /** |
| 190 | * Access the initial domain value, based on <code>p</code>, used to |
| 191 | * bracket a CDF root. This method is used by |
| 192 | * {@link #inverseCumulativeProbability(double)} to find critical values. |
| 193 | * |
| 194 | * @param p the desired probability for the critical value |
| 195 | * @return initial domain value |
| 196 | */ |
| 197 | protected abstract double getInitialDomain(double p); |
| 198 | |
| 199 | /** |
| 200 | * Access the domain value lower bound, based on <code>p</code>, used to |
| 201 | * bracket a CDF root. This method is used by |
| 202 | * {@link #inverseCumulativeProbability(double)} to find critical values. |
| 203 | * |
| 204 | * @param p the desired probability for the critical value |
| 205 | * @return domain value lower bound, i.e. |
| 206 | * P(X < <i>lower bound</i>) < <code>p</code> |
| 207 | */ |
| 208 | protected abstract double getDomainLowerBound(double p); |
| 209 | |
| 210 | /** |
| 211 | * Access the domain value upper bound, based on <code>p</code>, used to |
| 212 | * bracket a CDF root. This method is used by |
| 213 | * {@link #inverseCumulativeProbability(double)} to find critical values. |
| 214 | * |
| 215 | * @param p the desired probability for the critical value |
| 216 | * @return domain value upper bound, i.e. |
| 217 | * P(X < <i>upper bound</i>) > <code>p</code> |
| 218 | */ |
| 219 | protected abstract double getDomainUpperBound(double p); |
| 220 | |
| 221 | /** |
| 222 | * Returns the solver absolute accuracy for inverse cumulative computation. |
| 223 | * |
| 224 | * @return the maximum absolute error in inverse cumulative probability estimates |
| 225 | * @since 2.1 |
| 226 | */ |
| 227 | protected double getSolverAbsoluteAccuracy() { |
| 228 | return solverAbsoluteAccuracy; |
| 229 | } |
| 230 | |
| 231 | } |