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Posted to commits@commons.apache.org by er...@apache.org on 2016/04/22 01:15:31 UTC
[45/53] [abbrv] [math] MATH-1351
MATH-1351
New sampling API for multivariate distributions (similar to changes performed for MATH-1158).
Unit test file renamed in accordance to the class being tested.
One failing test "@Ignore"d (see comments on the bug-tracking system).
Project: http://git-wip-us.apache.org/repos/asf/commons-math/repo
Commit: http://git-wip-us.apache.org/repos/asf/commons-math/commit/3066a808
Tree: http://git-wip-us.apache.org/repos/asf/commons-math/tree/3066a808
Diff: http://git-wip-us.apache.org/repos/asf/commons-math/diff/3066a808
Branch: refs/heads/develop
Commit: 3066a8085f86b743da14a161427c403a7038e8b0
Parents: 880b048
Author: Gilles <er...@apache.org>
Authored: Mon Mar 28 13:45:42 2016 +0200
Committer: Gilles <er...@apache.org>
Committed: Mon Mar 28 13:45:42 2016 +0200
----------------------------------------------------------------------
.../AbstractMultivariateRealDistribution.java | 44 ++-
.../MixtureMultivariateNormalDistribution.java | 60 ++--
.../MixtureMultivariateRealDistribution.java | 124 ++++----
.../MultivariateNormalDistribution.java | 73 ++---
.../MultivariateRealDistribution.java | 37 ++-
...xtureMultivariateNormalDistributionTest.java | 268 +++++++++++++++++
.../MultivariateNormalDistributionTest.java | 6 +-
...riateNormalMixtureModelDistributionTest.java | 300 -------------------
8 files changed, 413 insertions(+), 499 deletions(-)
----------------------------------------------------------------------
http://git-wip-us.apache.org/repos/asf/commons-math/blob/3066a808/src/main/java/org/apache/commons/math4/distribution/AbstractMultivariateRealDistribution.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math4/distribution/AbstractMultivariateRealDistribution.java b/src/main/java/org/apache/commons/math4/distribution/AbstractMultivariateRealDistribution.java
index 93e4b7b..1c4adef 100644
--- a/src/main/java/org/apache/commons/math4/distribution/AbstractMultivariateRealDistribution.java
+++ b/src/main/java/org/apache/commons/math4/distribution/AbstractMultivariateRealDistribution.java
@@ -18,7 +18,7 @@ package org.apache.commons.math4.distribution;
import org.apache.commons.math4.exception.NotStrictlyPositiveException;
import org.apache.commons.math4.exception.util.LocalizedFormats;
-import org.apache.commons.math4.random.RandomGenerator;
+import org.apache.commons.math4.rng.UniformRandomProvider;
/**
* Base class for multivariate probability distributions.
@@ -27,48 +27,46 @@ import org.apache.commons.math4.random.RandomGenerator;
*/
public abstract class AbstractMultivariateRealDistribution
implements MultivariateRealDistribution {
- /** RNG instance used to generate samples from the distribution. */
- protected final RandomGenerator random;
/** The number of dimensions or columns in the multivariate distribution. */
private final int dimension;
/**
- * @param rng Random number generator.
* @param n Number of dimensions.
*/
- protected AbstractMultivariateRealDistribution(RandomGenerator rng,
- int n) {
- random = rng;
+ protected AbstractMultivariateRealDistribution(int n) {
dimension = n;
}
/** {@inheritDoc} */
@Override
- public void reseedRandomGenerator(long seed) {
- random.setSeed(seed);
- }
-
- /** {@inheritDoc} */
- @Override
public int getDimension() {
return dimension;
}
/** {@inheritDoc} */
@Override
- public abstract double[] sample();
+ public abstract Sampler createSampler(UniformRandomProvider rng);
- /** {@inheritDoc} */
- @Override
- public double[][] sample(final int sampleSize) {
- if (sampleSize <= 0) {
+ /**
+ * Utility function for creating {@code n} vectors generated by the
+ * given {@code sampler}.
+ *
+ * @param n Number of samples.
+ * @param sampler Sampler.
+ * @return an array of size {@code n} whose elements are random vectors
+ * sampled from this distribution.
+ */
+ public static double[][] sample(int n,
+ MultivariateRealDistribution.Sampler sampler) {
+ if (n <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_SAMPLES,
- sampleSize);
+ n);
}
- final double[][] out = new double[sampleSize][dimension];
- for (int i = 0; i < sampleSize; i++) {
- out[i] = sample();
+
+ final double[][] samples = new double[n][];
+ for (int i = 0; i < n; i++) {
+ samples[i] = sampler.sample();
}
- return out;
+ return samples;
}
}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/3066a808/src/main/java/org/apache/commons/math4/distribution/MixtureMultivariateNormalDistribution.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math4/distribution/MixtureMultivariateNormalDistribution.java b/src/main/java/org/apache/commons/math4/distribution/MixtureMultivariateNormalDistribution.java
index d7cd4cd..e24a2ac 100644
--- a/src/main/java/org/apache/commons/math4/distribution/MixtureMultivariateNormalDistribution.java
+++ b/src/main/java/org/apache/commons/math4/distribution/MixtureMultivariateNormalDistribution.java
@@ -21,7 +21,6 @@ import java.util.List;
import org.apache.commons.math4.exception.DimensionMismatchException;
import org.apache.commons.math4.exception.NotPositiveException;
-import org.apache.commons.math4.random.RandomGenerator;
import org.apache.commons.math4.util.Pair;
/**
@@ -33,63 +32,42 @@ import org.apache.commons.math4.util.Pair;
*/
public class MixtureMultivariateNormalDistribution
extends MixtureMultivariateRealDistribution<MultivariateNormalDistribution> {
-
- /**
- * Creates a multivariate normal mixture distribution.
- * <p>
- * <b>Note:</b> this constructor will implicitly create an instance of
- * {@link org.apache.commons.math4.random.Well19937c Well19937c} as random
- * generator to be used for sampling only (see {@link #sample()} and
- * {@link #sample(int)}). In case no sampling is needed for the created
- * distribution, it is advised to pass {@code null} as random generator via
- * the appropriate constructors to avoid the additional initialisation
- * overhead.
- *
- * @param weights Weights of each component.
- * @param means Mean vector for each component.
- * @param covariances Covariance matrix for each component.
- */
- public MixtureMultivariateNormalDistribution(double[] weights,
- double[][] means,
- double[][][] covariances) {
- super(createComponents(weights, means, covariances));
- }
-
/**
* Creates a mixture model from a list of distributions and their
* associated weights.
- * <p>
- * <b>Note:</b> this constructor will implicitly create an instance of
- * {@link org.apache.commons.math4.random.Well19937c Well19937c} as random
- * generator to be used for sampling only (see {@link #sample()} and
- * {@link #sample(int)}). In case no sampling is needed for the created
- * distribution, it is advised to pass {@code null} as random generator via
- * the appropriate constructors to avoid the additional initialisation
- * overhead.
*
- * @param components List of (weight, distribution) pairs from which to sample.
+ * @param components Distributions from which to sample.
+ * @throws NotPositiveException if any of the weights is negative.
+ * @throws DimensionMismatchException if not all components have the same
+ * number of variables.
*/
- public MixtureMultivariateNormalDistribution(List<Pair<Double, MultivariateNormalDistribution>> components) {
+ public MixtureMultivariateNormalDistribution(List<Pair<Double, MultivariateNormalDistribution>> components)
+ throws NotPositiveException,
+ DimensionMismatchException {
super(components);
}
/**
- * Creates a mixture model from a list of distributions and their
- * associated weights.
+ * Creates a multivariate normal mixture distribution.
*
- * @param rng Random number generator.
- * @param components Distributions from which to sample.
+ * @param weights Weights of each component.
+ * @param means Mean vector for each component.
+ * @param covariances Covariance matrix for each component.
* @throws NotPositiveException if any of the weights is negative.
* @throws DimensionMismatchException if not all components have the same
* number of variables.
*/
- public MixtureMultivariateNormalDistribution(RandomGenerator rng,
- List<Pair<Double, MultivariateNormalDistribution>> components)
- throws NotPositiveException, DimensionMismatchException {
- super(rng, components);
+ public MixtureMultivariateNormalDistribution(double[] weights,
+ double[][] means,
+ double[][][] covariances)
+ throws NotPositiveException,
+ DimensionMismatchException {
+ this(createComponents(weights, means, covariances));
}
/**
+ * Creates components of the mixture model.
+ *
* @param weights Weights of each component.
* @param means Mean vector for each component.
* @param covariances Covariance matrix for each component.
http://git-wip-us.apache.org/repos/asf/commons-math/blob/3066a808/src/main/java/org/apache/commons/math4/distribution/MixtureMultivariateRealDistribution.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math4/distribution/MixtureMultivariateRealDistribution.java b/src/main/java/org/apache/commons/math4/distribution/MixtureMultivariateRealDistribution.java
index ce8c7d9..4caee3f 100644
--- a/src/main/java/org/apache/commons/math4/distribution/MixtureMultivariateRealDistribution.java
+++ b/src/main/java/org/apache/commons/math4/distribution/MixtureMultivariateRealDistribution.java
@@ -23,8 +23,7 @@ import org.apache.commons.math4.exception.DimensionMismatchException;
import org.apache.commons.math4.exception.MathArithmeticException;
import org.apache.commons.math4.exception.NotPositiveException;
import org.apache.commons.math4.exception.util.LocalizedFormats;
-import org.apache.commons.math4.random.RandomGenerator;
-import org.apache.commons.math4.random.Well19937c;
+import org.apache.commons.math4.rng.UniformRandomProvider;
import org.apache.commons.math4.util.Pair;
/**
@@ -45,33 +44,14 @@ public class MixtureMultivariateRealDistribution<T extends MultivariateRealDistr
/**
* Creates a mixture model from a list of distributions and their
* associated weights.
- * <p>
- * <b>Note:</b> this constructor will implicitly create an instance of
- * {@link Well19937c} as random generator to be used for sampling only (see
- * {@link #sample()} and {@link #sample(int)}). In case no sampling is
- * needed for the created distribution, it is advised to pass {@code null}
- * as random generator via the appropriate constructors to avoid the
- * additional initialisation overhead.
*
- * @param components List of (weight, distribution) pairs from which to sample.
- */
- public MixtureMultivariateRealDistribution(List<Pair<Double, T>> components) {
- this(new Well19937c(), components);
- }
-
- /**
- * Creates a mixture model from a list of distributions and their
- * associated weights.
- *
- * @param rng Random number generator.
* @param components Distributions from which to sample.
* @throws NotPositiveException if any of the weights is negative.
* @throws DimensionMismatchException if not all components have the same
* number of variables.
*/
- public MixtureMultivariateRealDistribution(RandomGenerator rng,
- List<Pair<Double, T>> components) {
- super(rng, components.get(0).getSecond().getDimension());
+ public MixtureMultivariateRealDistribution(List<Pair<Double, T>> components) {
+ super(components.get(0).getSecond().getDimension());
final int numComp = components.size();
final int dim = getDimension();
@@ -112,61 +92,75 @@ public class MixtureMultivariateRealDistribution<T extends MultivariateRealDistr
return p;
}
- /** {@inheritDoc} */
- @Override
- public double[] sample() {
- // Sampled values.
- double[] vals = null;
-
- // Determine which component to sample from.
- final double randomValue = random.nextDouble();
- double sum = 0;
+ /**
+ * Gets the distributions that make up the mixture model.
+ *
+ * @return the component distributions and associated weights.
+ */
+ public List<Pair<Double, T>> getComponents() {
+ final List<Pair<Double, T>> list = new ArrayList<Pair<Double, T>>(weight.length);
for (int i = 0; i < weight.length; i++) {
- sum += weight[i];
- if (randomValue <= sum) {
- // pick model i
- vals = distribution.get(i).sample();
- break;
- }
- }
-
- if (vals == null) {
- // This should never happen, but it ensures we won't return a null in
- // case the loop above has some floating point inequality problem on
- // the final iteration.
- vals = distribution.get(weight.length - 1).sample();
+ list.add(new Pair<Double, T>(weight[i], distribution.get(i)));
}
- return vals;
+ return list;
}
/** {@inheritDoc} */
@Override
- public void reseedRandomGenerator(long seed) {
- // Seed needs to be propagated to underlying components
- // in order to maintain consistency between runs.
- super.reseedRandomGenerator(seed);
-
- for (int i = 0; i < distribution.size(); i++) {
- // Make each component's seed different in order to avoid
- // using the same sequence of random numbers.
- distribution.get(i).reseedRandomGenerator(i + 1 + seed);
- }
+ public MultivariateRealDistribution.Sampler createSampler(UniformRandomProvider rng) {
+ return new MixtureSampler(rng);
}
/**
- * Gets the distributions that make up the mixture model.
- *
- * @return the component distributions and associated weights.
+ * Sampler.
*/
- public List<Pair<Double, T>> getComponents() {
- final List<Pair<Double, T>> list = new ArrayList<Pair<Double, T>>(weight.length);
-
- for (int i = 0; i < weight.length; i++) {
- list.add(new Pair<Double, T>(weight[i], distribution.get(i)));
+ private class MixtureSampler implements MultivariateRealDistribution.Sampler {
+ /** RNG */
+ private final UniformRandomProvider rng;
+ /** Sampler for each of the distribution in the mixture. */
+ private final MultivariateRealDistribution.Sampler[] samplers;
+
+ /**
+ * @param generator RNG.
+ */
+ MixtureSampler(UniformRandomProvider generator) {
+ rng = generator;
+
+ samplers = new MultivariateRealDistribution.Sampler[weight.length];
+ for (int i = 0; i < weight.length; i++) {
+ samplers[i] = distribution.get(i).createSampler(rng);
+ }
}
- return list;
+ /** {@inheritDoc} */
+ @Override
+ public double[] sample() {
+ // Sampled values.
+ double[] vals = null;
+
+ // Determine which component to sample from.
+ final double randomValue = rng.nextDouble();
+ double sum = 0;
+
+ for (int i = 0; i < weight.length; i++) {
+ sum += weight[i];
+ if (randomValue <= sum) {
+ // pick model i
+ vals = samplers[i].sample();
+ break;
+ }
+ }
+
+ if (vals == null) {
+ // This should never happen, but it ensures we won't return a null in
+ // case the loop above has some floating point inequality problem on
+ // the final iteration.
+ vals = samplers[weight.length - 1].sample();
+ }
+
+ return vals;
+ }
}
}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/3066a808/src/main/java/org/apache/commons/math4/distribution/MultivariateNormalDistribution.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math4/distribution/MultivariateNormalDistribution.java b/src/main/java/org/apache/commons/math4/distribution/MultivariateNormalDistribution.java
index 212fb2a..da270ad 100644
--- a/src/main/java/org/apache/commons/math4/distribution/MultivariateNormalDistribution.java
+++ b/src/main/java/org/apache/commons/math4/distribution/MultivariateNormalDistribution.java
@@ -22,8 +22,7 @@ import org.apache.commons.math4.linear.EigenDecomposition;
import org.apache.commons.math4.linear.NonPositiveDefiniteMatrixException;
import org.apache.commons.math4.linear.RealMatrix;
import org.apache.commons.math4.linear.SingularMatrixException;
-import org.apache.commons.math4.random.RandomGenerator;
-import org.apache.commons.math4.random.Well19937c;
+import org.apache.commons.math4.rng.UniformRandomProvider;
import org.apache.commons.math4.util.FastMath;
import org.apache.commons.math4.util.MathArrays;
@@ -53,44 +52,12 @@ public class MultivariateNormalDistribution
/**
* Creates a multivariate normal distribution with the given mean vector and
* covariance matrix.
- * <br/>
- * The number of dimensions is equal to the length of the mean vector
- * and to the number of rows and columns of the covariance matrix.
- * It is frequently written as "p" in formulae.
* <p>
- * <b>Note:</b> this constructor will implicitly create an instance of
- * {@link Well19937c} as random generator to be used for sampling only (see
- * {@link #sample()} and {@link #sample(int)}). In case no sampling is
- * needed for the created distribution, it is advised to pass {@code null}
- * as random generator via the appropriate constructors to avoid the
- * additional initialisation overhead.
- *
- * @param means Vector of means.
- * @param covariances Covariance matrix.
- * @throws DimensionMismatchException if the arrays length are
- * inconsistent.
- * @throws SingularMatrixException if the eigenvalue decomposition cannot
- * be performed on the provided covariance matrix.
- * @throws NonPositiveDefiniteMatrixException if any of the eigenvalues is
- * negative.
- */
- public MultivariateNormalDistribution(final double[] means,
- final double[][] covariances)
- throws SingularMatrixException,
- DimensionMismatchException,
- NonPositiveDefiniteMatrixException {
- this(new Well19937c(), means, covariances);
- }
-
- /**
- * Creates a multivariate normal distribution with the given mean vector and
- * covariance matrix.
- * <br/>
* The number of dimensions is equal to the length of the mean vector
* and to the number of rows and columns of the covariance matrix.
* It is frequently written as "p" in formulae.
+ * </p>
*
- * @param rng Random Number Generator.
* @param means Vector of means.
* @param covariances Covariance matrix.
* @throws DimensionMismatchException if the arrays length are
@@ -100,13 +67,12 @@ public class MultivariateNormalDistribution
* @throws NonPositiveDefiniteMatrixException if any of the eigenvalues is
* negative.
*/
- public MultivariateNormalDistribution(RandomGenerator rng,
- final double[] means,
+ public MultivariateNormalDistribution(final double[] means,
final double[][] covariances)
throws SingularMatrixException,
DimensionMismatchException,
NonPositiveDefiniteMatrixException {
- super(rng, means.length);
+ super(means.length);
final int dim = means.length;
@@ -210,21 +176,30 @@ public class MultivariateNormalDistribution
/** {@inheritDoc} */
@Override
- public double[] sample() {
- final int dim = getDimension();
- final double[] normalVals = new double[dim];
+ public MultivariateRealDistribution.Sampler createSampler(final UniformRandomProvider rng) {
+ return new MultivariateRealDistribution.Sampler() {
+ /** Normal distribution. */
+ private final RealDistribution.Sampler gauss = new NormalDistribution().createSampler(rng);
- for (int i = 0; i < dim; i++) {
- normalVals[i] = random.nextGaussian();
- }
+ /** {@inheritDoc} */
+ @Override
+ public double[] sample() {
+ final int dim = getDimension();
+ final double[] normalVals = new double[dim];
- final double[] vals = samplingMatrix.operate(normalVals);
+ for (int i = 0; i < dim; i++) {
+ normalVals[i] = gauss.sample();
+ }
- for (int i = 0; i < dim; i++) {
- vals[i] += means[i];
- }
+ final double[] vals = samplingMatrix.operate(normalVals);
+
+ for (int i = 0; i < dim; i++) {
+ vals[i] += means[i];
+ }
- return vals;
+ return vals;
+ }
+ };
}
/**
http://git-wip-us.apache.org/repos/asf/commons-math/blob/3066a808/src/main/java/org/apache/commons/math4/distribution/MultivariateRealDistribution.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math4/distribution/MultivariateRealDistribution.java b/src/main/java/org/apache/commons/math4/distribution/MultivariateRealDistribution.java
index d734d96..eaaf35e 100644
--- a/src/main/java/org/apache/commons/math4/distribution/MultivariateRealDistribution.java
+++ b/src/main/java/org/apache/commons/math4/distribution/MultivariateRealDistribution.java
@@ -16,7 +16,7 @@
*/
package org.apache.commons.math4.distribution;
-import org.apache.commons.math4.exception.NotStrictlyPositiveException;
+import org.apache.commons.math4.rng.UniformRandomProvider;
/**
* Base interface for multivariate distributions on the reals.
@@ -42,13 +42,6 @@ public interface MultivariateRealDistribution {
double density(double[] x);
/**
- * Reseeds the random generator used to generate samples.
- *
- * @param seed Seed with which to initialize the random number generator.
- */
- void reseedRandomGenerator(long seed);
-
- /**
* Gets the number of random variables of the distribution.
* It is the size of the array returned by the {@link #sample() sample}
* method.
@@ -58,21 +51,27 @@ public interface MultivariateRealDistribution {
int getDimension();
/**
- * Generates a random value vector sampled from this distribution.
+ * Creates a sampler.
+ *
+ * @param rng Generator of uniformly distributed numbers.
+ * @return a sampler that produces random numbers according this
+ * distribution.
*
- * @return a random value vector.
+ * @since 4.0
*/
- double[] sample();
+ Sampler createSampler(UniformRandomProvider rng);
/**
- * Generates a list of a random value vectors from the distribution.
- *
- * @param sampleSize the number of random vectors to generate.
- * @return an array representing the random samples.
- * @throws org.apache.commons.math4.exception.NotStrictlyPositiveException
- * if {@code sampleSize} is not positive.
+ * Sampling functionality.
*
- * @see #sample()
+ * @since 4.0
*/
- double[][] sample(int sampleSize) throws NotStrictlyPositiveException;
+ interface Sampler {
+ /**
+ * Generates a random value vector sampled from this distribution.
+ *
+ * @return a random value vector.
+ */
+ double[] sample();
+ }
}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/3066a808/src/test/java/org/apache/commons/math4/distribution/MixtureMultivariateNormalDistributionTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/distribution/MixtureMultivariateNormalDistributionTest.java b/src/test/java/org/apache/commons/math4/distribution/MixtureMultivariateNormalDistributionTest.java
new file mode 100644
index 0000000..c4d3a8f
--- /dev/null
+++ b/src/test/java/org/apache/commons/math4/distribution/MixtureMultivariateNormalDistributionTest.java
@@ -0,0 +1,268 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math4.distribution;
+
+import java.util.List;
+import java.util.ArrayList;
+
+import org.apache.commons.math4.distribution.MixtureMultivariateRealDistribution;
+import org.apache.commons.math4.distribution.MultivariateNormalDistribution;
+import org.apache.commons.math4.exception.MathArithmeticException;
+import org.apache.commons.math4.exception.NotPositiveException;
+import org.apache.commons.math4.rng.RandomSource;
+import org.apache.commons.math4.util.Pair;
+import org.junit.Assert;
+import org.junit.Test;
+import org.junit.Ignore;
+
+/**
+ * Test case {@link MixtureMultivariateNormalDistribution}.
+ */
+public class MixtureMultivariateNormalDistributionTest {
+
+ @Test
+ public void testNonUnitWeightSum() {
+ final double[] weights = { 1, 2 };
+ final double[][] means = { { -1.5, 2.0 },
+ { 4.0, 8.2 } };
+ final double[][][] covariances = { { { 2.0, -1.1 },
+ { -1.1, 2.0 } },
+ { { 3.5, 1.5 },
+ { 1.5, 3.5 } } };
+ final MixtureMultivariateNormalDistribution d
+ = new MixtureMultivariateNormalDistribution(weights, means, covariances);
+
+ final List<Pair<Double, MultivariateNormalDistribution>> comp = d.getComponents();
+
+ Assert.assertEquals(1d / 3, comp.get(0).getFirst().doubleValue(), Math.ulp(1d));
+ Assert.assertEquals(2d / 3, comp.get(1).getFirst().doubleValue(), Math.ulp(1d));
+ }
+
+ @Test(expected=MathArithmeticException.class)
+ public void testWeightSumOverFlow() {
+ final double[] weights = { 0.5 * Double.MAX_VALUE, 0.51 * Double.MAX_VALUE };
+ final double[][] means = { { -1.5, 2.0 },
+ { 4.0, 8.2 } };
+ final double[][][] covariances = { { { 2.0, -1.1 },
+ { -1.1, 2.0 } },
+ { { 3.5, 1.5 },
+ { 1.5, 3.5 } } };
+ new MixtureMultivariateNormalDistribution(weights, means, covariances);
+ }
+
+ @Test(expected=NotPositiveException.class)
+ public void testPreconditionPositiveWeights() {
+ final double[] negativeWeights = { -0.5, 1.5 };
+ final double[][] means = { { -1.5, 2.0 },
+ { 4.0, 8.2 } };
+ final double[][][] covariances = { { { 2.0, -1.1 },
+ { -1.1, 2.0 } },
+ { { 3.5, 1.5 },
+ { 1.5, 3.5 } } };
+ new MixtureMultivariateNormalDistribution(negativeWeights, means, covariances);
+ }
+
+ /**
+ * Test the accuracy of the density calculation.
+ */
+ @Test
+ public void testDensities() {
+ final double[] weights = { 0.3, 0.7 };
+ final double[][] means = { { -1.5, 2.0 },
+ { 4.0, 8.2 } };
+ final double[][][] covariances = { { { 2.0, -1.1 },
+ { -1.1, 2.0 } },
+ { { 3.5, 1.5 },
+ { 1.5, 3.5 } } };
+ final MixtureMultivariateNormalDistribution d
+ = new MixtureMultivariateNormalDistribution(weights, means, covariances);
+
+ // Test vectors
+ final double[][] testValues = { { -1.5, 2 },
+ { 4, 8.2 },
+ { 1.5, -2 },
+ { 0, 0 } };
+
+ // Densities that we should get back.
+ // Calculated by assigning weights to multivariate normal distribution
+ // and summing
+ // values from dmvnorm function in R 2.15 CRAN package Mixtools v0.4.
+ // Like: .3*dmvnorm(val,mu1,sigma1)+.7*dmvnorm(val,mu2,sigma2)
+ final double[] correctDensities = { 0.02862037278930575,
+ 0.03523044847314091,
+ 0.000416241365629767,
+ 0.009932042831700297 };
+
+ for (int i = 0; i < testValues.length; i++) {
+ Assert.assertEquals(correctDensities[i], d.density(testValues[i]), Math.ulp(1d));
+ }
+ }
+
+ /**
+ * Test the accuracy of sampling from the distribution.
+ */
+ @Ignore@Test
+ public void testSampling() {
+ final double[] weights = { 0.3, 0.7 };
+ final double[][] means = { { -1.5, 2.0 },
+ { 4.0, 8.2 } };
+ final double[][][] covariances = { { { 2.0, -1.1 },
+ { -1.1, 2.0 } },
+ { { 3.5, 1.5 },
+ { 1.5, 3.5 } } };
+ final MixtureMultivariateNormalDistribution d =
+ new MixtureMultivariateNormalDistribution(weights, means, covariances);
+ final MultivariateRealDistribution.Sampler sampler =
+ d.createSampler(RandomSource.create(RandomSource.WELL_19937_C, 50));
+
+ final double[][] correctSamples = getCorrectSamples();
+ final int n = correctSamples.length;
+ final double[][] samples = AbstractMultivariateRealDistribution.sample(n, sampler);
+
+ for (int i = 0; i < n; i++) {
+ for (int j = 0; j < samples[i].length; j++) {
+ Assert.assertEquals("sample[" + j + "]",
+ correctSamples[i][j], samples[i][j], 1e-16);
+ }
+ }
+ }
+
+ /**
+ * Values used in {@link #testSampling()}.
+ */
+ private double[][] getCorrectSamples() {
+ // These were sampled from the MultivariateNormalMixtureModelDistribution class
+ // with seed 50.
+ //
+ // They were then fit to a MVN mixture model in R using mixtools.
+ //
+ // The optimal parameters were:
+ // - component weights: {0.3595186, 0.6404814}
+ // - mean vectors: {-1.645879, 1.989797}, {3.474328, 7.782232}
+ // - covariance matrices:
+ // { 1.397738 -1.167732
+ // -1.167732 1.801782 }
+ // and
+ // { 3.934593 2.354787
+ // 2.354787 4.428024 }
+ //
+ // It is considered fairly close to the actual test parameters,
+ // considering that the sample size is only 100.
+ return new double[][] {
+ { 6.259990922080121, 11.972954175355897 },
+ { -2.5296544304801847, 1.0031292519854365 },
+ { 0.49037886081440396, 0.9758251727325711 },
+ { 5.022970993312015, 9.289348879616787 },
+ { -1.686183146603914, 2.007244382745706 },
+ { -1.4729253946002685, 2.762166644212484 },
+ { 4.329788143963888, 11.514016497132253 },
+ { 3.008674596114442, 4.960246550446107 },
+ { 3.342379304090846, 5.937630105198625 },
+ { 2.6993068328674754, 7.42190871572571 },
+ { -2.446569340219571, 1.9687117791378763 },
+ { 1.922417883170056, 4.917616702617099 },
+ { -1.1969741543898518, 2.4576126277884387 },
+ { 2.4216948702967196, 8.227710158117134 },
+ { 6.701424725804463, 9.098666475042428 },
+ { 2.9890253545698964, 9.643807939324331 },
+ { 0.7162632354907799, 8.978811120287553 },
+ { -2.7548699149775877, 4.1354812280794215 },
+ { 8.304528180745018, 11.602319388898287 },
+ { -2.7633253389165926, 2.786173883989795 },
+ { 1.3322228389460813, 5.447481218602913 },
+ { -1.8120096092851508, 1.605624499560037 },
+ { 3.6546253437206504, 8.195304526564376 },
+ { -2.312349539658588, 1.868941220444169 },
+ { -1.882322136356522, 2.033795570464242 },
+ { 4.562770714939441, 7.414967958885031 },
+ { 4.731882017875329, 8.890676665580747 },
+ { 3.492186010427425, 8.9005225241848 },
+ { -1.619700190174894, 3.314060142479045 },
+ { 3.5466090064003315, 7.75182101001913 },
+ { 5.455682472787392, 8.143119287755635 },
+ { -2.3859602945473197, 1.8826732217294837 },
+ { 3.9095306088680015, 9.258129209626317 },
+ { 7.443020189508173, 7.837840713329312 },
+ { 2.136004873917428, 6.917636475958297 },
+ { -1.7203379410395119, 2.3212878757611524 },
+ { 4.618991257611526, 12.095065976419436 },
+ { -0.4837044029854387, 0.8255970441255125 },
+ { -4.438938966557163, 4.948666297280241 },
+ { -0.4539625134045906, 4.700922454655341 },
+ { 2.1285488271265356, 8.457941480487563 },
+ { 3.4873561871454393, 11.99809827845933 },
+ { 4.723049431412658, 7.813095742563365 },
+ { 1.1245583037967455, 5.20587873556688 },
+ { 1.3411933634409197, 6.069796875785409 },
+ { 4.585119332463686, 7.967669543767418 },
+ { 1.3076522817963823, -0.647431033653445 },
+ { -1.4449446442803178, 1.9400424267464862 },
+ { -2.069794456383682, 3.5824162107496544 },
+ { -0.15959481421417276, 1.5466782303315405 },
+ { -2.0823081278810136, 3.0914366458581437 },
+ { 3.521944615248141, 10.276112932926408 },
+ { 1.0164326704884257, 4.342329556442856 },
+ { 5.3718868590295275, 8.374761158360922 },
+ { 0.3673656866959396, 8.75168581694866 },
+ { -2.250268955954753, 1.4610850300996527 },
+ { -2.312739727403522, 1.5921126297576362 },
+ { 3.138993360831055, 6.7338392374947365 },
+ { 2.6978650950790115, 7.941857288979095 },
+ { 4.387985088655384, 8.253499976968 },
+ { -1.8928961721456705, 0.23631082388724223 },
+ { 4.43509029544109, 8.565290285488782 },
+ { 4.904728034106502, 5.79936660133754 },
+ { -1.7640371853739507, 2.7343727594167433 },
+ { 2.4553674733053463, 7.875871017408807 },
+ { -2.6478965122565006, 4.465127753193949 },
+ { 3.493873671142299, 10.443093773532448 },
+ { 1.1321916197409103, 7.127108479263268 },
+ { -1.7335075535240392, 2.550629648463023 },
+ { -0.9772679734368084, 4.377196298969238 },
+ { 3.6388366973980357, 6.947299283206256 },
+ { 0.27043799318823325, 6.587978599614367 },
+ { 5.356782352010253, 7.388957912116327 },
+ { -0.09187745751354681, 0.23612399246659743 },
+ { 2.903203580353435, 3.8076727621794415 },
+ { 5.297014824937293, 8.650985262326508 },
+ { 4.934508602170976, 9.164571423190052 },
+ { -1.0004911869654256, 4.797064194444461 },
+ { 6.782491700298046, 11.852373338280497 },
+ { 2.8983678524536014, 8.303837362117521 },
+ { 4.805003269830865, 6.790462904325329 },
+ { -0.8815799740744226, 1.3015810062131394 },
+ { 5.115138859802104, 6.376895810201089 },
+ { 4.301239328205988, 8.60546337560793 },
+ { 3.276423626317666, 9.889429652591947 },
+ { -4.001924973153122, 4.3353864592328515 },
+ { 3.9571892554119517, 4.500569057308562 },
+ { 4.783067027436208, 7.451125480601317 },
+ { 4.79065438272821, 9.614122776979698 },
+ { 2.677655270279617, 6.8875223698210135 },
+ { -1.3714746289327362, 2.3992153193382437 },
+ { 3.240136859745249, 7.748339397522042 },
+ { 5.107885374416291, 8.508324480583724 },
+ { -1.5830830226666048, 0.9139127045208315 },
+ { -1.1596156791652918, -0.04502759384531929 },
+ { -0.4670021307952068, 3.6193633227841624 },
+ { -0.7026065228267798, 0.4811423031997131 },
+ { -2.719979836732917, 2.5165041618080104 },
+ { 1.0336754331123372, -0.34966029029320644 },
+ { 4.743217291882213, 5.750060115251131 }
+ };
+ }
+}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/3066a808/src/test/java/org/apache/commons/math4/distribution/MultivariateNormalDistributionTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/distribution/MultivariateNormalDistributionTest.java b/src/test/java/org/apache/commons/math4/distribution/MultivariateNormalDistributionTest.java
index 41d526c..3e6d9ff 100644
--- a/src/test/java/org/apache/commons/math4/distribution/MultivariateNormalDistributionTest.java
+++ b/src/test/java/org/apache/commons/math4/distribution/MultivariateNormalDistributionTest.java
@@ -20,6 +20,7 @@ package org.apache.commons.math4.distribution;
import org.apache.commons.math4.distribution.MultivariateNormalDistribution;
import org.apache.commons.math4.distribution.NormalDistribution;
import org.apache.commons.math4.linear.RealMatrix;
+import org.apache.commons.math4.rng.RandomSource;
import org.apache.commons.math4.stat.correlation.Covariance;
import java.util.Random;
@@ -75,11 +76,12 @@ public class MultivariateNormalDistributionTest {
final double[][] sigma = { { 2, -1.1 },
{ -1.1, 2 } };
final MultivariateNormalDistribution d = new MultivariateNormalDistribution(mu, sigma);
- d.reseedRandomGenerator(50);
+ final MultivariateRealDistribution.Sampler sampler =
+ d.createSampler(RandomSource.create(RandomSource.WELL_19937_C, 50));
final int n = 500000;
+ final double[][] samples = AbstractMultivariateRealDistribution.sample(n, sampler);
- final double[][] samples = d.sample(n);
final int dim = d.getDimension();
final double[] sampleMeans = new double[dim];
http://git-wip-us.apache.org/repos/asf/commons-math/blob/3066a808/src/test/java/org/apache/commons/math4/distribution/MultivariateNormalMixtureModelDistributionTest.java
----------------------------------------------------------------------
diff --git a/src/test/java/org/apache/commons/math4/distribution/MultivariateNormalMixtureModelDistributionTest.java b/src/test/java/org/apache/commons/math4/distribution/MultivariateNormalMixtureModelDistributionTest.java
deleted file mode 100644
index 8bed770..0000000
--- a/src/test/java/org/apache/commons/math4/distribution/MultivariateNormalMixtureModelDistributionTest.java
+++ /dev/null
@@ -1,300 +0,0 @@
-/*
- * Licensed to the Apache Software Foundation (ASF) under one or more
- * contributor license agreements. See the NOTICE file distributed with
- * this work for additional information regarding copyright ownership.
- * The ASF licenses this file to You under the Apache License, Version 2.0
- * (the "License"); you may not use this file except in compliance with
- * the License. You may obtain a copy of the License at
- *
- * http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS,
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
-package org.apache.commons.math4.distribution;
-
-import java.util.List;
-import java.util.ArrayList;
-
-import org.apache.commons.math4.distribution.MixtureMultivariateRealDistribution;
-import org.apache.commons.math4.distribution.MultivariateNormalDistribution;
-import org.apache.commons.math4.exception.MathArithmeticException;
-import org.apache.commons.math4.exception.NotPositiveException;
-import org.apache.commons.math4.util.Pair;
-import org.junit.Assert;
-import org.junit.Test;
-
-/**
- * Test that demonstrates the use of {@link MixtureMultivariateRealDistribution}
- * in order to create a mixture model composed of {@link MultivariateNormalDistribution
- * normal distributions}.
- */
-public class MultivariateNormalMixtureModelDistributionTest {
-
- @Test
- public void testNonUnitWeightSum() {
- final double[] weights = { 1, 2 };
- final double[][] means = { { -1.5, 2.0 },
- { 4.0, 8.2 } };
- final double[][][] covariances = { { { 2.0, -1.1 },
- { -1.1, 2.0 } },
- { { 3.5, 1.5 },
- { 1.5, 3.5 } } };
- final MultivariateNormalMixtureModelDistribution d
- = create(weights, means, covariances);
-
- final List<Pair<Double, MultivariateNormalDistribution>> comp = d.getComponents();
-
- Assert.assertEquals(1d / 3, comp.get(0).getFirst().doubleValue(), Math.ulp(1d));
- Assert.assertEquals(2d / 3, comp.get(1).getFirst().doubleValue(), Math.ulp(1d));
- }
-
- @Test(expected=MathArithmeticException.class)
- public void testWeightSumOverFlow() {
- final double[] weights = { 0.5 * Double.MAX_VALUE, 0.51 * Double.MAX_VALUE };
- final double[][] means = { { -1.5, 2.0 },
- { 4.0, 8.2 } };
- final double[][][] covariances = { { { 2.0, -1.1 },
- { -1.1, 2.0 } },
- { { 3.5, 1.5 },
- { 1.5, 3.5 } } };
- create(weights, means, covariances);
- }
-
- @Test(expected=NotPositiveException.class)
- public void testPreconditionPositiveWeights() {
- final double[] negativeWeights = { -0.5, 1.5 };
- final double[][] means = { { -1.5, 2.0 },
- { 4.0, 8.2 } };
- final double[][][] covariances = { { { 2.0, -1.1 },
- { -1.1, 2.0 } },
- { { 3.5, 1.5 },
- { 1.5, 3.5 } } };
- create(negativeWeights, means, covariances);
- }
-
- /**
- * Test the accuracy of the density calculation.
- */
- @Test
- public void testDensities() {
- final double[] weights = { 0.3, 0.7 };
- final double[][] means = { { -1.5, 2.0 },
- { 4.0, 8.2 } };
- final double[][][] covariances = { { { 2.0, -1.1 },
- { -1.1, 2.0 } },
- { { 3.5, 1.5 },
- { 1.5, 3.5 } } };
- final MultivariateNormalMixtureModelDistribution d
- = create(weights, means, covariances);
-
- // Test vectors
- final double[][] testValues = { { -1.5, 2 },
- { 4, 8.2 },
- { 1.5, -2 },
- { 0, 0 } };
-
- // Densities that we should get back.
- // Calculated by assigning weights to multivariate normal distribution
- // and summing
- // values from dmvnorm function in R 2.15 CRAN package Mixtools v0.4.
- // Like: .3*dmvnorm(val,mu1,sigma1)+.7*dmvnorm(val,mu2,sigma2)
- final double[] correctDensities = { 0.02862037278930575,
- 0.03523044847314091,
- 0.000416241365629767,
- 0.009932042831700297 };
-
- for (int i = 0; i < testValues.length; i++) {
- Assert.assertEquals(correctDensities[i], d.density(testValues[i]), Math.ulp(1d));
- }
- }
-
- /**
- * Test the accuracy of sampling from the distribution.
- */
- @Test
- public void testSampling() {
- final double[] weights = { 0.3, 0.7 };
- final double[][] means = { { -1.5, 2.0 },
- { 4.0, 8.2 } };
- final double[][][] covariances = { { { 2.0, -1.1 },
- { -1.1, 2.0 } },
- { { 3.5, 1.5 },
- { 1.5, 3.5 } } };
- final MultivariateNormalMixtureModelDistribution d
- = create(weights, means, covariances);
- d.reseedRandomGenerator(50);
-
- final double[][] correctSamples = getCorrectSamples();
- final int n = correctSamples.length;
- final double[][] samples = d.sample(n);
-
- for (int i = 0; i < n; i++) {
- for (int j = 0; j < samples[i].length; j++) {
- Assert.assertEquals(correctSamples[i][j], samples[i][j], 1e-16);
- }
- }
- }
-
- /**
- * Creates a mixture of Gaussian distributions.
- *
- * @param weights Weights.
- * @param means Means.
- * @param covariances Covariances.
- * @return the mixture distribution.
- */
- private MultivariateNormalMixtureModelDistribution create(double[] weights,
- double[][] means,
- double[][][] covariances) {
- final List<Pair<Double, MultivariateNormalDistribution>> mvns
- = new ArrayList<Pair<Double, MultivariateNormalDistribution>>();
-
- for (int i = 0; i < weights.length; i++) {
- final MultivariateNormalDistribution dist
- = new MultivariateNormalDistribution(means[i], covariances[i]);
- mvns.add(new Pair<Double, MultivariateNormalDistribution>(weights[i], dist));
- }
-
- return new MultivariateNormalMixtureModelDistribution(mvns);
- }
-
- /**
- * Values used in {@link #testSampling()}.
- */
- private double[][] getCorrectSamples() {
- // These were sampled from the MultivariateNormalMixtureModelDistribution class
- // with seed 50.
- //
- // They were then fit to a MVN mixture model in R using mixtools.
- //
- // The optimal parameters were:
- // - component weights: {0.3595186, 0.6404814}
- // - mean vectors: {-1.645879, 1.989797}, {3.474328, 7.782232}
- // - covariance matrices:
- // { 1.397738 -1.167732
- // -1.167732 1.801782 }
- // and
- // { 3.934593 2.354787
- // 2.354787 4.428024 }
- //
- // It is considered fairly close to the actual test parameters,
- // considering that the sample size is only 100.
- return new double[][] {
- { 6.259990922080121, 11.972954175355897 },
- { -2.5296544304801847, 1.0031292519854365 },
- { 0.49037886081440396, 0.9758251727325711 },
- { 5.022970993312015, 9.289348879616787 },
- { -1.686183146603914, 2.007244382745706 },
- { -1.4729253946002685, 2.762166644212484 },
- { 4.329788143963888, 11.514016497132253 },
- { 3.008674596114442, 4.960246550446107 },
- { 3.342379304090846, 5.937630105198625 },
- { 2.6993068328674754, 7.42190871572571 },
- { -2.446569340219571, 1.9687117791378763 },
- { 1.922417883170056, 4.917616702617099 },
- { -1.1969741543898518, 2.4576126277884387 },
- { 2.4216948702967196, 8.227710158117134 },
- { 6.701424725804463, 9.098666475042428 },
- { 2.9890253545698964, 9.643807939324331 },
- { 0.7162632354907799, 8.978811120287553 },
- { -2.7548699149775877, 4.1354812280794215 },
- { 8.304528180745018, 11.602319388898287 },
- { -2.7633253389165926, 2.786173883989795 },
- { 1.3322228389460813, 5.447481218602913 },
- { -1.8120096092851508, 1.605624499560037 },
- { 3.6546253437206504, 8.195304526564376 },
- { -2.312349539658588, 1.868941220444169 },
- { -1.882322136356522, 2.033795570464242 },
- { 4.562770714939441, 7.414967958885031 },
- { 4.731882017875329, 8.890676665580747 },
- { 3.492186010427425, 8.9005225241848 },
- { -1.619700190174894, 3.314060142479045 },
- { 3.5466090064003315, 7.75182101001913 },
- { 5.455682472787392, 8.143119287755635 },
- { -2.3859602945473197, 1.8826732217294837 },
- { 3.9095306088680015, 9.258129209626317 },
- { 7.443020189508173, 7.837840713329312 },
- { 2.136004873917428, 6.917636475958297 },
- { -1.7203379410395119, 2.3212878757611524 },
- { 4.618991257611526, 12.095065976419436 },
- { -0.4837044029854387, 0.8255970441255125 },
- { -4.438938966557163, 4.948666297280241 },
- { -0.4539625134045906, 4.700922454655341 },
- { 2.1285488271265356, 8.457941480487563 },
- { 3.4873561871454393, 11.99809827845933 },
- { 4.723049431412658, 7.813095742563365 },
- { 1.1245583037967455, 5.20587873556688 },
- { 1.3411933634409197, 6.069796875785409 },
- { 4.585119332463686, 7.967669543767418 },
- { 1.3076522817963823, -0.647431033653445 },
- { -1.4449446442803178, 1.9400424267464862 },
- { -2.069794456383682, 3.5824162107496544 },
- { -0.15959481421417276, 1.5466782303315405 },
- { -2.0823081278810136, 3.0914366458581437 },
- { 3.521944615248141, 10.276112932926408 },
- { 1.0164326704884257, 4.342329556442856 },
- { 5.3718868590295275, 8.374761158360922 },
- { 0.3673656866959396, 8.75168581694866 },
- { -2.250268955954753, 1.4610850300996527 },
- { -2.312739727403522, 1.5921126297576362 },
- { 3.138993360831055, 6.7338392374947365 },
- { 2.6978650950790115, 7.941857288979095 },
- { 4.387985088655384, 8.253499976968 },
- { -1.8928961721456705, 0.23631082388724223 },
- { 4.43509029544109, 8.565290285488782 },
- { 4.904728034106502, 5.79936660133754 },
- { -1.7640371853739507, 2.7343727594167433 },
- { 2.4553674733053463, 7.875871017408807 },
- { -2.6478965122565006, 4.465127753193949 },
- { 3.493873671142299, 10.443093773532448 },
- { 1.1321916197409103, 7.127108479263268 },
- { -1.7335075535240392, 2.550629648463023 },
- { -0.9772679734368084, 4.377196298969238 },
- { 3.6388366973980357, 6.947299283206256 },
- { 0.27043799318823325, 6.587978599614367 },
- { 5.356782352010253, 7.388957912116327 },
- { -0.09187745751354681, 0.23612399246659743 },
- { 2.903203580353435, 3.8076727621794415 },
- { 5.297014824937293, 8.650985262326508 },
- { 4.934508602170976, 9.164571423190052 },
- { -1.0004911869654256, 4.797064194444461 },
- { 6.782491700298046, 11.852373338280497 },
- { 2.8983678524536014, 8.303837362117521 },
- { 4.805003269830865, 6.790462904325329 },
- { -0.8815799740744226, 1.3015810062131394 },
- { 5.115138859802104, 6.376895810201089 },
- { 4.301239328205988, 8.60546337560793 },
- { 3.276423626317666, 9.889429652591947 },
- { -4.001924973153122, 4.3353864592328515 },
- { 3.9571892554119517, 4.500569057308562 },
- { 4.783067027436208, 7.451125480601317 },
- { 4.79065438272821, 9.614122776979698 },
- { 2.677655270279617, 6.8875223698210135 },
- { -1.3714746289327362, 2.3992153193382437 },
- { 3.240136859745249, 7.748339397522042 },
- { 5.107885374416291, 8.508324480583724 },
- { -1.5830830226666048, 0.9139127045208315 },
- { -1.1596156791652918, -0.04502759384531929 },
- { -0.4670021307952068, 3.6193633227841624 },
- { -0.7026065228267798, 0.4811423031997131 },
- { -2.719979836732917, 2.5165041618080104 },
- { 1.0336754331123372, -0.34966029029320644 },
- { 4.743217291882213, 5.750060115251131 }
- };
- }
-}
-
-/**
- * Class that implements a mixture of Gaussian ditributions.
- */
-class MultivariateNormalMixtureModelDistribution
- extends MixtureMultivariateRealDistribution<MultivariateNormalDistribution> {
-
- public MultivariateNormalMixtureModelDistribution(List<Pair<Double, MultivariateNormalDistribution>> components) {
- super(components);
- }
-}