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From er...@apache.org
Subject [45/53] [abbrv] [math] MATH-1351
Date Thu, 21 Apr 2016 23:15:31 GMT
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 <erans@apache.org>
Authored: Mon Mar 28 13:45:42 2016 +0200
Committer: Gilles <erans@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);
-    }
-}


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