Examples of org.apache.mahout.math.random.MultiNormal

org.apache.mahout.math.random.MultiNormal
Samples from a multi-variate normal distribution.
This is done by sampling from several independent unit normal distributions to get a vector u. The sample value that is returned is then A u + m where A is derived from the covariance matrix and m is the mean of the result.
If \Sigma is the desired covariance matrix, then you can use any value of A such that A' A = \Sigma. The Cholesky decomposition can be used to compute A if \Sigma is positive definite. Slightly more expensive is to use the SVD U S V' = \Sigma and then set A = U \sqrt{S}. Useful special cases occur when \Sigma is diagonal so that A = \sqrt(\Sigma) or where \Sigma = r I. Another special case is where m = 0.

import static org.junit.Assert.fail;


public abstract class AbstractSearchTest {
  protected static Matrix randomData() {
    Matrix data = new DenseMatrix(1000, 20);
    MultiNormal gen = new MultiNormal(20);
    for (MatrixSlice slice : data) {
      slice.vector().assign(gen.sample());
    }
    return data;
  }

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  public void testNearMatch() {
    List<MatrixSlice> queries = Lists.newArrayList(Iterables.limit(testData(), 100));
    Searcher s = getSearch(20);
    s.addAllMatrixSlicesAsWeightedVectors(testData());


    MultiNormal noise = new MultiNormal(0.01, new DenseVector(20));
    for (MatrixSlice slice : queries) {
      Vector query = slice.vector();
      final Vector epsilon = noise.sample();
      List<WeightedThing<Vector>> r0 = s.search(query, 2);
      query = query.plus(epsilon);
      List<WeightedThing<Vector>> r = s.search(query, 2);
      r = s.search(query, 2);
      assertEquals("Distance has to be small", epsilon.norm(2), r.get(0).getWeight(), 1e-5);

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  }


  @Test
  public void testOrdering() {
    Matrix queries = new DenseMatrix(100, 20);
    MultiNormal gen = new MultiNormal(20);
    for (int i = 0; i < 100; i++) {
      queries.viewRow(i).assign(gen.sample());
    }


    Searcher s = getSearch(20);
    // s.setSearchSize(200);
    s.addAllMatrixSlices(testData());

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  private List<? extends WeightedVector> cubishTestData(double radius) {
    List<WeightedVector> data = Lists.newArrayListWithCapacity(K1 + 5000);
    int row = 0;


    MultiNormal g = new MultiNormal(radius, new ConstantVector(0, 10));
    for (int i = 0; i < K1; i++) {
      data.add(new WeightedVector(g.sample(), 1, row++));
    }


    for (int i = 0; i < 5; i++) {
      Vector m = new DenseVector(10);
      m.set(i, i == 0 ? 6 : 6);
      MultiNormal gx = new MultiNormal(radius, m);
      for (int j = 0; j < 1000; j++) {
        data.add(new WeightedVector(gx.sample(), 1, row++));
      }
    }
    return data;
  }

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  private static final int VECTOR_DIMENSION = 250;
  private static final int REFERENCE_SIZE = 10000;
  private static final int QUERY_SIZE = 100;


  public static void main(String[] args) {
    Sampler<Vector> rand = new MultiNormal(new ConstantVector(1, VECTOR_DIMENSION));
    List<WeightedVector> referenceVectors = Lists.newArrayListWithExpectedSize(REFERENCE_SIZE);
    for (int i = 0; i < REFERENCE_SIZE; ++i) {
      referenceVectors.add(new WeightedVector(rand.sample(), 1, i));
    }
    System.out.printf("Generated reference matrix.\n");


    List<WeightedVector> queryVectors = Lists.newArrayListWithExpectedSize(QUERY_SIZE);
    for (int i = 0; i < QUERY_SIZE; ++i) {
      queryVectors.add(new WeightedVector(rand.sample(), 1, i));
    }
    System.out.printf("Generated query matrix.\n");


    for (int threads : new int[]{1, 2, 3, 4, 5, 6, 10, 20, 50}) {
      for (int block : new int[]{1, 10, 50}) {

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   * @param dimension   The dimension of the vectors to return.
   * @param radius      The size of the clusters we sample from.
   * @param alpha       Controls the growth of the number of clusters.  The number of clusters will be about alpha * log(samples)
   */
  public LumpyData(int dimension, double radius, double alpha) {
    this.centers = new MultiNormal(dimension);
    this.radius = radius;
    cluster = new ChineseRestaurant(alpha);
  }

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  @Override
  public Vector sample() {
    int id = cluster.sample();
    if (id >= centroids.size()) {
      // need to invent a new cluster
      centroids.add(new MultiNormal(radius, centers.sample()));
    }
    return centroids.get(id).sample();
  }

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      for (int j = 0; j < numDimensions; ++j) {
        v.set(j, 1.0 / pow2J * (i & pow2J));
        pow2J >>= 1;
      }
      mean.add(new Centroid(i, v, 1));
      rowSamplers.add(new MultiNormal(distributionRadius, v));
    }


    // Sample the requested number of data points.
    List<Centroid> data = Lists.newArrayListWithCapacity(numDatapoints);
    for (int i = 0; i < numDatapoints; ++i) {

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  private static List<? extends WeightedVector> cubishTestData(double radius) {
    List<WeightedVector> data = Lists.newArrayListWithCapacity(K1 + 5000);
    int row = 0;


    MultiNormal g = new MultiNormal(radius, new ConstantVector(0, 10));
    for (int i = 0; i < K1; i++) {
      data.add(new WeightedVector(g.sample(), 1, row++));
    }


    for (int i = 0; i < 5; i++) {
      Vector m = new DenseVector(10);
      m.set(i, 6); // This was originally i == 0 ? 6 : 6 which can't be right
      MultiNormal gx = new MultiNormal(radius, m);
      for (int j = 0; j < 1000; j++) {
        data.add(new WeightedVector(gx.sample(), 1, row++));
      }
    }
    return data;
  }

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      for (int j = 0; j < numDimensions; ++j) {
        v.set(j, 1.0 / pow2J * (i & pow2J));
        pow2J >>= 1;
      }
      mean.add(new Centroid(i, v, 1));
      rowSamplers.add(new MultiNormal(distributionRadius, v));
    }


    // Sample the requested number of data points.
    List<Centroid> data = Lists.newArrayListWithCapacity(numDatapoints);
    for (int i = 0; i < numDatapoints; ++i) {

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