Examples of org.apache.commons.math3.random.Well1024a

org.apache.commons.math3.random.Well1024a
ro.umontreal.ca/~lecuyer/myftp/papers/wellrng.pdf">Improved Long-Period Generators Based on Linear Recurrences Modulo 2 ACM Transactions on Mathematical Software, 32, 1 (2006). The errata for the paper are in wellrng-errata.txt.
@see WELL Random number generator @since 2.2

     * @throws NonSquareMatrixException if the argument is not
     * a square matrix.
     */
    public Weight(RealMatrix weight) {
        if (weight.getColumnDimension() != weight.getRowDimension()) {
            throw new NonSquareMatrixException(weight.getColumnDimension(),
                                               weight.getRowDimension());
        }


        weightMatrix = weight.copy();
    }

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        // Compute transpose(J)J.
        final RealMatrix jTj = j.transpose().multiply(j);


        // Compute the covariances matrix.
        final DecompositionSolver solver
            = new QRDecomposition(jTj, threshold).getSolver();
        return solver.getInverse().getData();
    }

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        SiteWithPolynomial nearSite = nearestSites.get(row);
        DefaultPolynomial.populateMatrix(matrix, row, nearSite.pos.x, nearSite.pos.z);
        vector.setEntry(row, nearSite.pos.y);
      }
      
      QRDecomposition qr = new QRDecomposition(matrix);
      RealVector solution = qr.getSolver().solve(vector);
        
      double[] coeffs = solution.toArray();
      
      for (double coeff : coeffs) {
        if (coeff > 10e3) {

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     * if the covariance matrix cannot be computed (singular problem).
     */
    public double[][] computeCovariances(double[] params,
                                         double threshold) {
        // Set up the Jacobian.
        final RealMatrix j = computeWeightedJacobian(params);


        // Compute transpose(J)J.
        final RealMatrix jTj = j.transpose().multiply(j);


        // Compute the covariances matrix.
        final DecompositionSolver solver
            = new QRDecomposition(jTj, threshold).getSolver();
        return solver.getInverse().getData();

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     * @return the square-root of the weight matrix.
     */
    private RealMatrix squareRoot(RealMatrix m) {
        if (m instanceof DiagonalMatrix) {
            final int dim = m.getRowDimension();
            final RealMatrix sqrtM = new DiagonalMatrix(dim);
            for (int i = 0; i < dim; i++) {
                sqrtM.setEntry(i, i, FastMath.sqrt(m.getEntry(i, i)));
            }
            return sqrtM;
        } else {
            final EigenDecomposition dec = new EigenDecomposition(m);
            return dec.getSquareRoot();

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      List<SiteWithPolynomial> nearestSites =
          nearestSiteMap.get(site);
      
      RealVector vector = new ArrayRealVector(SITES_FOR_APPROX);
      RealMatrix matrix = new Array2DRowRealMatrix(
          SITES_FOR_APPROX, DefaultPolynomial.NUM_COEFFS);
      
      for (int row = 0; row < SITES_FOR_APPROX; row++) {
        SiteWithPolynomial nearSite = nearestSites.get(row);
        DefaultPolynomial.populateMatrix(matrix, row, nearSite.pos.x, nearSite.pos.z);

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    for (SiteWithPolynomial site : sites) {
      
      List<SiteWithPolynomial> nearestSites =
          nearestSiteMap.get(site);
      
      RealVector vector = new ArrayRealVector(SITES_FOR_APPROX);
      RealMatrix matrix = new Array2DRowRealMatrix(
          SITES_FOR_APPROX, DefaultPolynomial.NUM_COEFFS);
      
      for (int row = 0; row < SITES_FOR_APPROX; row++) {
        SiteWithPolynomial nearSite = nearestSites.get(row);
        DefaultPolynomial.populateMatrix(matrix, row, nearSite.pos.x, nearSite.pos.z);
        vector.setEntry(row, nearSite.pos.y);
      }
      
      QRDecomposition qr = new QRDecomposition(matrix);
      RealVector solution = qr.getSolver().solve(vector);
        
      double[] coeffs = solution.toArray();
      
      for (double coeff : coeffs) {
        if (coeff > 10e3) {
          continue calculatePolynomials;
        }

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                return Double.compare(weightedResidual(o1),
                                      weightedResidual(o2));
            }


            private double weightedResidual(final PointVectorValuePair pv) {
                final RealVector v = new ArrayRealVector(pv.getValueRef(), false);
                final RealVector r = target.subtract(v);
                return r.dotProduct(weight.operate(r));
            }
        };
    }

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    @Test
    public void testLinearCombination2() {
        // we compare accurate versus naive dot product implementations
        // on regular vectors (i.e. not extreme cases like in the previous test)
        Well1024a random = new Well1024a(553267312521321234l);


        for (int i = 0; i < 10000; ++i) {
            final double ux = 1e17 * random.nextDouble();
            final double uy = 1e17 * random.nextDouble();
            final double uz = 1e17 * random.nextDouble();
            final double vx = 1e17 * random.nextDouble();
            final double vy = 1e17 * random.nextDouble();
            final double vz = 1e17 * random.nextDouble();
            final double sInline = MathArrays.linearCombination(ux, vx,
                                                                uy, vy,
                                                                uz, vz);
            final double sArray = MathArrays.linearCombination(new double[] {ux, uy, uz},
                                                               new double[] {vx, vy, vz});

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    @Test
    public void testShuffleTail() {
        final int[] orig = new int[] { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 };
        final int[] list = orig.clone();
        final int start = 4;
        MathArrays.shuffle(list, start, MathArrays.Position.TAIL, new Well1024a(7654321L));


        // Ensure that all entries below index "start" did not move.
        for (int i = 0; i < start; i++) {
            Assert.assertEquals(orig[i], list[i]);
        }

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