Examples of CorrelatedRandomVectorGenerator

org.apache.commons.math.random.CorrelatedRandomVectorGenerator
kipedia.org/wiki/Multivariate_normal_distribution"> Multivariate Normal Distribution. The approach using a Cholesky decomposition is quite usual in this case. However, it can be extended to other cases as long as the underlying random generator provides {@link NormalizedRandomGenerator normalized values} like {@link GaussianRandomGenerator} or {@link UniformRandomGenerator}.

Sometimes, the covariance matrix for a given simulation is not strictly positive definite. This means that the correlations are not all independent from each other. In this case, however, the non strictly positive elements found during the Cholesky decomposition of the covariance matrix should not be negative either, they should be null. Another non-conventional extension handling this case is used here. Rather than computing C = U^T.U where C is the covariance matrix and U is an upper-triangular matrix, we compute C = B.B^T where B is a rectangular matrix having more rows than columns. The number of columns of B is the rank of the covariance matrix, and it is the dimension of the uncorrelated random vector that is needed to compute the component of the correlated vector. This class handles this situation automatically.
@version $Revision: 1043908 $ $Date: 2010-12-09 12:53:14 +0100 (jeu. 09 déc. 2010) $ @since 1.2
org.apache.commons.math3.random.CorrelatedRandomVectorGenerator
kipedia.org/wiki/Multivariate_normal_distribution"> Multivariate Normal Distribution. The approach using a Cholesky decomposition is quite usual in this case. However, it can be extended to other cases as long as the underlying random generator provides {@link NormalizedRandomGenerator normalized values} like {@link GaussianRandomGenerator} or {@link UniformRandomGenerator}.

Sometimes, the covariance matrix for a given simulation is not strictly positive definite. This means that the correlations are not all independent from each other. In this case, however, the non strictly positive elements found during the Cholesky decomposition of the covariance matrix should not be negative either, they should be null. Another non-conventional extension handling this case is used here. Rather than computing C = U^T.U where C is the covariance matrix and U is an upper-triangular matrix, we compute C = B.B^T where B is a rectangular matrix having more rows than columns. The number of columns of B is the rank of the covariance matrix, and it is the dimension of the uncorrelated random vector that is needed to compute the component of the correlated vector. This class handles this situation automatically.
@since 1.2

Examples of org.apache.commons.math.random.CorrelatedRandomVectorGenerator

        RealMatrix cov = (new Covariance(errorSeeds)).getCovarianceMatrix();
          
        // Create a CorrelatedRandomVectorGenerator to use to generate correlated errors
        GaussianRandomGenerator rawGenerator = new GaussianRandomGenerator(rg);
        double[] errorMeans = new double[nObs];  // Counting on init to 0 here
        CorrelatedRandomVectorGenerator gen = new CorrelatedRandomVectorGenerator(errorMeans, cov,
         1.0e-12 * cov.getNorm(), rawGenerator);
        
        // Now start generating models.  Use Longley X matrix on LHS
        // and Longley OLS beta vector as "true" beta.  Generate
        // Y values by XB + u where u is a CorrelatedRandomVector generated
        // from cov.
        OLSMultipleLinearRegression ols = new OLSMultipleLinearRegression();
        ols.newSampleData(longley, nObs, 6);
        final RealVector b = ols.calculateBeta().copy();
        final RealMatrix x = ols.X.copy();
        
        // Create a GLS model to reuse
        GLSMultipleLinearRegression gls = new GLSMultipleLinearRegression();
        gls.newSampleData(longley, nObs, 6);
        gls.newCovarianceData(cov.getData());
        
        // Create aggregators for stats measuring model performance
        DescriptiveStatistics olsBetaStats = new DescriptiveStatistics();
        DescriptiveStatistics glsBetaStats = new DescriptiveStatistics();
        
        // Generate Y vectors for 10000 models, estimate GLS and OLS and
        // Verify that OLS estimates are better
        final int nModels = 10000;
        for (int i = 0; i < nModels; i++) {
            
            // Generate y = xb + u with u cov
            RealVector u = MatrixUtils.createRealVector(gen.nextVector());
            double[] y = u.add(x.operate(b)).getData();
            
            // Estimate OLS parameters
            ols.newYSampleData(y);
            RealVector olsBeta = ols.calculateBeta();

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Examples of org.apache.commons.math.random.CorrelatedRandomVectorGenerator

            


            RandomGenerator rg = new JDKRandomGenerator();
            rg.setSeed(seed);
            RandomVectorGenerator rvg =
                new CorrelatedRandomVectorGenerator(mean,
                                                    covariance, 1.0e-12 * covariance.getNorm(),
                                                    new UniformRandomGenerator(rg));
            setMultiStart(starts, rvg);


            // compute minimum

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

        RealMatrix cov = (new Covariance(errorSeeds)).getCovarianceMatrix();
          
        // Create a CorrelatedRandomVectorGenerator to use to generate correlated errors
        GaussianRandomGenerator rawGenerator = new GaussianRandomGenerator(rg);
        double[] errorMeans = new double[nObs];  // Counting on init to 0 here
        CorrelatedRandomVectorGenerator gen = new CorrelatedRandomVectorGenerator(errorMeans, cov,
         1.0e-12 * cov.getNorm(), rawGenerator);
        
        // Now start generating models.  Use Longley X matrix on LHS
        // and Longley OLS beta vector as "true" beta.  Generate
        // Y values by XB + u where u is a CorrelatedRandomVector generated
        // from cov.
        OLSMultipleLinearRegression ols = new OLSMultipleLinearRegression();
        ols.newSampleData(longley, nObs, 6);
        final RealVector b = ols.calculateBeta().copy();
        final RealMatrix x = ols.getX().copy();
        
        // Create a GLS model to reuse
        GLSMultipleLinearRegression gls = new GLSMultipleLinearRegression();
        gls.newSampleData(longley, nObs, 6);
        gls.newCovarianceData(cov.getData());
        
        // Create aggregators for stats measuring model performance
        DescriptiveStatistics olsBetaStats = new DescriptiveStatistics();
        DescriptiveStatistics glsBetaStats = new DescriptiveStatistics();
        
        // Generate Y vectors for 10000 models, estimate GLS and OLS and
        // Verify that OLS estimates are better
        final int nModels = 10000;
        for (int i = 0; i < nModels; i++) {
            
            // Generate y = xb + u with u cov
            RealVector u = MatrixUtils.createRealVector(gen.nextVector());
            double[] y = u.add(x.operate(b)).toArray();
            
            // Estimate OLS parameters
            ols.newYSampleData(y);
            RealVector olsBeta = ols.calculateBeta();

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

    // Create a GassianRandomGenerator using rg as its source of randomness
    GaussianRandomGenerator rawGenerator = new GaussianRandomGenerator(rg);


    // Create a CorrelatedRandomVectorGenerator using rawGenerator for the
    // components
    CorrelatedRandomVectorGenerator generator = new CorrelatedRandomVectorGenerator(mean, covariance, 1.0e-12 * covariance.getNorm(), rawGenerator);


    // Use the generator to generate correlated vectors
    double[] randomVector = generator.nextVector();
  }

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

        RealMatrix cov = (new Covariance(errorSeeds)).getCovarianceMatrix();
          
        // Create a CorrelatedRandomVectorGenerator to use to generate correlated errors
        GaussianRandomGenerator rawGenerator = new GaussianRandomGenerator(rg);
        double[] errorMeans = new double[nObs];  // Counting on init to 0 here
        CorrelatedRandomVectorGenerator gen = new CorrelatedRandomVectorGenerator(errorMeans, cov,
         1.0e-12 * cov.getNorm(), rawGenerator);
        
        // Now start generating models.  Use Longley X matrix on LHS
        // and Longley OLS beta vector as "true" beta.  Generate
        // Y values by XB + u where u is a CorrelatedRandomVector generated
        // from cov.
        OLSMultipleLinearRegression ols = new OLSMultipleLinearRegression();
        ols.newSampleData(longley, nObs, 6);
        final RealVector b = ols.calculateBeta().copy();
        final RealMatrix x = ols.getX().copy();
        
        // Create a GLS model to reuse
        GLSMultipleLinearRegression gls = new GLSMultipleLinearRegression();
        gls.newSampleData(longley, nObs, 6);
        gls.newCovarianceData(cov.getData());
        
        // Create aggregators for stats measuring model performance
        DescriptiveStatistics olsBetaStats = new DescriptiveStatistics();
        DescriptiveStatistics glsBetaStats = new DescriptiveStatistics();
        
        // Generate Y vectors for 10000 models, estimate GLS and OLS and
        // Verify that OLS estimates are better
        final int nModels = 10000;
        for (int i = 0; i < nModels; i++) {
            
            // Generate y = xb + u with u cov
            RealVector u = MatrixUtils.createRealVector(gen.nextVector());
            double[] y = u.add(x.operate(b)).toArray();
            
            // Estimate OLS parameters
            ols.newYSampleData(y);
            RealVector olsBeta = ols.calculateBeta();

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