Examples of org.apache.commons.math.linear.RealMatrix

org.apache.commons.math.linear.RealMatrix
Interface defining a real-valued matrix with basic algebraic operations.
Matrix element indexing is 0-based -- e.g., getEntry(0, 0) returns the element in the first row, first column of the matrix.
@version $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $

            }
        }


        try {
            // compute the covariances matrix
            RealMatrix inverse =
                new LUDecompositionImpl(MatrixUtils.createRealMatrix(jTj)).getSolver().getInverse();
            return inverse.getData();
        } catch (InvalidMatrixException ime) {
            throw new OptimizationException("unable to compute covariances: singular problem");
        }


    }

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     * columns representing variable values.
     * 
     * @param covariance Covariance instance
     */
    public PearsonsCorrelation(Covariance covariance) {
        RealMatrix covarianceMatrix = covariance.getCovarianceMatrix();
        if (covarianceMatrix == null) {
            throw MathRuntimeException.createIllegalArgumentException("covariance matrix is null");
        }
        nObs = covariance.getN();
        correlationMatrix = covarianceToCorrelation(covarianceMatrix);

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     *
     * @param matrix matrix with columns representing variables to correlate
     * @return correlation matrix
     */
    public RealMatrix computeCorrelationMatrix(RealMatrix matrix) {
        RealMatrix matrixCopy = matrix.copy();
        rankTransform(matrixCopy);
        return new PearsonsCorrelation().computeCorrelationMatrix(matrixCopy);
    }

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            }
        }


        try {
            // compute the covariance matrix
            RealMatrix inverse =
                new LUDecompositionImpl(MatrixUtils.createRealMatrix(jTj)).getSolver().getInverse();
            return inverse.getData();
        } catch (InvalidMatrixException ime) {
            throw new OptimizationException(LocalizedFormats.UNABLE_TO_COMPUTE_COVARIANCE_SINGULAR_PROBLEM);
        }


    }

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            }


            try {


                // solve the linearized least squares problem
                RealMatrix mA = new BlockRealMatrix(a);
                DecompositionSolver solver = useLU ?
                        new LUDecompositionImpl(mA).getSolver() :
                        new QRDecompositionImpl(mA).getSolver();
                final double[] dX = solver.solve(b);

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          {27, 37, 47}   
        };
        double[][] covariance = MatrixUtils.createRealIdentityMatrix(4).scalarMultiply(2).getData();
        GLSMultipleLinearRegression regression = new GLSMultipleLinearRegression();
        regression.newSampleData(y, x, covariance);
        RealMatrix combinedX = regression.X.copy();
        RealVector combinedY = regression.Y.copy();
        RealMatrix combinedCovInv = regression.getOmegaInverse();
        regression.newXSampleData(x);
        regression.newYSampleData(y);
        assertEquals(combinedX, regression.X);
        assertEquals(combinedY, regression.Y);
        assertEquals(combinedCovInv, regression.getOmegaInverse());

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     * Verifies that GLS with identity covariance matrix gives the same results
     * as OLS.
     */
    @Test
    public void testGLSOLSConsistency() throws Exception {      
        RealMatrix identityCov = MatrixUtils.createRealIdentityMatrix(16);
        GLSMultipleLinearRegression glsModel = new GLSMultipleLinearRegression();
        OLSMultipleLinearRegression olsModel = new OLSMultipleLinearRegression();
        glsModel.newSampleData(longley, 16, 6);
        olsModel.newSampleData(longley, 16, 6);
        glsModel.newCovarianceData(identityCov.getData());
        double[] olsBeta = olsModel.calculateBeta().getData();
        double[] glsBeta = glsModel.calculateBeta().getData();
        // TODO:  Should have assertRelativelyEquals(double[], double[], eps) in TestUtils
        //        Should also add RealVector and RealMatrix versions
        for (int i = 0; i < olsBeta.length; i++) {

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        }
        
        // Now generate 1000 error vectors to use to estimate the covariance matrix
        // Columns are draws on N(0, sigma[col])
        final int numSeeds = 1000;
        RealMatrix errorSeeds = MatrixUtils.createRealMatrix(numSeeds, nObs);
        for (int i = 0; i < numSeeds; i++) {
            for (int j = 0; j < nObs; j++) {
                errorSeeds.setEntry(i, j, rg.nextGaussian() * sigma[j]);
            }
        }
        
        // Get covariance matrix for columns
        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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                               new double[]{ 11.0, 1.0 / 2.0, 2.0 / 3.0, 3.0 / 4.0, 4.0 / 5.0, 5.0 / 6.0 },
                               1e-14);
        double[] residuals = regression.estimateResiduals();
        TestUtils.assertEquals(residuals, new double[]{0d,0d,0d,0d,0d,0d},
                               1e-14);
        RealMatrix errors =
            new Array2DRowRealMatrix(regression.estimateRegressionParametersVariance(), false);
        final double[] s = { 1.0, -1.0 /  2.0, -1.0 /  3.0, -1.0 /  4.0, -1.0 /  5.0, -1.0 /  6.0 };
        RealMatrix referenceVariance = new Array2DRowRealMatrix(s.length, s.length);
        referenceVariance.walkInOptimizedOrder(new DefaultRealMatrixChangingVisitor() {
            @Override
            public double visit(int row, int column, double value) {
                if (row == 0) {
                    return s[column];
                }
                double x = s[row] * s[column];
                return (row == column) ? 2 * x : x;
            }
        });
       assertEquals(0.0,
                     errors.subtract(referenceVariance).getNorm(),
                     5.0e-16 * referenceVariance.getNorm());
       assertEquals(1, ((OLSMultipleLinearRegression) regression).calculateRSquared(), 1E-12);
    }

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        // Estimate the model
        OLSMultipleLinearRegression model = new OLSMultipleLinearRegression();
        model.newSampleData(design, nobs, nvars);


        RealMatrix hat = model.calculateHat();


        // Reference data is upper half of symmetric hat matrix
        double[] referenceData = new double[] {
                .418, -.002,  .079, -.274, -.046,  .181,  .128,  .222,  .050,  .242,
                       .242,  .292,  .136,  .243,  .128, -.041,  .033, -.035,  .004,
                              .417, -.019,  .273,  .187, -.126,  .044, -.153,  .004,
                                     .604,  .197, -.038,  .168, -.022,  .275, -.028,
                                            .252,  .111, -.030,  .019, -.010, -.010,
                                                   .148,  .042,  .117,  .012,  .111,
                                                          .262,  .145,  .277,  .174,
                                                                 .154,  .120,  .168,
                                                                        .315,  .148,
                                                                               .187
        };


        // Check against reference data and verify symmetry
        int k = 0;
        for (int i = 0; i < 10; i++) {
            for (int j = i; j < 10; j++) {
                assertEquals(referenceData[k], hat.getEntry(i, j), 10e-3);
                assertEquals(hat.getEntry(i, j), hat.getEntry(j, i), 10e-12);
                k++;
            }
        }


        /*
         * Verify that residuals computed using the hat matrix are close to
         * what we get from direct computation, i.e. r = (I - H) y
         */
        double[] residuals = model.estimateResiduals();
        RealMatrix I = MatrixUtils.createRealIdentityMatrix(10);
        double[] hatResiduals = I.subtract(hat).operate(model.Y).getData();
        TestUtils.assertEquals(residuals, hatResiduals, 10e-12);
    }

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