Package org.apache.commons.math.linear

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

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    @Override
    public void setUp() {
        try {
            mean = new double[] { 0.0, 1.0, -3.0, 2.3};

            RealMatrix b = MatrixUtils.createRealMatrix(4, 3);
            int counter = 0;
            for (int i = 0; i < b.getRowDimension(); ++i) {
                for (int j = 0; j < b.getColumnDimension(); ++j) {
                    b.setEntry(i, j, 1.0 + 0.1 * ++counter);
                }
            }
            RealMatrix bbt = b.multiply(b.transpose());
            covariance = MatrixUtils.createRealMatrix(mean.length, mean.length);
            for (int i = 0; i < covariance.getRowDimension(); ++i) {
                covariance.setEntry(i, i, bbt.getEntry(i, i));
                for (int j = 0; j < covariance.getColumnDimension(); ++j) {
                    double s = bbt.getEntry(i, j);
                    covariance.setEntry(i, j, s);
                    covariance.setEntry(j, i, s);
                }
            }

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    public void testSimplistic() throws DimensionMismatchException {
        VectorialCovariance stat = new VectorialCovariance(2, true);
        stat.increment(new double[] {-1.0,  1.0});
        stat.increment(new double[] { 1.0, -1.0});
        RealMatrix c = stat.getResult();
        assertEquals( 2.0, c.getEntry(0, 0), 1.0e-12);
        assertEquals(-2.0, c.getEntry(1, 0), 1.0e-12);
        assertEquals( 2.0, c.getEntry(1, 1), 1.0e-12);
    }
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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)
                throws MatrixVisitorException {
                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());
    }
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            stat.increment(points[i]);
        }

        assertEquals(points.length, stat.getN());

        RealMatrix c = stat.getResult();
        double[][] refC    = new double[][] {
                { 8.0470, -1.9195, -3.4445},
                {-1.9195,  1.0470,  3.2795},
                {-3.4445,  3.2795, 12.2070}
        };

        for (int i = 0; i < c.getRowDimension(); ++i) {
            for (int j = 0; j <= i; ++j) {
                assertEquals(refC[i][j], c.getEntry(i, j), 1.0e-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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    /**
     * Test Longley dataset against R.
     */
    public void testLongly() throws Exception {
        RealMatrix matrix = createRealMatrix(longleyData, 16, 7);
        PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
        RealMatrix correlationMatrix = corrInstance.getCorrelationMatrix();
        double[] rData = new double[] {
                1.000000000000000, 0.9708985250610560, 0.9835516111796693, 0.5024980838759942,
                0.4573073999764817, 0.960390571594376, 0.9713294591921188,
                0.970898525061056, 1.0000000000000000, 0.9915891780247822, 0.6206333925590966,
                0.4647441876006747, 0.979163432977498, 0.9911491900672053,
                0.983551611179669, 0.9915891780247822, 1.0000000000000000, 0.6042609398895580,
                0.4464367918926265, 0.991090069458478, 0.9952734837647849,
                0.502498083875994, 0.6206333925590966, 0.6042609398895580, 1.0000000000000000,
                -0.1774206295018783, 0.686551516365312, 0.6682566045621746,
                0.457307399976482, 0.4647441876006747, 0.4464367918926265, -0.1774206295018783,
                1.0000000000000000, 0.364416267189032, 0.4172451498349454,
                0.960390571594376, 0.9791634329774981, 0.9910900694584777, 0.6865515163653120,
                0.3644162671890320, 1.000000000000000, 0.9939528462329257,
                0.971329459192119, 0.9911491900672053, 0.9952734837647849, 0.6682566045621746,
                0.4172451498349454, 0.993952846232926, 1.0000000000000000
        };
        TestUtils.assertEquals("correlation matrix", createRealMatrix(rData, 7, 7), correlationMatrix, 10E-15);

        double[] rPvalues = new double[] {
                4.38904690369668e-10,
                8.36353208910623e-12, 7.8159700933611e-14,
                0.0472894097790304, 0.01030636128354301, 0.01316878049026582,
                0.0749178049642416, 0.06971758330341182, 0.0830166169296545, 0.510948586323452,
                3.693245043123738e-09, 4.327782576751815e-11, 1.167954621905665e-13, 0.00331028281967516, 0.1652293725106684,
                3.95834476307755e-10, 1.114663916723657e-13, 1.332267629550188e-15, 0.00466039138541463, 0.1078477071581498, 7.771561172376096e-15
        };
        RealMatrix rPMatrix = createLowerTriangularRealMatrix(rPvalues, 7);
        fillUpper(rPMatrix, 0d);
        TestUtils.assertEquals("correlation p values", rPMatrix, corrInstance.getCorrelationPValues(), 10E-15);
    }
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    /**
     * Test R Swiss fertility dataset against R.
     */
    public void testSwissFertility() throws Exception {
         RealMatrix matrix = createRealMatrix(swissData, 47, 5);
         PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
         RealMatrix correlationMatrix = corrInstance.getCorrelationMatrix();
         double[] rData = new double[] {
               1.0000000000000000, 0.3530791836199747, -0.6458827064572875, -0.6637888570350691,  0.4636847006517939,
                 0.3530791836199747, 1.0000000000000000,-0.6865422086171366, -0.6395225189483201, 0.4010950530487398,
                -0.6458827064572875, -0.6865422086171366, 1.0000000000000000, 0.6984152962884830, -0.5727418060641666,
                -0.6637888570350691, -0.6395225189483201, 0.6984152962884830, 1.0000000000000000, -0.1538589170909148,
                 0.4636847006517939, 0.4010950530487398, -0.5727418060641666, -0.1538589170909148, 1.0000000000000000
         };
         TestUtils.assertEquals("correlation matrix", createRealMatrix(rData, 5, 5), correlationMatrix, 10E-15);

         double[] rPvalues = new double[] {
                 0.01491720061472623,
                 9.45043734069043e-07, 9.95151527133974e-08,
                 3.658616965962355e-07, 1.304590105694471e-06, 4.811397236181847e-08,
                 0.001028523190118147, 0.005204433539191644, 2.588307925380906e-05, 0.301807756132683
         };
         RealMatrix rPMatrix = createLowerTriangularRealMatrix(rPvalues, 5);
         fillUpper(rPMatrix, 0d);
         TestUtils.assertEquals("correlation p values", rPMatrix, corrInstance.getCorrelationPValues(), 10E-15);
    }
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            new PearsonsCorrelation().correlation(one, two);
            fail("Expecting IllegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // Expected
        }
        RealMatrix matrix = new BlockRealMatrix(new double[][] {{0},{1}});
        try {
            new PearsonsCorrelation(matrix);
            fail("Expecting IllegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // Expected
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     * Verify that direct t-tests using standard error estimates are consistent
     * with reported p-values
     */
    public void testStdErrorConsistency() throws Exception {
        TDistribution tDistribution = new TDistributionImpl(45);
        RealMatrix matrix = createRealMatrix(swissData, 47, 5);
        PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
        RealMatrix rValues = corrInstance.getCorrelationMatrix();
        RealMatrix pValues = corrInstance.getCorrelationPValues();
        RealMatrix stdErrors = corrInstance.getCorrelationStandardErrors();
        for (int i = 0; i < 5; i++) {
            for (int j = 0; j < i; j++) {
                double t = Math.abs(rValues.getEntry(i, j)) / stdErrors.getEntry(i, j);
                double p = 2 * (1 - tDistribution.cumulativeProbability(t));
                assertEquals(p, pValues.getEntry(i, j), 10E-15);
            }
        }
    }
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    /**
     * Verify that creating correlation from covariance gives same results as
     * direct computation from the original matrix
     */
    public void testCovarianceConsistency() throws Exception {
        RealMatrix matrix = createRealMatrix(longleyData, 16, 7);
        PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
        Covariance covInstance = new Covariance(matrix);
        PearsonsCorrelation corrFromCovInstance = new PearsonsCorrelation(covInstance);
        TestUtils.assertEquals("correlation values", corrInstance.getCorrelationMatrix(),
                corrFromCovInstance.getCorrelationMatrix(), 10E-15);
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