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

org.apache.commons.math.linear.SingularValueDecompositionImpl
Calculates the compact Singular Value Decomposition of a matrix.
The Singular Value Decomposition of matrix A is a set of three matrices: U, Σ and V such that A = U × Σ × V^T. Let A be a m × n matrix, then U is a m × p orthogonal matrix, Σ is a p × p diagonal matrix with positive or null elements, V is a p × n orthogonal matrix (hence V^T is also orthogonal) where p=min(m,n).
@version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $ @since 2.0

    }


    /** test solve dimension errors */
    public void testSolveDimensionErrors() {
        DecompositionSolver solver =
            new SingularValueDecompositionImpl(MatrixUtils.createRealMatrix(testSquare)).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[3][2]);
        try {
            solver.solve(b);
            fail("an exception should have been thrown");
        } catch (IllegalArgumentException iae) {

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        RealMatrix m =
            MatrixUtils.createRealMatrix(new double[][] {
                                   { 1.0, 0.0 },
                                   { 0.0, 0.0 }
                               });
        DecompositionSolver solver = new SingularValueDecompositionImpl(m).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[2][2]);
        try {
            solver.solve(b);
            fail("an exception should have been thrown");
        } catch (InvalidMatrixException ime) {

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    }


    /** test solve */
    public void testSolve() {
        DecompositionSolver solver =
            new SingularValueDecompositionImpl(MatrixUtils.createRealMatrix(testSquare)).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[][] {
                { 1, 2, 3 }, { 0, -5, 1 }
        });
        RealMatrix xRef = MatrixUtils.createRealMatrix(new double[][] {
                { -8.0 / 25.0, -263.0 / 75.0, -29.0 / 75.0 },

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    }


    /** test condition number */
    public void testConditionNumber() {
        SingularValueDecompositionImpl svd =
            new SingularValueDecompositionImpl(MatrixUtils.createRealMatrix(testSquare));
        assertEquals(3.0, svd.getConditionNumber(), 1.0e-15);
    }

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        final double[] singularValues = { 123.456, 2.3, 1.001, 0.999 };
        final int rows    = singularValues.length + 2;
        final int columns = singularValues.length;
        Random r = new Random(15338437322523l);
        SingularValueDecomposition svd =
            new SingularValueDecompositionImpl(createTestMatrix(r, rows, columns, singularValues));
        double[] computedSV = svd.getSingularValues();
        assertEquals(singularValues.length, computedSV.length);
        for (int i = 0; i < singularValues.length; ++i) {
            assertEquals(singularValues[i], computedSV[i], 1.0e-10);
        }
    }

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        final double[] singularValues = { 123.456, 2.3, 1.001, 0.999 };
        final int rows    = singularValues.length;
        final int columns = singularValues.length + 2;
        Random r = new Random(732763225836210l);
        SingularValueDecomposition svd =
            new SingularValueDecompositionImpl(createTestMatrix(r, rows, columns, singularValues));
        double[] computedSV = svd.getSingularValues();
        assertEquals(singularValues.length, computedSV.length);
        for (int i = 0; i < singularValues.length; ++i) {
            assertEquals(singularValues[i], computedSV[i], 1.0e-10);
        }
    }

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    /** test dimensions */
    public void testDimensions() {
        RealMatrix matrix = MatrixUtils.createRealMatrix(testSquare);
        final int m = matrix.getRowDimension();
        final int n = matrix.getColumnDimension();
        SingularValueDecomposition svd = new SingularValueDecompositionImpl(matrix);
        assertEquals(m, svd.getU().getRowDimension());
        assertEquals(m, svd.getU().getColumnDimension());
        assertEquals(m, svd.getS().getColumnDimension());
        assertEquals(n, svd.getS().getColumnDimension());
        assertEquals(n, svd.getV().getRowDimension());
        assertEquals(n, svd.getV().getColumnDimension());


    }

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                {15.0 / 2.0,  5.0 / 2.0,  9.0 / 2.0,  3.0 / 2.0 },
                { 5.0 / 2.0, 15.0 / 2.0,  3.0 / 2.0,  9.0 / 2.0 },
                { 9.0 / 2.0,  3.0 / 2.0, 15.0 / 2.0,  5.0 / 2.0 },
                { 3.0 / 2.0,  9.0 / 2.0,  5.0 / 2.0, 15.0 / 2.0 }
        }, false);
        SingularValueDecomposition svd = new SingularValueDecompositionImpl(matrix);
        assertEquals(16.0, svd.getSingularValues()[0], 1.0e-14);
        assertEquals( 8.0, svd.getSingularValues()[1], 1.0e-14);
        assertEquals( 4.0, svd.getSingularValues()[2], 1.0e-14);
        assertEquals( 2.0, svd.getSingularValues()[3], 1.0e-14);


        RealMatrix fullCovariance = new Array2DRowRealMatrix(new double[][] {
                {  85.0 / 1024, -51.0 / 1024, -75.0 / 1024,  45.0 / 1024 },
                { -51.0 / 1024,  85.0 / 1024,  45.0 / 1024, -75.0 / 1024 },
                { -75.0 / 1024,  45.0 / 1024,  85.0 / 1024, -51.0 / 1024 },
                {  45.0 / 1024, -75.0 / 1024, -51.0 / 1024,  85.0 / 1024 }
        }, false);
        assertEquals(0.0,
                     fullCovariance.subtract(svd.getCovariance(0.0)).getNorm(),
                     1.0e-14);


        RealMatrix halfCovariance = new Array2DRowRealMatrix(new double[][] {
                {   5.0 / 1024,  -3.0 / 1024,   5.0 / 1024,  -3.0 / 1024 },
                {  -3.0 / 1024,   5.0 / 1024,  -3.0 / 1024,   5.0 / 1024 },
                {   5.0 / 1024,  -3.0 / 1024,   5.0 / 1024,  -3.0 / 1024 },
                {  -3.0 / 1024,   5.0 / 1024,  -3.0 / 1024,   5.0 / 1024 }
        }, false);
        assertEquals(0.0,
                     halfCovariance.subtract(svd.getCovariance(6.0)).getNorm(),
                     1.0e-14);


    }

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        checkAEqualUSVt(MatrixUtils.createRealMatrix(testNonSquare));
        checkAEqualUSVt(MatrixUtils.createRealMatrix(testNonSquare).transpose());
    }


    public void checkAEqualUSVt(final RealMatrix matrix) {
        SingularValueDecomposition svd = new SingularValueDecompositionImpl(matrix);
        RealMatrix u = svd.getU();
        RealMatrix s = svd.getS();
        RealMatrix v = svd.getV();
        double norm = u.multiply(s).multiply(v.transpose()).subtract(matrix).getNorm();
        assertEquals(0, norm, normTolerance);


    }

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    }


    /** test that U is orthogonal */
    public void testUOrthogonal() {
        checkOrthogonal(new SingularValueDecompositionImpl(MatrixUtils.createRealMatrix(testSquare)).getU());
        checkOrthogonal(new SingularValueDecompositionImpl(MatrixUtils.createRealMatrix(testNonSquare)).getU());
        checkOrthogonal(new SingularValueDecompositionImpl(MatrixUtils.createRealMatrix(testNonSquare).transpose()).getU());
    }

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