Examples of TriDiagonalTransformer

org.apache.commons.math.linear.TriDiagonalTransformer
Class transforming a symmetrical matrix to tridiagonal shape.
A symmetrical m × m matrix A can be written as the product of three matrices: A = Q × T × Q^T with Q an orthogonal matrix and T a symmetrical tridiagonal matrix. Both Q and T are m × m matrices.

This implementation only uses the upper part of the matrix, the part below the diagonal is not accessed at all.

Transformation to tridiagonal shape is often not a goal by itself, but it is an intermediate step in more general decomposition algorithms like {@link EigenDecomposition eigen decomposition}. This class is therefore intended for internal use by the library and is not public. As a consequence of this explicitly limited scope, many methods directly returns references to internal arrays, not copies.
@version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $ @since 2.0

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

        super(name);
    }


    public void testNonSquare() {
        try {
            new TriDiagonalTransformer(MatrixUtils.createRealMatrix(new double[3][2]));
            fail("an exception should have been thrown");
        } catch (InvalidMatrixException ime) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");

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

        checkAEqualQTQt(MatrixUtils.createRealMatrix(testSquare5));
        checkAEqualQTQt(MatrixUtils.createRealMatrix(testSquare3));
    }


    private void checkAEqualQTQt(RealMatrix matrix) {
        TriDiagonalTransformer transformer = new TriDiagonalTransformer(matrix);
        RealMatrix q  = transformer.getQ();
        RealMatrix qT = transformer.getQT();
        RealMatrix t  = transformer.getT();
        double norm = q.multiply(t).multiply(qT).subtract(matrix).getNorm();
        assertEquals(0, norm, 4.0e-15);
    }

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

        for (int i = 0; i < data.length; ++i) {
            modifiedData[i] = data[i].clone();
            Arrays.fill(modifiedData[i], 0, i, Double.NaN);
        }
        RealMatrix matrix = MatrixUtils.createRealMatrix(modifiedData);
        TriDiagonalTransformer transformer = new TriDiagonalTransformer(matrix);
        RealMatrix q  = transformer.getQ();
        RealMatrix qT = transformer.getQT();
        RealMatrix t  = transformer.getT();
        double norm = q.multiply(t).multiply(qT).subtract(MatrixUtils.createRealMatrix(data)).getNorm();
        assertEquals(0, norm, 4.0e-15);
    }

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

        double norm = q.multiply(t).multiply(qT).subtract(MatrixUtils.createRealMatrix(data)).getNorm();
        assertEquals(0, norm, 4.0e-15);
    }


    public void testQOrthogonal() {
        checkOrthogonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare5)).getQ());
        checkOrthogonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare3)).getQ());
    }

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

        checkOrthogonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare5)).getQ());
        checkOrthogonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare3)).getQ());
    }


    public void testQTOrthogonal() {
        checkOrthogonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare5)).getQT());
        checkOrthogonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare3)).getQT());
    }

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

            } else {
                ref[i] = 0.0001 * r.nextDouble() + 6;                
            }
        }
        Arrays.sort(ref);
        TriDiagonalTransformer t =
            new TriDiagonalTransformer(createTestMatrix(r, ref));
        EigenDecomposition ed =
            new EigenDecompositionImpl(t.getMainDiagonalRef(),
                                       t.getSecondaryDiagonalRef(),
                                       MathUtils.SAFE_MIN);
        double[] eigenValues = ed.getRealEigenvalues();
        assertEquals(ref.length, eigenValues.length);
        for (int i = 0; i < ref.length; ++i) {
            assertEquals(ref[ref.length - i - 1], eigenValues[i], 2.0e-14);

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

            } else {
                ref[i] = 0.0001 * r.nextDouble() + 6;                
            }
        }
        Arrays.sort(ref);
        TriDiagonalTransformer t =
            new TriDiagonalTransformer(createTestMatrix(r, ref));
        EigenDecomposition ed =
            new EigenDecompositionImpl(t.getMainDiagonalRef(),
                                       t.getSecondaryDiagonalRef(),
                                       MathUtils.SAFE_MIN);
        double[] eigenValues = ed.getRealEigenvalues();
        assertEquals(ref.length, eigenValues.length);
        for (int i = 0; i < ref.length; ++i) {
            assertEquals(ref[ref.length - i - 1], eigenValues[i], 2.0e-14);

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

        super(name);
    }


    public void testNonSquare() {
        try {
            new TriDiagonalTransformer(MatrixUtils.createRealMatrix(new double[3][2]));
            fail("an exception should have been thrown");
        } catch (InvalidMatrixException ime) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");

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

        checkAEqualQTQt(MatrixUtils.createRealMatrix(testSquare5));
        checkAEqualQTQt(MatrixUtils.createRealMatrix(testSquare3));
    }


    private void checkAEqualQTQt(RealMatrix matrix) {
        TriDiagonalTransformer transformer = new TriDiagonalTransformer(matrix);
        RealMatrix q  = transformer.getQ();
        RealMatrix qT = transformer.getQT();
        RealMatrix t  = transformer.getT();
        double norm = q.multiply(t).multiply(qT).subtract(matrix).getNorm();
        assertEquals(0, norm, 4.0e-15);
    }

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

        for (int i = 0; i < data.length; ++i) {
            modifiedData[i] = data[i].clone();
            Arrays.fill(modifiedData[i], 0, i, Double.NaN);
        }
        RealMatrix matrix = MatrixUtils.createRealMatrix(modifiedData);
        TriDiagonalTransformer transformer = new TriDiagonalTransformer(matrix);
        RealMatrix q  = transformer.getQ();
        RealMatrix qT = transformer.getQT();
        RealMatrix t  = transformer.getT();
        double norm = q.multiply(t).multiply(qT).subtract(MatrixUtils.createRealMatrix(data)).getNorm();
        assertEquals(0, norm, 4.0e-15);
    }

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