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

        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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        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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        RealMatrix id  = MatrixUtils.createRealIdentityMatrix(mTm.getRowDimension());
        assertEquals(0, mTm.subtract(id).getNorm(), 1.0e-15);        
    }


    public void testTTriDiagonal() {
        checkTriDiagonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare5)).getT());
        checkTriDiagonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare3)).getT());
    }

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    }


    private void checkMatricesValues(double[][] matrix, double[][] qRef,
                                     double[] mainDiagnonal,
                                     double[] secondaryDiagonal) {
        TriDiagonalTransformer transformer =
            new TriDiagonalTransformer(MatrixUtils.createRealMatrix(matrix));


        // check values against known references
        RealMatrix q = transformer.getQ();
        assertEquals(0, q.subtract(MatrixUtils.createRealMatrix(qRef)).getNorm(), 1.0e-14);


        RealMatrix t = transformer.getT();
        double[][] tData = new double[mainDiagnonal.length][mainDiagnonal.length];
        for (int i = 0; i < mainDiagnonal.length; ++i) {
            tData[i][i] = mainDiagnonal[i];
            if (i > 0) {
                tData[i][i - 1] = secondaryDiagonal[i - 1];
            }
            if (i < secondaryDiagonal.length) {
                tData[i][i + 1] = secondaryDiagonal[i];
            }
        }
        assertEquals(0, t.subtract(MatrixUtils.createRealMatrix(tData)).getNorm(), 1.0e-14);


        // check the same cached instance is returned the second time
        assertTrue(q == transformer.getQ());
        assertTrue(t == transformer.getT());
        
    }

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Related Classes of org.apache.commons.math.linear.TriDiagonalTransformer

org.apache.commons.math.linear.EigenDecompositionImplTest

org.apache.commons.math.linear.TriDiagonalTransformerTest

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