Examples of org.apache.commons.math3.linear.BiDiagonalTransformer

org.apache.commons.math3.linear.EigenDecomposition
Class transforming any matrix to bi-diagonal shape.
Any m × n matrix A can be written as the product of three matrices: A = U × B × V^T with U an m × m orthogonal matrix, B an m × n bi-diagonal matrix (lower diagonal if m < n, upper diagonal otherwise), and V an n × n orthogonal matrix.

Transformation to bi-diagonal shape is often not a goal by itself, but it is an intermediate step in more general decomposition algorithms like {@link SingularValueDecomposition Singular Value 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.
@since 2.0


    }


    @Test
    public void testMatricesValues() {
       BiDiagonalTransformer transformer =
            new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare));
       final double s17 = FastMath.sqrt(17.0);
        RealMatrix uRef = MatrixUtils.createRealMatrix(new double[][] {
                {  -8 / (5 * s17), 19 / (5 * s17) },
                { -19 / (5 * s17), -8 / (5 * s17) }
        });
        RealMatrix bRef = MatrixUtils.createRealMatrix(new double[][] {
                { -3 * s17 / 5, 32 * s17 / 85 },
                {      0.0,     -5 * s17 / 17 }
        });
        RealMatrix vRef = MatrixUtils.createRealMatrix(new double[][] {
                { 1.0,  0.0 },
                { 0.0, -1.0 }
        });


        // check values against known references
        RealMatrix u = transformer.getU();
        Assert.assertEquals(0, u.subtract(uRef).getNorm(), 1.0e-14);
        RealMatrix b = transformer.getB();
        Assert.assertEquals(0, b.subtract(bRef).getNorm(), 1.0e-14);
        RealMatrix v = transformer.getV();
        Assert.assertEquals(0, v.subtract(vRef).getNorm(), 1.0e-14);


        // check the same cached instance is returned the second time
        Assert.assertTrue(u == transformer.getU());
        Assert.assertTrue(b == transformer.getB());
        Assert.assertTrue(v == transformer.getV());


    }

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    }


    @Test
    public void testUpperOrLower() {
        Assert.assertTrue(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare)).isUpperBiDiagonal());
        Assert.assertTrue(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare)).isUpperBiDiagonal());
        Assert.assertFalse(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare).transpose()).isUpperBiDiagonal());
    }

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     * @param matrix matrix with columns representing variables to correlate
     * @return correlation matrix
     */
    public RealMatrix computeCorrelationMatrix(final RealMatrix matrix) {
        int nVars = matrix.getColumnDimension();
        RealMatrix outMatrix = new BlockRealMatrix(nVars, nVars);
        for (int i = 0; i < nVars; i++) {
            for (int j = 0; j < i; j++) {
                double corr = correlation(matrix.getColumn(i), matrix.getColumn(j));
                outMatrix.setEntry(i, j, corr);
                outMatrix.setEntry(j, i, corr);
            }
            outMatrix.setEntry(i, i, 1d);
        }
        return outMatrix;
    }

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     *
     * @param matrix matrix with columns representing variables to correlate
     * @return correlation matrix
     */
    public RealMatrix computeCorrelationMatrix(final double[][] matrix) {
       return computeCorrelationMatrix(new BlockRealMatrix(matrix));
    }

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        // Compute transpose(J)J.
        final RealMatrix jTj = j.transpose().multiply(j);


        // Compute the covariances matrix.
        final DecompositionSolver solver
            = new QRDecomposition(jTj, threshold).getSolver();
        return solver.getInverse().getData();
    }

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     * Creates a diagonal weight matrix.
     *
     * @param weight List of the values of the diagonal.
     */
    public Weight(double[] weight) {
        weightMatrix = new DiagonalMatrix(weight);
    }

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     * @return the square-root of the weight matrix.
     */
    private RealMatrix squareRoot(RealMatrix m) {
        if (m instanceof DiagonalMatrix) {
            final int dim = m.getRowDimension();
            final RealMatrix sqrtM = new DiagonalMatrix(dim);
            for (int i = 0; i < dim; i++) {
                sqrtM.setEntry(i, i, FastMath.sqrt(m.getEntry(i, i)));
            }
            return sqrtM;
        } else {
            final EigenDecomposition dec = new EigenDecomposition(m);
            return dec.getSquareRoot();

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     * Creates a diagonal weight matrix.
     *
     * @param weight List of the values of the diagonal.
     */
    public Weight(double[] weight) {
        weightMatrix = new DiagonalMatrix(weight);
    }

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     * Creates a diagonal weight matrix.
     *
     * @param weight List of the values of the diagonal.
     */
    public Weight(double[] weight) {
        weightMatrix = new DiagonalMatrix(weight);
    }

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            for (int i = 0; i < dim; i++) {
                sqrtM.setEntry(i, i, FastMath.sqrt(m.getEntry(i, i)));
            }
            return sqrtM;
        } else {
            final EigenDecomposition dec = new EigenDecomposition(m);
            return dec.getSquareRoot();
        }
    }

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