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

org.apache.commons.math.linear.LUDecompositionImpl
Calculates the LUP-decomposition of a square matrix.
The LUP-decomposition of a matrix A consists of three matrices L, U and P that satisfy: PA = LU, L is lower triangular, and U is upper triangular and P is a permutation matrix. All matrices are m×m.

As shown by the presence of the P matrix, this decomposition is implemented using partial pivoting.
@version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $ @since 2.0

    }


    /** test matrices values */
    public void testMatricesValues2() {
       LUDecomposition lu =
            new LUDecompositionImpl(MatrixUtils.createRealMatrix(luData));
        RealMatrix lRef = MatrixUtils.createRealMatrix(new double[][] {
                {    1.0,    0.0, 0.0 },
                {    0.0,    1.0, 0.0 },
                { 1.0 / 3.0, 0.0, 1.0 }
        });
        RealMatrix uRef = MatrixUtils.createRealMatrix(new double[][] {
                { 6.0, 9.0,    8.0    },
                { 0.0, 5.0,    7.0    },
                { 0.0, 0.0, 1.0 / 3.0 }
        });
        RealMatrix pRef = MatrixUtils.createRealMatrix(new double[][] {
                { 0.0, 0.0, 1.0 },
                { 0.0, 1.0, 0.0 },
                { 1.0, 0.0, 0.0 }
        });
        int[] pivotRef = { 2, 1, 0 };


        // check values against known references
        RealMatrix l = lu.getL();
        assertEquals(0, l.subtract(lRef).getNorm(), 1.0e-13);
        RealMatrix u = lu.getU();
        assertEquals(0, u.subtract(uRef).getNorm(), 1.0e-13);
        RealMatrix p = lu.getP();
        assertEquals(0, p.subtract(pRef).getNorm(), 1.0e-13);
        int[] pivot = lu.getPivot();
        for (int i = 0; i < pivotRef.length; ++i) {
            assertEquals(pivotRef[i], pivot[i]);
        }


        // check the same cached instance is returned the second time
        assertTrue(l == lu.getL());
        assertTrue(u == lu.getU());
        assertTrue(p == lu.getP());
        
    }

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        }


        try {
            // compute the covariances matrix
            RealMatrix inverse =
                new LUDecompositionImpl(MatrixUtils.createRealMatrix(jTj)).getSolver().getInverse();
            return inverse.getData();
        } catch (InvalidMatrixException ime) {
            throw new OptimizationException("unable to compute covariances: singular problem");
        }

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            try {


                // solve the linearized least squares problem
                RealMatrix mA = new BlockRealMatrix(a);
                DecompositionSolver solver = useLU ?
                        new LUDecompositionImpl(mA).getSolver() :
                        new QRDecompositionImpl(mA).getSolver();
                final double[] dX = solver.solve(b);


                // update the estimated parameters
                for (int i = 0; i < cols; ++i) {

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     */
    @Override
    protected RealMatrix calculateBetaVariance() {
        int p = X.getColumnDimension();
        RealMatrix Raug = qr.getR().getSubMatrix(0, p - 1 , 0, p - 1);
        RealMatrix Rinv = new LUDecompositionImpl(Raug).getSolver().getInverse();
        return Rinv.multiply(Rinv.transpose());
    }

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     * <p>The inverse of the covariance matrix is lazily evaluated and cached.</p>
     * @return inverse of the covariance
     */
    protected RealMatrix getOmegaInverse() {
        if (OmegaInverse == null) {
            OmegaInverse = new LUDecompositionImpl(Omega).getSolver().getInverse();
        }
        return OmegaInverse;
    }

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    @Override
    protected RealVector calculateBeta() {
        RealMatrix OI = getOmegaInverse();
        RealMatrix XT = X.transpose();
        RealMatrix XTOIX = XT.multiply(OI).multiply(X);
        RealMatrix inverse = new LUDecompositionImpl(XTOIX).getSolver().getInverse();
        return inverse.multiply(XT).multiply(OI).operate(Y);
    }

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     */
    @Override
    protected RealMatrix calculateBetaVariance() {
        RealMatrix OI = getOmegaInverse();
        RealMatrix XTOIX = X.transpose().multiply(OI).multiply(X);
        return new LUDecompositionImpl(XTOIX).getSolver().getInverse();
    }

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        final RealMatrix matrix = MatrixUtils.createRealMatrix(new double[][] {
                                                       { 1.0, 2.0, 3.0},
                                                       { 2.0, 5.0, 3.0},
                                                       { 4.000001, 9.0, 9.0}
                                                     });
        assertFalse(new LUDecompositionImpl(matrix, 1.0e-5).getSolver().isNonSingular());
        assertTrue(new LUDecompositionImpl(matrix, 1.0e-10).getSolver().isNonSingular());
    }

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    }


    /** test singular */
    public void testSingular() {
        DecompositionSolver solver =
            new LUDecompositionImpl(MatrixUtils.createRealMatrix(testData)).getSolver();
        assertTrue(solver.isNonSingular());
        solver = new LUDecompositionImpl(MatrixUtils.createRealMatrix(singular)).getSolver();
        assertFalse(solver.isNonSingular());
        solver = new LUDecompositionImpl(MatrixUtils.createRealMatrix(bigSingular)).getSolver();
        assertFalse(solver.isNonSingular());
    }

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    }


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

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