Package org.apache.commons.math.linear

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

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            }

            try {

                // solve the linearized least squares problem
                RealVector dX = new LUDecompositionImpl(a).getSolver().solve(b);

                // update the estimated parameters
                for (int i = 0; i < parameters.length; ++i) {
                    parameters[i].setEstimate(parameters[i].getEstimate() + dX.getEntry(i));
                }
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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 EstimationException("unable to compute covariances: singular problem");
        }
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    }

    /** test dimensions */
    public void testDimensions() {
        RealMatrix matrix = MatrixUtils.createRealMatrix(testData);
        LUDecomposition LU = new LUDecompositionImpl(matrix);
        assertEquals(testData.length, LU.getL().getRowDimension());
        assertEquals(testData.length, LU.getL().getColumnDimension());
        assertEquals(testData.length, LU.getU().getRowDimension());
        assertEquals(testData.length, LU.getU().getColumnDimension());
        assertEquals(testData.length, LU.getP().getRowDimension());
        assertEquals(testData.length, LU.getP().getColumnDimension());

    }
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    }

    /** test non-square matrix */
    public void testNonSquare() {
        try {
            new LUDecompositionImpl(MatrixUtils.createRealMatrix(new double[3][2]));
        } catch (InvalidMatrixException ime) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
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    }

    /** test PA = LU */
    public void testPAEqualLU() {
        RealMatrix matrix = MatrixUtils.createRealMatrix(testData);
        LUDecomposition lu = new LUDecompositionImpl(matrix);
        RealMatrix l = lu.getL();
        RealMatrix u = lu.getU();
        RealMatrix p = lu.getP();
        double norm = l.multiply(u).subtract(p.multiply(matrix)).getNorm();
        assertEquals(0, norm, normTolerance);

        matrix = MatrixUtils.createRealMatrix(testDataMinus);
        lu = new LUDecompositionImpl(matrix);
        l = lu.getL();
        u = lu.getU();
        p = lu.getP();
        norm = l.multiply(u).subtract(p.multiply(matrix)).getNorm();
        assertEquals(0, norm, normTolerance);

        matrix = MatrixUtils.createRealIdentityMatrix(17);
        lu = new LUDecompositionImpl(matrix);
        l = lu.getL();
        u = lu.getU();
        p = lu.getP();
        norm = l.multiply(u).subtract(p.multiply(matrix)).getNorm();
        assertEquals(0, norm, normTolerance);

        matrix = MatrixUtils.createRealMatrix(singular);
        lu = new LUDecompositionImpl(matrix);
        assertFalse(lu.getSolver().isNonSingular());
        assertNull(lu.getL());
        assertNull(lu.getU());
        assertNull(lu.getP());

        matrix = MatrixUtils.createRealMatrix(bigSingular);
        lu = new LUDecompositionImpl(matrix);
        assertFalse(lu.getSolver().isNonSingular());
        assertNull(lu.getL());
        assertNull(lu.getU());
        assertNull(lu.getP());

    }
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    }

    /** test that L is lower triangular with unit diagonal */
    public void testLLowerTriangular() {
        RealMatrix matrix = MatrixUtils.createRealMatrix(testData);
        RealMatrix l = new LUDecompositionImpl(matrix).getL();
        for (int i = 0; i < l.getRowDimension(); i++) {
            assertEquals(l.getEntry(i, i), 1, entryTolerance);
            for (int j = i + 1; j < l.getColumnDimension(); j++) {
                assertEquals(l.getEntry(i, j), 0, entryTolerance);
            }
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    }

    /** test that U is upper triangular */
    public void testUUpperTriangular() {
        RealMatrix matrix = MatrixUtils.createRealMatrix(testData);
        RealMatrix u = new LUDecompositionImpl(matrix).getU();
        for (int i = 0; i < u.getRowDimension(); i++) {
            for (int j = 0; j < i; j++) {
                assertEquals(u.getEntry(i, j), 0, entryTolerance);
            }
        }
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    }

    /** test that P is a permutation matrix */
    public void testPPermutation() {
        RealMatrix matrix = MatrixUtils.createRealMatrix(testData);
        RealMatrix p   = new LUDecompositionImpl(matrix).getP();

        RealMatrix ppT = p.multiply(p.transpose());
        RealMatrix id  = MatrixUtils.createRealIdentityMatrix(p.getRowDimension());
        assertEquals(0, ppT.subtract(id).getNorm(), normTolerance);

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

    /** test matrices values */
    public void testMatricesValues1() {
       LUDecomposition lu =
            new LUDecompositionImpl(MatrixUtils.createRealMatrix(testData));
        RealMatrix lRef = MatrixUtils.createRealMatrix(new double[][] {
                { 1.0, 0.0, 0.0 },
                { 0.5, 1.0, 0.0 },
                { 0.5, 0.2, 1.0 }
        });
        RealMatrix uRef = MatrixUtils.createRealMatrix(new double[][] {
                { 2.0,  5.0, 3.0 },
                { 0.0, -2.5, 6.5 },
                { 0.0,  0.0, 0.2 }
        });
        RealMatrix pRef = MatrixUtils.createRealMatrix(new double[][] {
                { 0.0, 1.0, 0.0 },
                { 0.0, 0.0, 1.0 },
                { 1.0, 0.0, 0.0 }
        });
        int[] pivotRef = { 1, 2, 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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  • org.apache.commons.math.estimation.AbstractEstimator
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  • org.apache.commons.math.linear.LUDecompositionImplTest
  • org.apache.commons.math.linear.LUSolverTest
  • org.apache.commons.math.optimization.general.AbstractLeastSquaresOptimizer
  • org.apache.commons.math.optimization.general.GaussNewtonOptimizer
  • org.apache.commons.math.stat.regression.GLSMultipleLinearRegression
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