Examples of DecompositionSolver

org.apache.commons.math.linear.DecompositionSolver
Interface handling decomposition algorithms that can solve A × X = B.
Decomposition algorithms decompose an A matrix has a product of several specific matrices from which they can solve A × X = B in least squares sense: they find X such that ||A × X - B|| is minimal.

Some solvers like {@link LUDecomposition} can only find the solution forsquare matrices and when the solution is an exact linear solution, i.e. when ||A × X - B|| is exactly 0. Other solvers can also find solutions with non-square matrix A and with non-null minimal norm. If an exact linear solution exists it is also the minimal norm solution.
@version $Revision: 811685 $ $Date: 2009-09-05 19:36:48 +0200 (sam. 05 sept. 2009) $ @since 2.0
org.apache.commons.math3.linear.DecompositionSolver
Interface handling decomposition algorithms that can solve A × X = B.
Decomposition algorithms decompose an A matrix has a product of several specific matrices from which they can solve A × X = B in least squares sense: they find X such that ||A × X - B|| is minimal.
Some solvers like {@link LUDecomposition} can only find the solution forsquare matrices and when the solution is an exact linear solution, i.e. when ||A × X - B|| is exactly 0. Other solvers can also find solutions with non-square matrix A and with non-null minimal norm. If an exact linear solution exists it is also the minimal norm solution. @since 2.0

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


    Vector2d direction = rm.getNewDirectionVector();
    direction.normalize();
    RealMatrix coefficients = new Array2DRowRealMatrix(new double[][] { { direction.getX(), -(sideVectX) },
        { direction.getY(), -(sideVectY) } }, false);
    DecompositionSolver solver = new LUDecompositionImpl(coefficients).getSolver();
    RealVector constants = new ArrayRealVector(new double[] { sideX - roboter1.getX(), sideY - roboter1.getY() }, false);
    RealVector solution = solver.solve(constants);


    double r = solution.getEntry(0);
    // double s = solution.getEntry(1);


    double res1 = roboter1.getX() + direction.getX() * r;

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


            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) {
                    point[i] += dX[i];
                }

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

        return suite;
    }


    /** test solve dimension errors */
    public void testSolveDimensionErrors() throws MathException {
        DecompositionSolver solver =
            new CholeskyDecompositionImpl(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) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
        try {
            solver.solve(b.getColumn(0));
            fail("an exception should have been thrown");
        } catch (IllegalArgumentException iae) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
        try {
            solver.solve(new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(0)));
            fail("an exception should have been thrown");
        } catch (IllegalArgumentException iae) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");

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

        }
    }


    /** test solve */
    public void testSolve() throws MathException {
        DecompositionSolver solver =
            new CholeskyDecompositionImpl(MatrixUtils.createRealMatrix(testData)).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[][] {
                {   78,  -13,    1 },
                {  414,  -62,   -1 },
                { 1312, -202,  -37 },
                { 2989, -542,  145 },
                { 5510, -1465, 201 }
        });
        RealMatrix xRef = MatrixUtils.createRealMatrix(new double[][] {
                { 1,  0,  1 },
                { 0,  1,  1 },
                { 2,  1, -4 },
                { 2,  2,  2 },
                { 5, -3,  0 }
        });


        // using RealMatrix
        assertEquals(0, solver.solve(b).subtract(xRef).getNorm(), 1.0e-13);


        // using double[]
        for (int i = 0; i < b.getColumnDimension(); ++i) {
            assertEquals(0,
                         new ArrayRealVector(solver.solve(b.getColumn(i))).subtract(xRef.getColumnVector(i)).getNorm(),
                         1.0e-13);
        }


        // using ArrayRealVector
        for (int i = 0; i < b.getColumnDimension(); ++i) {
            assertEquals(0,
                         solver.solve(b.getColumnVector(i)).subtract(xRef.getColumnVector(i)).getNorm(),
                         1.0e-13);
        }


        // using RealVector with an alternate implementation
        for (int i = 0; i < b.getColumnDimension(); ++i) {
            ArrayRealVectorTest.RealVectorTestImpl v =
                new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(i));
            assertEquals(0,
                         solver.solve(v).subtract(xRef.getColumnVector(i)).getNorm(),
                         1.0e-13);
        }


    }

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

    /** test non invertible matrix */
    public void testNonInvertible() {
        Random r = new Random(9994100315209l);
        RealMatrix m =
            EigenDecompositionImplTest.createTestMatrix(r, new double[] { 1.0, 0.0, -1.0, -2.0, -3.0 });
        DecompositionSolver es = new EigenDecompositionImpl(m, MathUtils.SAFE_MIN).getSolver();
        assertFalse(es.isNonSingular());
        try {
            es.getInverse();
            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.DecompositionSolver

    /** test invertible matrix */
    public void testInvertible() {
        Random r = new Random(9994100315209l);
        RealMatrix m =
            EigenDecompositionImplTest.createTestMatrix(r, new double[] { 1.0, 0.5, -1.0, -2.0, -3.0 });
        DecompositionSolver es = new EigenDecompositionImpl(m, MathUtils.SAFE_MIN).getSolver();
        assertTrue(es.isNonSingular());
        RealMatrix inverse = es.getInverse();
        RealMatrix error =
            m.multiply(inverse).subtract(MatrixUtils.createRealIdentityMatrix(m.getRowDimension()));
        assertEquals(0, error.getNorm(), 4.0e-15);
    }

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

        assertEquals(0, error.getNorm(), 4.0e-15);
    }


    /** test solve dimension errors */
    public void testSolveDimensionErrors() {
        DecompositionSolver es = new EigenDecompositionImpl(matrix, MathUtils.SAFE_MIN).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[2][2]);
        try {
            es.solve(b);
            fail("an exception should have been thrown");
        } catch (IllegalArgumentException iae) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
        try {
            es.solve(b.getColumn(0));
            fail("an exception should have been thrown");
        } catch (IllegalArgumentException iae) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
        try {
            es.solve(new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(0)));
            fail("an exception should have been thrown");
        } catch (IllegalArgumentException iae) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");

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

                { 29, -1, 12,  9, 21,  8 },
                { 32,  0,  9, 14,  9,  0 },
                { 40,  2, 21,  9, 51, 19 },
                { 14, -1,  8,  0, 19, 14 }
        });
        DecompositionSolver es = new EigenDecompositionImpl(m, MathUtils.SAFE_MIN).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[][] {
                { 1561, 269, 188 },
                {   69, -21,  70 },
                {  739, 108,  63 },
                {  324,  86,  59 },
                { 1624, 194, 107 },
                {  796,  69,  36 }
        });
        RealMatrix xRef = MatrixUtils.createRealMatrix(new double[][] {
                { 1,   2, 1 },
                { 2,  -1, 2 },
                { 4,   2, 3 },
                { 8,  -1, 0 },
                { 16,  2, 0 },
                { 32, -1, 0 }
        });


        // using RealMatrix
        assertEquals(0, es.solve(b).subtract(xRef).getNorm(), 2.0e-12);


        // using double[]
        for (int i = 0; i < b.getColumnDimension(); ++i) {
            assertEquals(0,
                         new ArrayRealVector(es.solve(b.getColumn(i))).subtract(xRef.getColumnVector(i)).getNorm(),
                         2.0e-11);
        }


        // using Array2DRowRealMatrix
        for (int i = 0; i < b.getColumnDimension(); ++i) {
            assertEquals(0,
                         es.solve(b.getColumnVector(i)).subtract(xRef.getColumnVector(i)).getNorm(),
                         2.0e-11);
        }


        // using RealMatrix with an alternate implementation
        for (int i = 0; i < b.getColumnDimension(); ++i) {
            ArrayRealVectorTest.RealVectorTestImpl v =
                new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(i));
            assertEquals(0,
                         es.solve(v).subtract(xRef.getColumnVector(i)).getNorm(),
                         2.0e-11);
        }


    }

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

        return suite;
    }


    /** test rank */
    public void testRank() {
        DecompositionSolver solver =
            new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x3NonSingular)).getSolver();
        assertTrue(solver.isNonSingular());


        solver = new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x3Singular)).getSolver();
        assertFalse(solver.isNonSingular());


        solver = new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x4)).getSolver();
        assertTrue(solver.isNonSingular());


        solver = new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData4x3)).getSolver();
        assertTrue(solver.isNonSingular());


    }

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


    }


    /** test solve dimension errors */
    public void testSolveDimensionErrors() {
        DecompositionSolver solver =
            new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x3NonSingular)).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[2][2]);
        try {
            solver.solve(b);
            fail("an exception should have been thrown");
        } catch (IllegalArgumentException iae) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
        try {
            solver.solve(b.getColumn(0));
            fail("an exception should have been thrown");
        } catch (IllegalArgumentException iae) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
        try {
            solver.solve(b.getColumnVector(0));
            fail("an exception should have been thrown");
        } catch (IllegalArgumentException iae) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");

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