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

        }
    }


    /** test solve rank errors */
    public void testSolveRankErrors() {
        DecompositionSolver solver =
            new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x3Singular)).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[3][2]);
        try {
            solver.solve(b);
            fail("an exception should have been thrown");
        } catch (InvalidMatrixException iae) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
        try {
            solver.solve(b.getColumn(0));
            fail("an exception should have been thrown");
        } catch (InvalidMatrixException iae) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
        try {
            solver.solve(b.getColumnVector(0));
            fail("an exception should have been thrown");
        } catch (InvalidMatrixException iae) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");

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    /** test solve */
    public void testSolve() {
        QRDecomposition decomposition =
            new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x3NonSingular));
        DecompositionSolver solver = decomposition.getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[][] {
                { -102, 12250 }, { 544, 24500 }, { 167, -36750 }
        });
        RealMatrix xRef = MatrixUtils.createRealMatrix(new double[][] {
                { 1, 2515 }, { 2, 422 }, { -3, 898 }
        });


        // using RealMatrix
        assertEquals(0, solver.solve(b).subtract(xRef).getNorm(), 2.0e-16 * xRef.getNorm());


        // using double[]
        for (int i = 0; i < b.getColumnDimension(); ++i) {
            final double[] x = solver.solve(b.getColumn(i));
            final double error = new ArrayRealVector(x).subtract(xRef.getColumnVector(i)).getNorm();
            assertEquals(0, error, 3.0e-16 * xRef.getColumnVector(i).getNorm());
        }


        // using ArrayRealVector
        for (int i = 0; i < b.getColumnDimension(); ++i) {
            final RealVector x = solver.solve(b.getColumnVector(i));
            final double error = x.subtract(xRef.getColumnVector(i)).getNorm();
            assertEquals(0, error, 3.0e-16 * xRef.getColumnVector(i).getNorm());
        }


        // using RealVector with an alternate implementation
        for (int i = 0; i < b.getColumnDimension(); ++i) {
            ArrayRealVectorTest.RealVectorTestImpl v =
                new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(i));
            final RealVector x = solver.solve(v);
            final double error = x.subtract(xRef.getColumnVector(i)).getNorm();
            assertEquals(0, error, 3.0e-16 * xRef.getColumnVector(i).getNorm());
        }


    }

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        return suite;
    }


    /** test solve dimension errors */
    public void testSolveDimensionErrors() {
        DecompositionSolver solver =
            new SingularValueDecompositionImpl(MatrixUtils.createRealMatrix(testSquare)).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[3][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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        RealMatrix m =
            MatrixUtils.createRealMatrix(new double[][] {
                                   { 1.0, 0.0 },
                                   { 0.0, 0.0 }
                               });
        DecompositionSolver solver = new SingularValueDecompositionImpl(m).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[2][2]);
        try {
            solver.solve(b);
            fail("an exception should have been thrown");
        } catch (InvalidMatrixException ime) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
        try {
            solver.solve(b.getColumn(0));
            fail("an exception should have been thrown");
        } catch (InvalidMatrixException ime) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
        try {
            solver.solve(b.getColumnVector(0));
            fail("an exception should have been thrown");
        } catch (InvalidMatrixException ime) {
            // 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 (InvalidMatrixException ime) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");

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        }
    }


    /** test solve */
    public void testSolve() {
        DecompositionSolver solver =
            new SingularValueDecompositionImpl(MatrixUtils.createRealMatrix(testSquare)).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[][] {
                { 1, 2, 3 }, { 0, -5, 1 }
        });
        RealMatrix xRef = MatrixUtils.createRealMatrix(new double[][] {
                { -8.0 / 25.0, -263.0 / 75.0, -29.0 / 75.0 },
                { 19.0 / 25.0,   78.0 / 25.0,  49.0 / 25.0 }
        });


        // using RealMatrix
        assertEquals(0, solver.solve(b).subtract(xRef).getNorm(), normTolerance);


        // 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 Array2DRowRealMatrix
        for (int i = 0; i < b.getColumnDimension(); ++i) {
            assertEquals(0,
                         solver.solve(b.getColumnVector(i)).subtract(xRef.getColumnVector(i)).getNorm(),
                         1.0e-13);
        }


        // 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,
                         solver.solve(v).subtract(xRef.getColumnVector(i)).getNorm(),
                         1.0e-13);
        }


    }

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

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        assertTrue(new LUDecompositionImpl(matrix, 1.0e-10).getSolver().isNonSingular());
    }


    /** 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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        assertFalse(solver.isNonSingular());
    }


    /** 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) {
            // 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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        }
    }


    /** test solve singularity errors */
    public void testSolveSingularityErrors() {
        DecompositionSolver solver =
            new LUDecompositionImpl(MatrixUtils.createRealMatrix(singular)).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[2][2]);
        try {
            solver.solve(b);
            fail("an exception should have been thrown");
        } catch (InvalidMatrixException ime) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
        try {
            solver.solve(b.getColumn(0));
            fail("an exception should have been thrown");
        } catch (InvalidMatrixException ime) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
        try {
            solver.solve(b.getColumnVector(0));
            fail("an exception should have been thrown");
        } catch (InvalidMatrixException ime) {
            // 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 (InvalidMatrixException ime) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");

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        }
    }


    /** test solve */
    public void testSolve() {
        DecompositionSolver solver =
            new LUDecompositionImpl(MatrixUtils.createRealMatrix(testData)).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[][] {
                { 1, 0 }, { 2, -5 }, { 3, 1 }
        });
        RealMatrix xRef = MatrixUtils.createRealMatrix(new double[][] {
                { 19, -71 }, { -6, 22 }, { -2, 9 }
        });


        // 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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