Commons Math example source code file (LUDecompositionImplTest.java)

This example Commons Math source code file (LUDecompositionImplTest.java) is included in the DevDaily.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" ^TM.

Java - Commons Math tags/keywords

exception, invalidmatrixexception, lu, ludecomposition, ludecomposition, ludecompositionimpl, ludecompositionimpl, ludecompositionimpltest, ludecompositionimpltest, realmatrix, realmatrix, testcase

The Commons Math LUDecompositionImplTest.java source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package org.apache.commons.math.linear;

import junit.framework.TestCase;

public class LUDecompositionImplTest extends TestCase {
    private double[][] testData = {
            { 1.0, 2.0, 3.0},
            { 2.0, 5.0, 3.0},
            { 1.0, 0.0, 8.0}
    };
    private double[][] testDataMinus = {
            { -1.0, -2.0, -3.0},
            { -2.0, -5.0, -3.0},
            { -1.0,  0.0, -8.0}
    };
    private double[][] luData = {
            { 2.0, 3.0, 3.0 },
            { 0.0, 5.0, 7.0 },
            { 6.0, 9.0, 8.0 }
    };

    // singular matrices
    private double[][] singular = {
            { 2.0, 3.0 },
            { 2.0, 3.0 }
    };
    private double[][] bigSingular = {
            { 1.0, 2.0,   3.0,    4.0 },
            { 2.0, 5.0,   3.0,    4.0 },
            { 7.0, 3.0, 256.0, 1930.0 },
            { 3.0, 7.0,   6.0,    8.0 }
    }; // 4th row = 1st + 2nd

    private static final double entryTolerance = 10e-16;

    private static final double normTolerance = 10e-14;

    public LUDecompositionImplTest(String name) {
        super(name);
    }

    /** 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());

    }

    /** 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");
        }
    }

    /** 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());

    }

    /** 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);
            }
        }
    }

    /** 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);
            }
        }
    }

    /** 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);

        for (int i = 0; i < p.getRowDimension(); i++) {
            int zeroCount  = 0;
            int oneCount   = 0;
            int otherCount = 0;
            for (int j = 0; j < p.getColumnDimension(); j++) {
                final double e = p.getEntry(i, j);
                if (e == 0) {
                    ++zeroCount;
                } else if (e == 1) {
                    ++oneCount;
                } else {
                    ++otherCount;
                }
            }
            assertEquals(p.getColumnDimension() - 1, zeroCount);
            assertEquals(1, oneCount);
            assertEquals(0, otherCount);
        }

        for (int j = 0; j < p.getColumnDimension(); j++) {
            int zeroCount  = 0;
            int oneCount   = 0;
            int otherCount = 0;
            for (int i = 0; i < p.getRowDimension(); i++) {
                final double e = p.getEntry(i, j);
                if (e == 0) {
                    ++zeroCount;
                } else if (e == 1) {
                    ++oneCount;
                } else {
                    ++otherCount;
                }
            }
            assertEquals(p.getRowDimension() - 1, zeroCount);
            assertEquals(1, oneCount);
            assertEquals(0, otherCount);
        }

    }


    /** 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());
    }

    /** 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());

    }

    /** 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());

    }

}