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Java example source code file (LUDecompositionTest.java)

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

Learn more about this Java project at its project page.

Java - Java tags/keywords

expecting, ludecomposition, ludecompositiontest, nonsquarematrixexception, realmatrix, test

The LUDecompositionTest.java Java example 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.math3.linear;

import org.junit.Test;
import org.junit.Assert;

public class LUDecompositionTest {
    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;

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

    }

    /** test non-square matrix */
    @Test
    public void testNonSquare() {
        try {
            new LUDecomposition(MatrixUtils.createRealMatrix(new double[3][2]));
            Assert.fail("Expecting NonSquareMatrixException");
        } catch (NonSquareMatrixException ime) {
            // expected behavior
        }
    }

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

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

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

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

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

    }

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

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

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

        RealMatrix ppT = p.multiply(p.transpose());
        RealMatrix id  = MatrixUtils.createRealIdentityMatrix(p.getRowDimension());
        Assert.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;
                }
            }
            Assert.assertEquals(p.getColumnDimension() - 1, zeroCount);
            Assert.assertEquals(1, oneCount);
            Assert.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;
                }
            }
            Assert.assertEquals(p.getRowDimension() - 1, zeroCount);
            Assert.assertEquals(1, oneCount);
            Assert.assertEquals(0, otherCount);
        }

    }

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

    /** test matrices values */
    @Test
    public void testMatricesValues1() {
       LUDecomposition lu =
            new LUDecomposition(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();
        Assert.assertEquals(0, l.subtract(lRef).getNorm(), 1.0e-13);
        RealMatrix u = lu.getU();
        Assert.assertEquals(0, u.subtract(uRef).getNorm(), 1.0e-13);
        RealMatrix p = lu.getP();
        Assert.assertEquals(0, p.subtract(pRef).getNorm(), 1.0e-13);
        int[] pivot = lu.getPivot();
        for (int i = 0; i < pivotRef.length; ++i) {
            Assert.assertEquals(pivotRef[i], pivot[i]);
        }

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

    }

    /** test matrices values */
    @Test
    public void testMatricesValues2() {
       LUDecomposition lu =
            new LUDecomposition(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();
        Assert.assertEquals(0, l.subtract(lRef).getNorm(), 1.0e-13);
        RealMatrix u = lu.getU();
        Assert.assertEquals(0, u.subtract(uRef).getNorm(), 1.0e-13);
        RealMatrix p = lu.getP();
        Assert.assertEquals(0, p.subtract(pRef).getNorm(), 1.0e-13);
        int[] pivot = lu.getPivot();
        for (int i = 0; i < pivotRef.length; ++i) {
            Assert.assertEquals(pivotRef[i], pivot[i]);
        }

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

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