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Java example source code file (FieldLUDecompositionTest.java)

This example Java source code file (FieldLUDecompositionTest.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

array2drowfieldmatrix, expected, fieldludecomposition, fieldludecompositiontest, fieldmatrix, fraction, nonsquarematrixexception, test

The FieldLUDecompositionTest.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;

import org.apache.commons.math3.TestUtils;
import org.apache.commons.math3.fraction.Fraction;
import org.apache.commons.math3.fraction.FractionField;

public class FieldLUDecompositionTest {
    private Fraction[][] testData = {
            { new Fraction(1), new Fraction(2), new Fraction(3)},
            { new Fraction(2), new Fraction(5), new Fraction(3)},
            { new Fraction(1), new Fraction(0), new Fraction(8)}
    };
    private Fraction[][] testDataMinus = {
            { new Fraction(-1), new Fraction(-2), new Fraction(-3)},
            { new Fraction(-2), new Fraction(-5), new Fraction(-3)},
            { new Fraction(-1),  new Fraction(0), new Fraction(-8)}
    };
    private Fraction[][] luData = {
            { new Fraction(2), new Fraction(3), new Fraction(3) },
            { new Fraction(2), new Fraction(3), new Fraction(7) },
            { new Fraction(6), new Fraction(6), new Fraction(8) }
    };

    // singular matrices
    private Fraction[][] singular = {
            { new Fraction(2), new Fraction(3) },
            { new Fraction(2), new Fraction(3) }
    };
    private Fraction[][] bigSingular = {
            { new Fraction(1), new Fraction(2),   new Fraction(3),    new Fraction(4) },
            { new Fraction(2), new Fraction(5),   new Fraction(3),    new Fraction(4) },
            { new Fraction(7), new Fraction(3), new Fraction(256), new Fraction(1930) },
            { new Fraction(3), new Fraction(7),   new Fraction(6),    new Fraction(8) }
    }; // 4th row = 1st + 2nd

    /** test dimensions */
    @Test
    public void testDimensions() {
        FieldMatrix<Fraction> matrix =
            new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), testData);
        FieldLUDecomposition<Fraction> LU = new FieldLUDecomposition(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 {
            // we don't use FractionField.getInstance() for testing purposes
            new FieldLUDecomposition<Fraction>(new Array2DRowFieldMatrix(new Fraction[][] {
                    { Fraction.ZERO, Fraction.ZERO },
                    { Fraction.ZERO, Fraction.ZERO },
                    { Fraction.ZERO, Fraction.ZERO }
            }));
            Assert.fail("Expected NonSquareMatrixException");
        } catch (NonSquareMatrixException ime) {
            // expected behavior
        }
    }

    /** test PA = LU */
    @Test
    public void testPAEqualLU() {
        FieldMatrix<Fraction> matrix = new Array2DRowFieldMatrix(FractionField.getInstance(), testData);
        FieldLUDecomposition<Fraction> lu = new FieldLUDecomposition(matrix);
        FieldMatrix<Fraction> l = lu.getL();
        FieldMatrix<Fraction> u = lu.getU();
        FieldMatrix<Fraction> p = lu.getP();
        TestUtils.assertEquals(p.multiply(matrix), l.multiply(u));

        matrix = new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), testDataMinus);
        lu = new FieldLUDecomposition<Fraction>(matrix);
        l = lu.getL();
        u = lu.getU();
        p = lu.getP();
        TestUtils.assertEquals(p.multiply(matrix), l.multiply(u));

        matrix = new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), 17, 17);
        for (int i = 0; i < matrix.getRowDimension(); ++i) {
            matrix.setEntry(i, i, Fraction.ONE);
        }
        lu = new FieldLUDecomposition<Fraction>(matrix);
        l = lu.getL();
        u = lu.getU();
        p = lu.getP();
        TestUtils.assertEquals(p.multiply(matrix), l.multiply(u));

        matrix = new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), singular);
        lu = new FieldLUDecomposition<Fraction>(matrix);
        Assert.assertFalse(lu.getSolver().isNonSingular());
        Assert.assertNull(lu.getL());
        Assert.assertNull(lu.getU());
        Assert.assertNull(lu.getP());

        matrix = new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), bigSingular);
        lu = new FieldLUDecomposition<Fraction>(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() {
        FieldMatrix<Fraction> matrix = new Array2DRowFieldMatrix(FractionField.getInstance(), testData);
        FieldMatrix<Fraction> l = new FieldLUDecomposition(matrix).getL();
        for (int i = 0; i < l.getRowDimension(); i++) {
            Assert.assertEquals(Fraction.ONE, l.getEntry(i, i));
            for (int j = i + 1; j < l.getColumnDimension(); j++) {
                Assert.assertEquals(Fraction.ZERO, l.getEntry(i, j));
            }
        }
    }

    /** test that U is upper triangular */
    @Test
    public void testUUpperTriangular() {
        FieldMatrix<Fraction> matrix = new Array2DRowFieldMatrix(FractionField.getInstance(), testData);
        FieldMatrix<Fraction> u = new FieldLUDecomposition(matrix).getU();
        for (int i = 0; i < u.getRowDimension(); i++) {
            for (int j = 0; j < i; j++) {
                Assert.assertEquals(Fraction.ZERO, u.getEntry(i, j));
            }
        }
    }

    /** test that P is a permutation matrix */
    @Test
    public void testPPermutation() {
        FieldMatrix<Fraction> matrix = new Array2DRowFieldMatrix(FractionField.getInstance(), testData);
        FieldMatrix<Fraction> p   = new FieldLUDecomposition(matrix).getP();

        FieldMatrix<Fraction> ppT = p.multiply(p.transpose());
        FieldMatrix<Fraction> id  =
            new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(),
                                          p.getRowDimension(), p.getRowDimension());
        for (int i = 0; i < id.getRowDimension(); ++i) {
            id.setEntry(i, i, Fraction.ONE);
        }
        TestUtils.assertEquals(id, ppT);

        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 Fraction e = p.getEntry(i, j);
                if (e.equals(Fraction.ZERO)) {
                    ++zeroCount;
                } else if (e.equals(Fraction.ONE)) {
                    ++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 Fraction e = p.getEntry(i, j);
                if (e.equals(Fraction.ZERO)) {
                    ++zeroCount;
                } else if (e.equals(Fraction.ONE)) {
                    ++oneCount;
                } else {
                    ++otherCount;
                }
            }
            Assert.assertEquals(p.getRowDimension() - 1, zeroCount);
            Assert.assertEquals(1, oneCount);
            Assert.assertEquals(0, otherCount);
        }

    }


    /** test singular */
    @Test
    public void testSingular() {
        FieldLUDecomposition<Fraction> lu =
            new FieldLUDecomposition<Fraction>(new Array2DRowFieldMatrix(FractionField.getInstance(), testData));
        Assert.assertTrue(lu.getSolver().isNonSingular());
        lu = new FieldLUDecomposition<Fraction>(new Array2DRowFieldMatrix(FractionField.getInstance(), singular));
        Assert.assertFalse(lu.getSolver().isNonSingular());
        lu = new FieldLUDecomposition<Fraction>(new Array2DRowFieldMatrix(FractionField.getInstance(), bigSingular));
        Assert.assertFalse(lu.getSolver().isNonSingular());
    }

    /** test matrices values */
    @Test
    public void testMatricesValues1() {
       FieldLUDecomposition<Fraction> lu =
            new FieldLUDecomposition<Fraction>(new Array2DRowFieldMatrix(FractionField.getInstance(), testData));
        FieldMatrix<Fraction> lRef = new Array2DRowFieldMatrix(FractionField.getInstance(), new Fraction[][] {
                { new Fraction(1), new Fraction(0), new Fraction(0) },
                { new Fraction(2), new Fraction(1), new Fraction(0) },
                { new Fraction(1), new Fraction(-2), new Fraction(1) }
        });
        FieldMatrix<Fraction> uRef = new Array2DRowFieldMatrix(FractionField.getInstance(), new Fraction[][] {
                { new Fraction(1),  new Fraction(2), new Fraction(3) },
                { new Fraction(0), new Fraction(1), new Fraction(-3) },
                { new Fraction(0),  new Fraction(0), new Fraction(-1) }
        });
        FieldMatrix<Fraction> pRef = new Array2DRowFieldMatrix(FractionField.getInstance(), new Fraction[][] {
                { new Fraction(1), new Fraction(0), new Fraction(0) },
                { new Fraction(0), new Fraction(1), new Fraction(0) },
                { new Fraction(0), new Fraction(0), new Fraction(1) }
        });
        int[] pivotRef = { 0, 1, 2 };

        // check values against known references
        FieldMatrix<Fraction> l = lu.getL();
        TestUtils.assertEquals(lRef, l);
        FieldMatrix<Fraction> u = lu.getU();
        TestUtils.assertEquals(uRef, u);
        FieldMatrix<Fraction> p = lu.getP();
        TestUtils.assertEquals(pRef, p);
        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() {
       FieldLUDecomposition<Fraction> lu =
            new FieldLUDecomposition<Fraction>(new Array2DRowFieldMatrix(FractionField.getInstance(), luData));
        FieldMatrix<Fraction> lRef = new Array2DRowFieldMatrix(FractionField.getInstance(), new Fraction[][] {
                { new Fraction(1), new Fraction(0), new Fraction(0) },
                { new Fraction(3), new Fraction(1), new Fraction(0) },
                { new Fraction(1), new Fraction(0), new Fraction(1) }
        });
        FieldMatrix<Fraction> uRef = new Array2DRowFieldMatrix(FractionField.getInstance(), new Fraction[][] {
                { new Fraction(2), new Fraction(3), new Fraction(3)    },
                { new Fraction(0), new Fraction(-3), new Fraction(-1)  },
                { new Fraction(0), new Fraction(0), new Fraction(4) }
        });
        FieldMatrix<Fraction> pRef = new Array2DRowFieldMatrix(FractionField.getInstance(), new Fraction[][] {
                { new Fraction(1), new Fraction(0), new Fraction(0) },
                { new Fraction(0), new Fraction(0), new Fraction(1) },
                { new Fraction(0), new Fraction(1), new Fraction(0) }
        });
        int[] pivotRef = { 0, 2, 1 };

        // check values against known references
        FieldMatrix<Fraction> l = lu.getL();
        TestUtils.assertEquals(lRef, l);
        FieldMatrix<Fraction> u = lu.getU();
        TestUtils.assertEquals(uRef, u);
        FieldMatrix<Fraction> p = lu.getP();
        TestUtils.assertEquals(pRef, p);
        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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