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Java example source code file (EigenSolverTest.java)

This example Java source code file (EigenSolverTest.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

decompositionsolver, eigendecomposition, eigensolvertest, mathillegalargumentexception, random, realmatrix, singular, singularmatrixexception, test, util

The EigenSolverTest.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 java.util.Random;

import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.util.Precision;

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

public class EigenSolverTest {

    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

    /** test non invertible matrix */
    @Test
    public void testNonInvertible() {
        Random r = new Random(9994100315209l);
        RealMatrix m =
            EigenDecompositionTest.createTestMatrix(r, new double[] { 1.0, 0.0, -1.0, -2.0, -3.0 });
        DecompositionSolver es = new EigenDecomposition(m).getSolver();
        Assert.assertFalse(es.isNonSingular());
        try {
            es.getInverse();
            Assert.fail("an exception should have been thrown");
        } catch (SingularMatrixException ime) {
            // expected behavior
        }
    }

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

    /**
     * Verifies operation on very small values.
     * Matrix with eigenvalues {8e-100, -1e-100, -1e-100}
     */
    @Test
    public void testInvertibleTinyValues() {
        final double tiny = 1e-100;
        RealMatrix m = MatrixUtils.createRealMatrix(new double[][] {
                {3,  2,  4},
                {2,  0,  2},
                {4,  2,  3}
        });
        m = m.scalarMultiply(tiny);

        final EigenDecomposition ed = new EigenDecomposition(m);
        RealMatrix inv = ed.getSolver().getInverse();

        final RealMatrix id = m.multiply(inv);
        for (int i = 0; i < m.getRowDimension(); i++) {
            for (int j = 0; j < m.getColumnDimension(); j++) {
                if (i == j) {
                    Assert.assertTrue(Precision.equals(1, id.getEntry(i, j), 1e-15));
                } else {
                    Assert.assertTrue(Precision.equals(0, id.getEntry(i, j), 1e-15));
                }
            }
        }
    }

    @Test(expected=SingularMatrixException.class)
    public void testNonInvertibleMath1045() {
        EigenDecomposition eigen =
            new EigenDecomposition(MatrixUtils.createRealMatrix(bigSingular));
        eigen.getSolver().getInverse();
    }

    @Test(expected=SingularMatrixException.class)
    public void testZeroMatrix() {
        EigenDecomposition eigen =
            new EigenDecomposition(MatrixUtils.createRealMatrix(new double[][] {{0}}));
        eigen.getSolver().getInverse();
    }

    @Test
    public void testIsNonSingularTinyOutOfOrderEigenvalue() {
        final EigenDecomposition eigen
            = new EigenDecomposition(MatrixUtils.createRealMatrix(new double[][] {
                        { 1e-13, 0 },
                        { 1,     1 },
                    }));
        Assert.assertFalse("Singular matrix not detected",
                           eigen.getSolver().isNonSingular());
    }

    /** test solve dimension errors */
    @Test
    public void testSolveDimensionErrors() {
        final double[] refValues = new double[] {
            2.003, 2.002, 2.001, 1.001, 1.000, 0.001
        };
        final RealMatrix matrix = EigenDecompositionTest.createTestMatrix(new Random(35992629946426l), refValues);

        DecompositionSolver es = new EigenDecomposition(matrix).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[2][2]);
        try {
            es.solve(b);
            Assert.fail("an exception should have been thrown");
        } catch (MathIllegalArgumentException iae) {
            // expected behavior
        }
        try {
            es.solve(b.getColumnVector(0));
            Assert.fail("an exception should have been thrown");
        } catch (MathIllegalArgumentException iae) {
            // expected behavior
        }
        try {
            es.solve(new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(0)));
            Assert.fail("an exception should have been thrown");
        } catch (MathIllegalArgumentException iae) {
            // expected behavior
        }
    }

    /** test solve */
    @Test
    public void testSolve() {
        RealMatrix m = MatrixUtils.createRealMatrix(new double[][] {
                { 91,  5, 29, 32, 40, 14 },
                {  5, 34, -1,  0,  2, -1 },
                { 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 EigenDecomposition(m).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
        RealMatrix solution=es.solve(b);
        Assert.assertEquals(0, solution.subtract(xRef).getNorm(), 2.5e-12);

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

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

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