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Java example source code file (SchurTransformerTest.java)

This example Java source code file (SchurTransformerTest.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

nonsquarematrixexception, normaldistribution, random, realmatrix, schurtransformer, schurtransformertest, suppresswarnings, test, util

The SchurTransformerTest.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.distribution.NormalDistribution;
import org.junit.Test;
import org.junit.Assert;

public class SchurTransformerTest {

    private double[][] testSquare5 = {
            { 5, 4, 3, 2, 1 },
            { 1, 4, 0, 3, 3 },
            { 2, 0, 3, 0, 0 },
            { 3, 2, 1, 2, 5 },
            { 4, 2, 1, 4, 1 }
    };

    private double[][] testSquare3 = {
            {  2, -1, 1 },
            { -1,  2, 1 },
            {  1, -1, 2 }
    };

    // from http://eigen.tuxfamily.org/dox/classEigen_1_1RealSchur.html
    private double[][] testRandom = {
            {  0.680, -0.3300, -0.2700, -0.717, -0.687,  0.0259 },
            { -0.211,  0.5360,  0.0268,  0.214, -0.198,  0.6780 },
            {  0.566, -0.4440,  0.9040, -0.967, -0.740,  0.2250 },
            {  0.597,  0.1080,  0.8320, -0.514, -0.782, -0.4080 },
            {  0.823, -0.0452,  0.2710, -0.726,  0.998,  0.2750 },
            { -0.605,  0.2580,  0.4350,  0.608, -0.563,  0.0486 }
    };

    @Test
    public void testNonSquare() {
        try {
            new SchurTransformer(MatrixUtils.createRealMatrix(new double[3][2]));
            Assert.fail("an exception should have been thrown");
        } catch (NonSquareMatrixException ime) {
            // expected behavior
        }
    }

    @Test
    public void testAEqualPTPt() {
        checkAEqualPTPt(MatrixUtils.createRealMatrix(testSquare5));
        checkAEqualPTPt(MatrixUtils.createRealMatrix(testSquare3));
        checkAEqualPTPt(MatrixUtils.createRealMatrix(testRandom));
   }

    @Test
    public void testPOrthogonal() {
        checkOrthogonal(new SchurTransformer(MatrixUtils.createRealMatrix(testSquare5)).getP());
        checkOrthogonal(new SchurTransformer(MatrixUtils.createRealMatrix(testSquare3)).getP());
        checkOrthogonal(new SchurTransformer(MatrixUtils.createRealMatrix(testRandom)).getP());
    }

    @Test
    public void testPTOrthogonal() {
        checkOrthogonal(new SchurTransformer(MatrixUtils.createRealMatrix(testSquare5)).getPT());
        checkOrthogonal(new SchurTransformer(MatrixUtils.createRealMatrix(testSquare3)).getPT());
        checkOrthogonal(new SchurTransformer(MatrixUtils.createRealMatrix(testRandom)).getPT());
    }

    @Test
    public void testSchurForm() {
        checkSchurForm(new SchurTransformer(MatrixUtils.createRealMatrix(testSquare5)).getT());
        checkSchurForm(new SchurTransformer(MatrixUtils.createRealMatrix(testSquare3)).getT());
        checkSchurForm(new SchurTransformer(MatrixUtils.createRealMatrix(testRandom)).getT());
    }

    @Test
    public void testRandomData() {
        for (int run = 0; run < 100; run++) {
            Random r = new Random(System.currentTimeMillis());

            // matrix size
            int size = r.nextInt(20) + 4;

            double[][] data = new double[size][size];
            for (int i = 0; i < size; i++) {
                for (int j = 0; j < size; j++) {
                    data[i][j] = r.nextInt(100);
                }
            }

            RealMatrix m = MatrixUtils.createRealMatrix(data);
            RealMatrix s = checkAEqualPTPt(m);
            checkSchurForm(s);
        }
    }

    @Test
    public void testRandomDataNormalDistribution() {
        for (int run = 0; run < 100; run++) {
            Random r = new Random(System.currentTimeMillis());
            NormalDistribution dist = new NormalDistribution(0.0, r.nextDouble() * 5);

            // matrix size
            int size = r.nextInt(20) + 4;

            double[][] data = new double[size][size];
            for (int i = 0; i < size; i++) {
                for (int j = 0; j < size; j++) {
                    data[i][j] = dist.sample();
                }
            }

            RealMatrix m = MatrixUtils.createRealMatrix(data);
            RealMatrix s = checkAEqualPTPt(m);
            checkSchurForm(s);
        }
    }

    @Test
    public void testMath848() {
        double[][] data = {
                { 0.1849449280, -0.0646971046,  0.0774755812, -0.0969651755, -0.0692648806,  0.3282344352, -0.0177423074,  0.2063136340},
                {-0.0742700134, -0.0289063030, -0.0017269460, -0.0375550146, -0.0487737922, -0.2616837868, -0.0821201295, -0.2530000167},
                { 0.2549910127,  0.0995733692, -0.0009718388,  0.0149282808,  0.1791878897, -0.0823182816,  0.0582629256,  0.3219545182},
                {-0.0694747557, -0.1880649148, -0.2740630911,  0.0720096468, -0.1800836914, -0.3518996425,  0.2486747833,  0.6257938167},
                { 0.0536360918, -0.1339297778,  0.2241579764, -0.0195327484, -0.0054103808,  0.0347564518,  0.5120802482, -0.0329902864},
                {-0.5933332356, -0.2488721082,  0.2357173629,  0.0177285473,  0.0856630593, -0.3567126300, -0.1600668126, -0.1010899621},
                {-0.0514349819, -0.0854319435,  0.1125050061,  0.0063453560, -0.2250000688, -0.2209343090,  0.1964623477, -0.1512329924},
                { 0.0197395947, -0.1997170581, -0.1425959019, -0.2749477910, -0.0969467073,  0.0603688520, -0.2826905192,  0.1794315473}};
        RealMatrix m = MatrixUtils.createRealMatrix(data);
        RealMatrix s = checkAEqualPTPt(m);
        checkSchurForm(s);
    }

    ///////////////////////////////////////////////////////////////////////////
    // Test helpers
    ///////////////////////////////////////////////////////////////////////////

    private RealMatrix checkAEqualPTPt(RealMatrix matrix) {
        SchurTransformer transformer = new SchurTransformer(matrix);
        RealMatrix p  = transformer.getP();
        RealMatrix t  = transformer.getT();
        RealMatrix pT = transformer.getPT();

        RealMatrix result = p.multiply(t).multiply(pT);

        double norm = result.subtract(matrix).getNorm();
        Assert.assertEquals(0, norm, 1.0e-9);

        return t;
    }

    private void checkOrthogonal(RealMatrix m) {
        RealMatrix mTm = m.transpose().multiply(m);
        RealMatrix id  = MatrixUtils.createRealIdentityMatrix(mTm.getRowDimension());
        Assert.assertEquals(0, mTm.subtract(id).getNorm(), 1.0e-14);
    }

    private void checkSchurForm(final RealMatrix m) {
        final int rows = m.getRowDimension();
        final int cols = m.getColumnDimension();
        for (int i = 0; i < rows; ++i) {
            for (int j = 0; j < cols; ++j) {
                if (i > j + 1) {
                    Assert.assertEquals(0, m.getEntry(i, j), 1.0e-16);
                }
            }
        }
    }

    @SuppressWarnings("unused")
    private void checkMatricesValues(double[][] matrix, double[][] pRef, double[][] hRef) {

        SchurTransformer transformer =
            new SchurTransformer(MatrixUtils.createRealMatrix(matrix));

        // check values against known references
        RealMatrix p = transformer.getP();
        Assert.assertEquals(0, p.subtract(MatrixUtils.createRealMatrix(pRef)).getNorm(), 1.0e-14);

        RealMatrix t = transformer.getT();
        Assert.assertEquals(0, t.subtract(MatrixUtils.createRealMatrix(hRef)).getNorm(), 1.0e-14);

        // check the same cached instance is returned the second time
        Assert.assertTrue(p == transformer.getP());
        Assert.assertTrue(t == transformer.getT());
    }
}

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