home | career | drupal | java | mac | mysql | perl | scala | uml | unix  

Java example source code file (SingularValueDecompositionTest.java)

This example Java source code file (SingularValueDecompositionTest.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

array2drowrealmatrix, bufferedreader, datainputstream, exception, inputstreamreader, ioexception, random, realmatrix, singularvaluedecomposition, singularvaluedecompositiontest, string, svd, test, throwable, util

The SingularValueDecompositionTest.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.io.BufferedReader;
import java.io.DataInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Random;

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


public class SingularValueDecompositionTest {

    private double[][] testSquare = {
            { 24.0 / 25.0, 43.0 / 25.0 },
            { 57.0 / 25.0, 24.0 / 25.0 }
    };

    private double[][] testNonSquare = {
        {  -540.0 / 625.0,  963.0 / 625.0, -216.0 / 625.0 },
        { -1730.0 / 625.0, -744.0 / 625.0, 1008.0 / 625.0 },
        {  -720.0 / 625.0, 1284.0 / 625.0, -288.0 / 625.0 },
        {  -360.0 / 625.0,  192.0 / 625.0, 1756.0 / 625.0 },
    };

    private static final double normTolerance = 10e-14;

    @Test
    public void testMoreRows() {
        final double[] singularValues = { 123.456, 2.3, 1.001, 0.999 };
        final int rows    = singularValues.length + 2;
        final int columns = singularValues.length;
        Random r = new Random(15338437322523l);
        SingularValueDecomposition svd =
            new SingularValueDecomposition(createTestMatrix(r, rows, columns, singularValues));
        double[] computedSV = svd.getSingularValues();
        Assert.assertEquals(singularValues.length, computedSV.length);
        for (int i = 0; i < singularValues.length; ++i) {
            Assert.assertEquals(singularValues[i], computedSV[i], 1.0e-10);
        }
    }

    @Test
    public void testMoreColumns() {
        final double[] singularValues = { 123.456, 2.3, 1.001, 0.999 };
        final int rows    = singularValues.length;
        final int columns = singularValues.length + 2;
        Random r = new Random(732763225836210l);
        SingularValueDecomposition svd =
            new SingularValueDecomposition(createTestMatrix(r, rows, columns, singularValues));
        double[] computedSV = svd.getSingularValues();
        Assert.assertEquals(singularValues.length, computedSV.length);
        for (int i = 0; i < singularValues.length; ++i) {
            Assert.assertEquals(singularValues[i], computedSV[i], 1.0e-10);
        }
    }

    /** test dimensions */
    @Test
    public void testDimensions() {
        RealMatrix matrix = MatrixUtils.createRealMatrix(testSquare);
        final int m = matrix.getRowDimension();
        final int n = matrix.getColumnDimension();
        SingularValueDecomposition svd = new SingularValueDecomposition(matrix);
        Assert.assertEquals(m, svd.getU().getRowDimension());
        Assert.assertEquals(m, svd.getU().getColumnDimension());
        Assert.assertEquals(m, svd.getS().getColumnDimension());
        Assert.assertEquals(n, svd.getS().getColumnDimension());
        Assert.assertEquals(n, svd.getV().getRowDimension());
        Assert.assertEquals(n, svd.getV().getColumnDimension());

    }

    /** Test based on a dimension 4 Hadamard matrix. */
    @Test
    public void testHadamard() {
        RealMatrix matrix = new Array2DRowRealMatrix(new double[][] {
                {15.0 / 2.0,  5.0 / 2.0,  9.0 / 2.0,  3.0 / 2.0 },
                { 5.0 / 2.0, 15.0 / 2.0,  3.0 / 2.0,  9.0 / 2.0 },
                { 9.0 / 2.0,  3.0 / 2.0, 15.0 / 2.0,  5.0 / 2.0 },
                { 3.0 / 2.0,  9.0 / 2.0,  5.0 / 2.0, 15.0 / 2.0 }
        }, false);
        SingularValueDecomposition svd = new SingularValueDecomposition(matrix);
        Assert.assertEquals(16.0, svd.getSingularValues()[0], 1.0e-14);
        Assert.assertEquals( 8.0, svd.getSingularValues()[1], 1.0e-14);
        Assert.assertEquals( 4.0, svd.getSingularValues()[2], 1.0e-14);
        Assert.assertEquals( 2.0, svd.getSingularValues()[3], 1.0e-14);

        RealMatrix fullCovariance = new Array2DRowRealMatrix(new double[][] {
                {  85.0 / 1024, -51.0 / 1024, -75.0 / 1024,  45.0 / 1024 },
                { -51.0 / 1024,  85.0 / 1024,  45.0 / 1024, -75.0 / 1024 },
                { -75.0 / 1024,  45.0 / 1024,  85.0 / 1024, -51.0 / 1024 },
                {  45.0 / 1024, -75.0 / 1024, -51.0 / 1024,  85.0 / 1024 }
        }, false);
        Assert.assertEquals(0.0,
                     fullCovariance.subtract(svd.getCovariance(0.0)).getNorm(),
                     1.0e-14);

        RealMatrix halfCovariance = new Array2DRowRealMatrix(new double[][] {
                {   5.0 / 1024,  -3.0 / 1024,   5.0 / 1024,  -3.0 / 1024 },
                {  -3.0 / 1024,   5.0 / 1024,  -3.0 / 1024,   5.0 / 1024 },
                {   5.0 / 1024,  -3.0 / 1024,   5.0 / 1024,  -3.0 / 1024 },
                {  -3.0 / 1024,   5.0 / 1024,  -3.0 / 1024,   5.0 / 1024 }
        }, false);
        Assert.assertEquals(0.0,
                     halfCovariance.subtract(svd.getCovariance(6.0)).getNorm(),
                     1.0e-14);

    }

    /** test A = USVt */
    @Test
    public void testAEqualUSVt() {
        checkAEqualUSVt(MatrixUtils.createRealMatrix(testSquare));
        checkAEqualUSVt(MatrixUtils.createRealMatrix(testNonSquare));
        checkAEqualUSVt(MatrixUtils.createRealMatrix(testNonSquare).transpose());
    }

    public void checkAEqualUSVt(final RealMatrix matrix) {
        SingularValueDecomposition svd = new SingularValueDecomposition(matrix);
        RealMatrix u = svd.getU();
        RealMatrix s = svd.getS();
        RealMatrix v = svd.getV();
        double norm = u.multiply(s).multiply(v.transpose()).subtract(matrix).getNorm();
        Assert.assertEquals(0, norm, normTolerance);

    }

    /** test that U is orthogonal */
    @Test
    public void testUOrthogonal() {
        checkOrthogonal(new SingularValueDecomposition(MatrixUtils.createRealMatrix(testSquare)).getU());
        checkOrthogonal(new SingularValueDecomposition(MatrixUtils.createRealMatrix(testNonSquare)).getU());
        checkOrthogonal(new SingularValueDecomposition(MatrixUtils.createRealMatrix(testNonSquare).transpose()).getU());
    }

    /** test that V is orthogonal */
    @Test
    public void testVOrthogonal() {
        checkOrthogonal(new SingularValueDecomposition(MatrixUtils.createRealMatrix(testSquare)).getV());
        checkOrthogonal(new SingularValueDecomposition(MatrixUtils.createRealMatrix(testNonSquare)).getV());
        checkOrthogonal(new SingularValueDecomposition(MatrixUtils.createRealMatrix(testNonSquare).transpose()).getV());
    }

    public void checkOrthogonal(final RealMatrix m) {
        RealMatrix mTm = m.transpose().multiply(m);
        RealMatrix id  = MatrixUtils.createRealIdentityMatrix(mTm.getRowDimension());
        Assert.assertEquals(0, mTm.subtract(id).getNorm(), normTolerance);
    }

    /** test matrices values */
    // This test is useless since whereas the columns of U and V are linked
    // together, the actual triplet (U,S,V) is not uniquely defined.
    public void testMatricesValues1() {
       SingularValueDecomposition svd =
            new SingularValueDecomposition(MatrixUtils.createRealMatrix(testSquare));
        RealMatrix uRef = MatrixUtils.createRealMatrix(new double[][] {
                { 3.0 / 5.0, -4.0 / 5.0 },
                { 4.0 / 5.0,  3.0 / 5.0 }
        });
        RealMatrix sRef = MatrixUtils.createRealMatrix(new double[][] {
                { 3.0, 0.0 },
                { 0.0, 1.0 }
        });
        RealMatrix vRef = MatrixUtils.createRealMatrix(new double[][] {
                { 4.0 / 5.0,  3.0 / 5.0 },
                { 3.0 / 5.0, -4.0 / 5.0 }
        });

        // check values against known references
        RealMatrix u = svd.getU();
        Assert.assertEquals(0, u.subtract(uRef).getNorm(), normTolerance);
        RealMatrix s = svd.getS();
        Assert.assertEquals(0, s.subtract(sRef).getNorm(), normTolerance);
        RealMatrix v = svd.getV();
        Assert.assertEquals(0, v.subtract(vRef).getNorm(), normTolerance);

        // check the same cached instance is returned the second time
        Assert.assertTrue(u == svd.getU());
        Assert.assertTrue(s == svd.getS());
        Assert.assertTrue(v == svd.getV());

    }

    /** test matrices values */
    // This test is useless since whereas the columns of U and V are linked
    // together, the actual triplet (U,S,V) is not uniquely defined.
    public void useless_testMatricesValues2() {

        RealMatrix uRef = MatrixUtils.createRealMatrix(new double[][] {
            {  0.0 / 5.0,  3.0 / 5.0,  0.0 / 5.0 },
            { -4.0 / 5.0,  0.0 / 5.0, -3.0 / 5.0 },
            {  0.0 / 5.0,  4.0 / 5.0,  0.0 / 5.0 },
            { -3.0 / 5.0,  0.0 / 5.0,  4.0 / 5.0 }
        });
        RealMatrix sRef = MatrixUtils.createRealMatrix(new double[][] {
            { 4.0, 0.0, 0.0 },
            { 0.0, 3.0, 0.0 },
            { 0.0, 0.0, 2.0 }
        });
        RealMatrix vRef = MatrixUtils.createRealMatrix(new double[][] {
            {  80.0 / 125.0,  -60.0 / 125.0, 75.0 / 125.0 },
            {  24.0 / 125.0,  107.0 / 125.0, 60.0 / 125.0 },
            { -93.0 / 125.0,  -24.0 / 125.0, 80.0 / 125.0 }
        });

        // check values against known references
        SingularValueDecomposition svd =
            new SingularValueDecomposition(MatrixUtils.createRealMatrix(testNonSquare));
        RealMatrix u = svd.getU();
        Assert.assertEquals(0, u.subtract(uRef).getNorm(), normTolerance);
        RealMatrix s = svd.getS();
        Assert.assertEquals(0, s.subtract(sRef).getNorm(), normTolerance);
        RealMatrix v = svd.getV();
        Assert.assertEquals(0, v.subtract(vRef).getNorm(), normTolerance);

        // check the same cached instance is returned the second time
        Assert.assertTrue(u == svd.getU());
        Assert.assertTrue(s == svd.getS());
        Assert.assertTrue(v == svd.getV());

    }

     /** test MATH-465 */
    @Test
    public void testRank() {
        double[][] d = { { 1, 1, 1 }, { 0, 0, 0 }, { 1, 2, 3 } };
        RealMatrix m = new Array2DRowRealMatrix(d);
        SingularValueDecomposition svd = new SingularValueDecomposition(m);
        Assert.assertEquals(2, svd.getRank());
    }

    /** test MATH-583 */
    @Test
    public void testStability1() {
        RealMatrix m = new Array2DRowRealMatrix(201, 201);
        loadRealMatrix(m,"matrix1.csv");
        try {
            new SingularValueDecomposition(m);
        } catch (Exception e) {
            Assert.fail("Exception whilst constructing SVD");
        }
    }

    /** test MATH-327 */
    @Test
    public void testStability2() {
        RealMatrix m = new Array2DRowRealMatrix(7, 168);
        loadRealMatrix(m,"matrix2.csv");
        try {
            new SingularValueDecomposition(m);
        } catch (Throwable e) {
            Assert.fail("Exception whilst constructing SVD");
        }
    }

    private void loadRealMatrix(RealMatrix m, String resourceName) {
        try {
            DataInputStream in = new DataInputStream(getClass().getResourceAsStream(resourceName));
            BufferedReader br = new BufferedReader(new InputStreamReader(in));
            String strLine;
            int row = 0;
            while ((strLine = br.readLine()) != null) {
                if (!strLine.startsWith("#")) {
                    int col = 0;
                    for (String entry : strLine.split(",")) {
                        m.setEntry(row, col++, Double.parseDouble(entry));
                    }
                    row++;
                }
            }
            in.close();
        } catch (IOException e) {}
    }

    /** test condition number */
    @Test
    public void testConditionNumber() {
        SingularValueDecomposition svd =
            new SingularValueDecomposition(MatrixUtils.createRealMatrix(testSquare));
        // replace 1.0e-15 with 1.5e-15
        Assert.assertEquals(3.0, svd.getConditionNumber(), 1.5e-15);
    }

    @Test
    public void testInverseConditionNumber() {
        SingularValueDecomposition svd =
            new SingularValueDecomposition(MatrixUtils.createRealMatrix(testSquare));
        Assert.assertEquals(1.0/3.0, svd.getInverseConditionNumber(), 1.5e-15);
    }

    private RealMatrix createTestMatrix(final Random r, final int rows, final int columns,
                                        final double[] singularValues) {
        final RealMatrix u = EigenDecompositionTest.createOrthogonalMatrix(r, rows);
        final RealMatrix d = new Array2DRowRealMatrix(rows, columns);
        d.setSubMatrix(MatrixUtils.createRealDiagonalMatrix(singularValues).getData(), 0, 0);
        final RealMatrix v = EigenDecompositionTest.createOrthogonalMatrix(r, columns);
        return u.multiply(d).multiply(v);
    }

    @Test
    public void testIssue947() {
        double[][] nans = new double[][] {
            { Double.NaN, Double.NaN },
            { Double.NaN, Double.NaN }
        };
        RealMatrix m = new Array2DRowRealMatrix(nans, false);
        SingularValueDecomposition svd = new SingularValueDecomposition(m);
        Assert.assertTrue(Double.isNaN(svd.getSingularValues()[0]));
        Assert.assertTrue(Double.isNaN(svd.getSingularValues()[1]));
    }

}

Other Java examples (source code examples)

Here is a short list of links related to this Java SingularValueDecompositionTest.java source code file:



my book on functional programming

 

new blog posts

 

Copyright 1998-2019 Alvin Alexander, alvinalexander.com
All Rights Reserved.

A percentage of advertising revenue from
pages under the /java/jwarehouse URI on this website is
paid back to open source projects.