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Commons Math example source code file (SingularValueDecompositionImplTest.java)

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

Java - Commons Math tags/keywords

array2drowrealmatrix, random, random, realmatrix, realmatrix, singularvaluedecomposition, singularvaluedecomposition, singularvaluedecompositionimpl, singularvaluedecompositionimpl, singularvaluedecompositionimpltest, testcase, util

The Commons Math SingularValueDecompositionImplTest.java 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.math.linear;

import java.util.Random;

import junit.framework.TestCase;

public class SingularValueDecompositionImplTest extends TestCase {

    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;

    public SingularValueDecompositionImplTest(String name) {
        super(name);
    }

    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 SingularValueDecompositionImpl(createTestMatrix(r, rows, columns, singularValues));
        double[] computedSV = svd.getSingularValues();
        assertEquals(singularValues.length, computedSV.length);
        for (int i = 0; i < singularValues.length; ++i) {
            assertEquals(singularValues[i], computedSV[i], 1.0e-10);
        }
    }

    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 SingularValueDecompositionImpl(createTestMatrix(r, rows, columns, singularValues));
        double[] computedSV = svd.getSingularValues();
        assertEquals(singularValues.length, computedSV.length);
        for (int i = 0; i < singularValues.length; ++i) {
            assertEquals(singularValues[i], computedSV[i], 1.0e-10);
        }
    }

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

    }

    /** Test based on a dimension 4 Hadamard matrix. */
    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 SingularValueDecompositionImpl(matrix);
        assertEquals(16.0, svd.getSingularValues()[0], 1.0e-14);
        assertEquals( 8.0, svd.getSingularValues()[1], 1.0e-14);
        assertEquals( 4.0, svd.getSingularValues()[2], 1.0e-14);
        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);
        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);
        assertEquals(0.0,
                     halfCovariance.subtract(svd.getCovariance(6.0)).getNorm(),
                     1.0e-14);

    }

    /** test A = USVt */
    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 SingularValueDecompositionImpl(matrix);
        RealMatrix u = svd.getU();
        RealMatrix s = svd.getS();
        RealMatrix v = svd.getV();
        double norm = u.multiply(s).multiply(v.transpose()).subtract(matrix).getNorm();
        assertEquals(0, norm, normTolerance);

    }

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

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

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

    /** test matrices values */
    public void testMatricesValues1() {
       SingularValueDecomposition svd =
            new SingularValueDecompositionImpl(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();
        assertEquals(0, u.subtract(uRef).getNorm(), normTolerance);
        RealMatrix s = svd.getS();
        assertEquals(0, s.subtract(sRef).getNorm(), normTolerance);
        RealMatrix v = svd.getV();
        assertEquals(0, v.subtract(vRef).getNorm(), normTolerance);

        // check the same cached instance is returned the second time
        assertTrue(u == svd.getU());
        assertTrue(s == svd.getS());
        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 SingularValueDecompositionImpl(MatrixUtils.createRealMatrix(testNonSquare));
        RealMatrix u = svd.getU();
        assertEquals(0, u.subtract(uRef).getNorm(), normTolerance);
        RealMatrix s = svd.getS();
        assertEquals(0, s.subtract(sRef).getNorm(), normTolerance);
        RealMatrix v = svd.getV();
        assertEquals(0, v.subtract(vRef).getNorm(), normTolerance);

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

    }

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

    private RealMatrix createTestMatrix(final Random r, final int rows, final int columns,
                                        final double[] singularValues) {
        final RealMatrix u =
            EigenDecompositionImplTest.createOrthogonalMatrix(r, rows);
        final RealMatrix d =
            EigenDecompositionImplTest.createDiagonalMatrix(singularValues, rows, columns);
        final RealMatrix v =
            EigenDecompositionImplTest.createOrthogonalMatrix(r, columns);
        return u.multiply(d).multiply(v);
    }

}

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