alvinalexander.com | career | drupal | java | mac | mysql | perl | scala | uml | unix  

Commons Math example source code file (QRDecompositionImplTest.java)

This example Commons Math source code file (QRDecompositionImplTest.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

defaultrealmatrixchangingvisitor, defaultrealmatrixpreservingvisitor, matrixvisitorexception, override, qrdecomposition, qrdecomposition, qrdecompositionimpl, qrdecompositionimpl, qrdecompositionimpltest, random, random, realmatrix, realmatrix, testcase, util

The Commons Math QRDecompositionImplTest.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 QRDecompositionImplTest extends TestCase {
    double[][] testData3x3NonSingular = {
            { 12, -51, 4 },
            { 6, 167, -68 },
            { -4, 24, -41 }, };

    double[][] testData3x3Singular = {
            { 1, 4, 7, },
            { 2, 5, 8, },
            { 3, 6, 9, }, };

    double[][] testData3x4 = {
            { 12, -51, 4, 1 },
            { 6, 167, -68, 2 },
            { -4, 24, -41, 3 }, };

    double[][] testData4x3 = {
            { 12, -51, 4, },
            { 6, 167, -68, },
            { -4, 24, -41, },
            { -5, 34, 7, }, };

    private static final double entryTolerance = 10e-16;

    private static final double normTolerance = 10e-14;

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

    /** test dimensions */
    public void testDimensions() {
        checkDimension(MatrixUtils.createRealMatrix(testData3x3NonSingular));

        checkDimension(MatrixUtils.createRealMatrix(testData4x3));

        checkDimension(MatrixUtils.createRealMatrix(testData3x4));

        Random r = new Random(643895747384642l);
        int    p = (5 * BlockRealMatrix.BLOCK_SIZE) / 4;
        int    q = (7 * BlockRealMatrix.BLOCK_SIZE) / 4;
        checkDimension(createTestMatrix(r, p, q));
        checkDimension(createTestMatrix(r, q, p));

    }

    private void checkDimension(RealMatrix m) {
        int rows = m.getRowDimension();
        int columns = m.getColumnDimension();
        QRDecomposition qr = new QRDecompositionImpl(m);
        assertEquals(rows,    qr.getQ().getRowDimension());
        assertEquals(rows,    qr.getQ().getColumnDimension());
        assertEquals(rows,    qr.getR().getRowDimension());
        assertEquals(columns, qr.getR().getColumnDimension());
    }

    /** test A = QR */
    public void testAEqualQR() {
        checkAEqualQR(MatrixUtils.createRealMatrix(testData3x3NonSingular));

        checkAEqualQR(MatrixUtils.createRealMatrix(testData3x3Singular));

        checkAEqualQR(MatrixUtils.createRealMatrix(testData3x4));

        checkAEqualQR(MatrixUtils.createRealMatrix(testData4x3));

        Random r = new Random(643895747384642l);
        int    p = (5 * BlockRealMatrix.BLOCK_SIZE) / 4;
        int    q = (7 * BlockRealMatrix.BLOCK_SIZE) / 4;
        checkAEqualQR(createTestMatrix(r, p, q));

        checkAEqualQR(createTestMatrix(r, q, p));

    }

    private void checkAEqualQR(RealMatrix m) {
        QRDecomposition qr = new QRDecompositionImpl(m);
        double norm = qr.getQ().multiply(qr.getR()).subtract(m).getNorm();
        assertEquals(0, norm, normTolerance);
    }

    /** test the orthogonality of Q */
    public void testQOrthogonal() {
        checkQOrthogonal(MatrixUtils.createRealMatrix(testData3x3NonSingular));

        checkQOrthogonal(MatrixUtils.createRealMatrix(testData3x3Singular));

        checkQOrthogonal(MatrixUtils.createRealMatrix(testData3x4));

        checkQOrthogonal(MatrixUtils.createRealMatrix(testData4x3));

        Random r = new Random(643895747384642l);
        int    p = (5 * BlockRealMatrix.BLOCK_SIZE) / 4;
        int    q = (7 * BlockRealMatrix.BLOCK_SIZE) / 4;
        checkQOrthogonal(createTestMatrix(r, p, q));

        checkQOrthogonal(createTestMatrix(r, q, p));

    }

    private void checkQOrthogonal(RealMatrix m) {
        QRDecomposition qr = new QRDecompositionImpl(m);
        RealMatrix eye = MatrixUtils.createRealIdentityMatrix(m.getRowDimension());
        double norm = qr.getQT().multiply(qr.getQ()).subtract(eye).getNorm();
        assertEquals(0, norm, normTolerance);
    }

    /** test that R is upper triangular */
    public void testRUpperTriangular() {
        RealMatrix matrix = MatrixUtils.createRealMatrix(testData3x3NonSingular);
        checkUpperTriangular(new QRDecompositionImpl(matrix).getR());

        matrix = MatrixUtils.createRealMatrix(testData3x3Singular);
        checkUpperTriangular(new QRDecompositionImpl(matrix).getR());

        matrix = MatrixUtils.createRealMatrix(testData3x4);
        checkUpperTriangular(new QRDecompositionImpl(matrix).getR());

        matrix = MatrixUtils.createRealMatrix(testData4x3);
        checkUpperTriangular(new QRDecompositionImpl(matrix).getR());

        Random r = new Random(643895747384642l);
        int    p = (5 * BlockRealMatrix.BLOCK_SIZE) / 4;
        int    q = (7 * BlockRealMatrix.BLOCK_SIZE) / 4;
        matrix = createTestMatrix(r, p, q);
        checkUpperTriangular(new QRDecompositionImpl(matrix).getR());

        matrix = createTestMatrix(r, p, q);
        checkUpperTriangular(new QRDecompositionImpl(matrix).getR());

    }

    private void checkUpperTriangular(RealMatrix m) {
        m.walkInOptimizedOrder(new DefaultRealMatrixPreservingVisitor() {
            @Override
            public void visit(int row, int column, double value) {
                if (column < row) {
                    assertEquals(0.0, value, entryTolerance);
                }
            }
        });
    }

    /** test that H is trapezoidal */
    public void testHTrapezoidal() {
        RealMatrix matrix = MatrixUtils.createRealMatrix(testData3x3NonSingular);
        checkTrapezoidal(new QRDecompositionImpl(matrix).getH());

        matrix = MatrixUtils.createRealMatrix(testData3x3Singular);
        checkTrapezoidal(new QRDecompositionImpl(matrix).getH());

        matrix = MatrixUtils.createRealMatrix(testData3x4);
        checkTrapezoidal(new QRDecompositionImpl(matrix).getH());

        matrix = MatrixUtils.createRealMatrix(testData4x3);
        checkTrapezoidal(new QRDecompositionImpl(matrix).getH());

        Random r = new Random(643895747384642l);
        int    p = (5 * BlockRealMatrix.BLOCK_SIZE) / 4;
        int    q = (7 * BlockRealMatrix.BLOCK_SIZE) / 4;
        matrix = createTestMatrix(r, p, q);
        checkTrapezoidal(new QRDecompositionImpl(matrix).getH());

        matrix = createTestMatrix(r, p, q);
        checkTrapezoidal(new QRDecompositionImpl(matrix).getH());

    }

    private void checkTrapezoidal(RealMatrix m) {
        m.walkInOptimizedOrder(new DefaultRealMatrixPreservingVisitor() {
            @Override
            public void visit(int row, int column, double value) {
                if (column > row) {
                    assertEquals(0.0, value, entryTolerance);
                }
            }
        });
    }
    /** test matrices values */
    public void testMatricesValues() {
        QRDecomposition qr =
            new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x3NonSingular));
        RealMatrix qRef = MatrixUtils.createRealMatrix(new double[][] {
                { -12.0 / 14.0,   69.0 / 175.0,  -58.0 / 175.0 },
                {  -6.0 / 14.0, -158.0 / 175.0,    6.0 / 175.0 },
                {   4.0 / 14.0,  -30.0 / 175.0, -165.0 / 175.0 }
        });
        RealMatrix rRef = MatrixUtils.createRealMatrix(new double[][] {
                { -14.0,  -21.0, 14.0 },
                {   0.0, -175.0, 70.0 },
                {   0.0,    0.0, 35.0 }
        });
        RealMatrix hRef = MatrixUtils.createRealMatrix(new double[][] {
                { 26.0 / 14.0, 0.0, 0.0 },
                {  6.0 / 14.0, 648.0 / 325.0, 0.0 },
                { -4.0 / 14.0,  36.0 / 325.0, 2.0 }
        });

        // check values against known references
        RealMatrix q = qr.getQ();
        assertEquals(0, q.subtract(qRef).getNorm(), 1.0e-13);
        RealMatrix qT = qr.getQT();
        assertEquals(0, qT.subtract(qRef.transpose()).getNorm(), 1.0e-13);
        RealMatrix r = qr.getR();
        assertEquals(0, r.subtract(rRef).getNorm(), 1.0e-13);
        RealMatrix h = qr.getH();
        assertEquals(0, h.subtract(hRef).getNorm(), 1.0e-13);

        // check the same cached instance is returned the second time
        assertTrue(q == qr.getQ());
        assertTrue(r == qr.getR());
        assertTrue(h == qr.getH());

    }

    private RealMatrix createTestMatrix(final Random r, final int rows, final int columns) {
        RealMatrix m = MatrixUtils.createRealMatrix(rows, columns);
        m.walkInOptimizedOrder(new DefaultRealMatrixChangingVisitor(){
            @Override
            public double visit(int row, int column, double value)
                throws MatrixVisitorException {
                return 2.0 * r.nextDouble() - 1.0;
            }
        });
        return m;
    }

}

Other Commons Math examples (source code examples)

Here is a short list of links related to this Commons Math QRDecompositionImplTest.java source code file:

... this post is sponsored by my books ...

#1 New Release!

FP Best Seller

 

new blog posts

 

Copyright 1998-2021 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.