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Java example source code file (QRDecompositionTest.java)

This example Java source code file (QRDecompositionTest.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

arrayrealvector, defaultrealmatrixchangingvisitor, defaultrealmatrixpreservingvisitor, override, qrdecomposition, qrdecompositiontest, random, realmatrix, test, util

The QRDecompositionTest.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.linear.SingularMatrixException;

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


public class QRDecompositionTest {
    private double[][] testData3x3NonSingular = {
            { 12, -51, 4 },
            { 6, 167, -68 },
            { -4, 24, -41 }, };

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

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

    private 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;

    /** test dimensions */
    @Test
    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 QRDecomposition(m);
        Assert.assertEquals(rows,    qr.getQ().getRowDimension());
        Assert.assertEquals(rows,    qr.getQ().getColumnDimension());
        Assert.assertEquals(rows,    qr.getR().getRowDimension());
        Assert.assertEquals(columns, qr.getR().getColumnDimension());
    }

    /** test A = QR */
    @Test
    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 QRDecomposition(m);
        double norm = qr.getQ().multiply(qr.getR()).subtract(m).getNorm();
        Assert.assertEquals(0, norm, normTolerance);
    }

    /** test the orthogonality of Q */
    @Test
    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 QRDecomposition(m);
        RealMatrix eye = MatrixUtils.createRealIdentityMatrix(m.getRowDimension());
        double norm = qr.getQT().multiply(qr.getQ()).subtract(eye).getNorm();
        Assert.assertEquals(0, norm, normTolerance);
    }

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

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

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

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

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

    }

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

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

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

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

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

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

    }

    private void checkTrapezoidal(RealMatrix m) {
        m.walkInOptimizedOrder(new DefaultRealMatrixPreservingVisitor() {
            @Override
            public void visit(int row, int column, double value) {
                if (column > row) {
                    Assert.assertEquals(0.0, value, entryTolerance);
                }
            }
        });
    }
    /** test matrices values */
    @Test
    public void testMatricesValues() {
        QRDecomposition qr =
            new QRDecomposition(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();
        Assert.assertEquals(0, q.subtract(qRef).getNorm(), 1.0e-13);
        RealMatrix qT = qr.getQT();
        Assert.assertEquals(0, qT.subtract(qRef.transpose()).getNorm(), 1.0e-13);
        RealMatrix r = qr.getR();
        Assert.assertEquals(0, r.subtract(rRef).getNorm(), 1.0e-13);
        RealMatrix h = qr.getH();
        Assert.assertEquals(0, h.subtract(hRef).getNorm(), 1.0e-13);

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

    }

    @Test(expected=SingularMatrixException.class)
    public void testNonInvertible() {
        QRDecomposition qr =
            new QRDecomposition(MatrixUtils.createRealMatrix(testData3x3Singular));
        qr.getSolver().getInverse();
    }

    @Test
    public void testInvertTallSkinny() {
        RealMatrix a     = MatrixUtils.createRealMatrix(testData4x3);
        RealMatrix pinv  = new QRDecomposition(a).getSolver().getInverse();
        Assert.assertEquals(0, pinv.multiply(a).subtract(MatrixUtils.createRealIdentityMatrix(3)).getNorm(), 1.0e-6);
    }

    @Test
    public void testInvertShortWide() {
        RealMatrix a = MatrixUtils.createRealMatrix(testData3x4);
        RealMatrix pinv  = new QRDecomposition(a).getSolver().getInverse();
        Assert.assertEquals(0, a.multiply(pinv).subtract(MatrixUtils.createRealIdentityMatrix(3)).getNorm(), 1.0e-6);
        Assert.assertEquals(0, pinv.multiply(a).getSubMatrix(0, 2, 0, 2).subtract(MatrixUtils.createRealIdentityMatrix(3)).getNorm(), 1.0e-6);
    }

    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) {
                return 2.0 * r.nextDouble() - 1.0;
            }
        });
        return m;
    }

    @Test(expected=SingularMatrixException.class)
    public void testQRSingular() {
        final RealMatrix a = MatrixUtils.createRealMatrix(new double[][] {
            { 1, 6, 4 }, { 2, 4, -1 }, { -1, 2, 5 }
        });
        final RealVector b = new ArrayRealVector(new double[]{ 5, 6, 1 });
        new QRDecomposition(a, 1.0e-15).getSolver().solve(b);
    }

}

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