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Java example source code file (RRQRDecompositionTest.java)

This example Java source code file (RRQRDecompositionTest.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, defaultrealmatrixchangingvisitor, defaultrealmatrixpreservingvisitor, override, random, realmatrix, rrqrdecomposition, rrqrdecompositiontest, test, util

The RRQRDecompositionTest.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.junit.Assert;
import org.junit.Test;


public class RRQRDecompositionTest {
    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();
        RRQRDecomposition qr = new RRQRDecomposition(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 AP = QR */
    @Test
    public void testAPEqualQR() {
        checkAPEqualQR(MatrixUtils.createRealMatrix(testData3x3NonSingular));

        checkAPEqualQR(MatrixUtils.createRealMatrix(testData3x3Singular));

        checkAPEqualQR(MatrixUtils.createRealMatrix(testData3x4));

        checkAPEqualQR(MatrixUtils.createRealMatrix(testData4x3));

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

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

    }

    private void checkAPEqualQR(RealMatrix m) {
        RRQRDecomposition rrqr = new RRQRDecomposition(m);
        double norm = rrqr.getQ().multiply(rrqr.getR()).subtract(m.multiply(rrqr.getP())).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) {
        RRQRDecomposition qr = new RRQRDecomposition(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 RRQRDecomposition(matrix).getR());

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

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

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

        matrix = createTestMatrix(r, p, q);
        checkUpperTriangular(new RRQRDecomposition(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 RRQRDecomposition(matrix).getH());

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

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

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

        matrix = createTestMatrix(r, p, q);
        checkTrapezoidal(new RRQRDecomposition(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(expected=SingularMatrixException.class)
    public void testNonInvertible() {
        RRQRDecomposition qr =
            new RRQRDecomposition(MatrixUtils.createRealMatrix(testData3x3Singular), 3.0e-16);
        qr.getSolver().getInverse();
    }

    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 the rank is returned correctly */
    @Test
    public void testRank() {
        double[][] d = { { 1, 1, 1 }, { 0, 0, 0 }, { 1, 2, 3 } };
        RealMatrix m = new Array2DRowRealMatrix(d);
        RRQRDecomposition qr = new RRQRDecomposition(m);
        Assert.assertEquals(2, qr.getRank(1.0e-16));
    }

}

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