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Java example source code file (RRQRSolverTest.java)

This example Java source code file (RRQRSolverTest.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

decompositionsolver, defaultrealmatrixchangingvisitor, mathillegalargumentexception, override, random, realmatrix, realvector, rrqrdecomposition, rrqrsolvertest, singularmatrixexception, test, util

The RRQRSolverTest.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.exception.MathIllegalArgumentException;

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

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

    double[][] testData3x3Singular = {
            { 1, 2,  2 },
            { 2, 4,  6 },
            { 4, 8, 12 }
    };

    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 }
    };

    /** test rank */
    @Test
    public void testRank() {
        DecompositionSolver solver =
            new RRQRDecomposition(MatrixUtils.createRealMatrix(testData3x3NonSingular), 1.0e-16).getSolver();
        Assert.assertTrue(solver.isNonSingular());

        solver = new RRQRDecomposition(MatrixUtils.createRealMatrix(testData3x3Singular), 1.0e-16).getSolver();
        Assert.assertFalse(solver.isNonSingular());

        solver = new RRQRDecomposition(MatrixUtils.createRealMatrix(testData3x4), 1.0e-16).getSolver();
        Assert.assertTrue(solver.isNonSingular());

        solver = new RRQRDecomposition(MatrixUtils.createRealMatrix(testData4x3), 1.0e-16).getSolver();
        Assert.assertTrue(solver.isNonSingular());

    }

    /** test solve dimension errors */
    @Test
    public void testSolveDimensionErrors() {
        DecompositionSolver solver =
            new RRQRDecomposition(MatrixUtils.createRealMatrix(testData3x3NonSingular)).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[2][2]);
        try {
            solver.solve(b);
            Assert.fail("an exception should have been thrown");
        } catch (MathIllegalArgumentException iae) {
            // expected behavior
        }
        try {
            solver.solve(b.getColumnVector(0));
            Assert.fail("an exception should have been thrown");
        } catch (MathIllegalArgumentException iae) {
            // expected behavior
        }

    }

    /** test solve rank errors */
    @Test
    public void testSolveRankErrors() {
        DecompositionSolver solver =
            new RRQRDecomposition(MatrixUtils.createRealMatrix(testData3x3Singular), 1.0e-16).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[3][2]);
        try {
            solver.solve(b);
            Assert.fail("an exception should have been thrown");
        } catch (SingularMatrixException iae) {
            // expected behavior
        }
        try {
            solver.solve(b.getColumnVector(0));
            Assert.fail("an exception should have been thrown");
        } catch (SingularMatrixException iae) {
            // expected behavior
        }

    }

    /** test solve */
    @Test
    public void testSolve() {
        RealMatrix b = MatrixUtils.createRealMatrix(new double[][] {
                { -102, 12250 }, { 544, 24500 }, { 167, -36750 }
        });
        RealMatrix xRef = MatrixUtils.createRealMatrix(new double[][] {
                { 1, 2515 }, { 2, 422 }, { -3, 898 }
        });


        RRQRDecomposition decomposition = new RRQRDecomposition(MatrixUtils.createRealMatrix(testData3x3NonSingular));
        DecompositionSolver solver = decomposition.getSolver();

        // using RealMatrix
        Assert.assertEquals(0, solver.solve(b).subtract(xRef).getNorm(), 3.0e-16 * xRef.getNorm());

        // using ArrayRealVector
        for (int i = 0; i < b.getColumnDimension(); ++i) {
            final RealVector x = solver.solve(b.getColumnVector(i));
            final double error = x.subtract(xRef.getColumnVector(i)).getNorm();
            Assert.assertEquals(0, error, 3.0e-16 * xRef.getColumnVector(i).getNorm());
        }

        // using RealVector with an alternate implementation
        for (int i = 0; i < b.getColumnDimension(); ++i) {
            ArrayRealVectorTest.RealVectorTestImpl v =
                new ArrayRealVectorTest.RealVectorTestImpl(b.getColumn(i));
            final RealVector x = solver.solve(v);
            final double error = x.subtract(xRef.getColumnVector(i)).getNorm();
            Assert.assertEquals(0, error, 3.0e-16 * xRef.getColumnVector(i).getNorm());
        }

    }

    @Test
    public void testOverdetermined() {
        final Random r    = new Random(5559252868205245l);
        int          p    = (7 * BlockRealMatrix.BLOCK_SIZE) / 4;
        int          q    = (5 * BlockRealMatrix.BLOCK_SIZE) / 4;
        RealMatrix   a    = createTestMatrix(r, p, q);
        RealMatrix   xRef = createTestMatrix(r, q, BlockRealMatrix.BLOCK_SIZE + 3);

        // build a perturbed system: A.X + noise = B
        RealMatrix b = a.multiply(xRef);
        final double noise = 0.001;
        b.walkInOptimizedOrder(new DefaultRealMatrixChangingVisitor() {
            @Override
            public double visit(int row, int column, double value) {
                return value * (1.0 + noise * (2 * r.nextDouble() - 1));
            }
        });

        // despite perturbation, the least square solution should be pretty good
        RealMatrix x = new RRQRDecomposition(a).getSolver().solve(b);
        Assert.assertEquals(0, x.subtract(xRef).getNorm(), 0.01 * noise * p * q);

    }

    @Test
    public void testUnderdetermined() {
        final Random r    = new Random(42185006424567123l);
        int          p    = (5 * BlockRealMatrix.BLOCK_SIZE) / 4;
        int          q    = (7 * BlockRealMatrix.BLOCK_SIZE) / 4;
        RealMatrix   a    = createTestMatrix(r, p, q);
        RealMatrix   xRef = createTestMatrix(r, q, BlockRealMatrix.BLOCK_SIZE + 3);
        RealMatrix   b    = a.multiply(xRef);
        RRQRDecomposition rrqrd = new RRQRDecomposition(a);
        RealMatrix   x = rrqrd.getSolver().solve(b);

        // too many equations, the system cannot be solved at all
        Assert.assertTrue(x.subtract(xRef).getNorm() / (p * q) > 0.01);

        // the last permuted unknown should have been set to 0
        RealMatrix permuted = rrqrd.getP().transpose().multiply(x);
        Assert.assertEquals(0.0, permuted.getSubMatrix(p, q - 1, 0, permuted.getColumnDimension() - 1).getNorm(), 0);

    }

    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;
    }
}

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