Commons Math example source code file (QRSolverTest.java)

This example Commons Math source code file (QRSolverTest.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

decompositionsolver, decompositionsolver, defaultrealmatrixchangingvisitor, exception, exception, illegalargumentexception, invalidmatrixexception, override, qrsolvertest, random, random, realmatrix, realmatrix, realvector, util

The Commons Math QRSolverTest.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 QRSolverTest extends TestCase {
    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 }
    };

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

    /** test rank */
    public void testRank() {
        DecompositionSolver solver =
            new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x3NonSingular)).getSolver();
        assertTrue(solver.isNonSingular());

        solver = new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x3Singular)).getSolver();
        assertFalse(solver.isNonSingular());

        solver = new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x4)).getSolver();
        assertTrue(solver.isNonSingular());

        solver = new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData4x3)).getSolver();
        assertTrue(solver.isNonSingular());

    }

    /** test solve dimension errors */
    public void testSolveDimensionErrors() {
        DecompositionSolver solver =
            new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x3NonSingular)).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[2][2]);
        try {
            solver.solve(b);
            fail("an exception should have been thrown");
        } catch (IllegalArgumentException iae) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
        try {
            solver.solve(b.getColumn(0));
            fail("an exception should have been thrown");
        } catch (IllegalArgumentException iae) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
        try {
            solver.solve(b.getColumnVector(0));
            fail("an exception should have been thrown");
        } catch (IllegalArgumentException iae) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
    }

    /** test solve rank errors */
    public void testSolveRankErrors() {
        DecompositionSolver solver =
            new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x3Singular)).getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[3][2]);
        try {
            solver.solve(b);
            fail("an exception should have been thrown");
        } catch (InvalidMatrixException iae) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
        try {
            solver.solve(b.getColumn(0));
            fail("an exception should have been thrown");
        } catch (InvalidMatrixException iae) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
        try {
            solver.solve(b.getColumnVector(0));
            fail("an exception should have been thrown");
        } catch (InvalidMatrixException iae) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
    }

    /** test solve */
    public void testSolve() {
        QRDecomposition decomposition =
            new QRDecompositionImpl(MatrixUtils.createRealMatrix(testData3x3NonSingular));
        DecompositionSolver solver = decomposition.getSolver();
        RealMatrix b = MatrixUtils.createRealMatrix(new double[][] {
                { -102, 12250 }, { 544, 24500 }, { 167, -36750 }
        });
        RealMatrix xRef = MatrixUtils.createRealMatrix(new double[][] {
                { 1, 2515 }, { 2, 422 }, { -3, 898 }
        });

        // using RealMatrix
        assertEquals(0, solver.solve(b).subtract(xRef).getNorm(), 2.0e-16 * xRef.getNorm());

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

    }

    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 QRDecompositionImpl(a).getSolver().solve(b);
        assertEquals(0, x.subtract(xRef).getNorm(), 0.01 * noise * p * q);

    }

    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);
        RealMatrix   x = new QRDecompositionImpl(a).getSolver().solve(b);

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

        // the last unknown should have been set to 0
        assertEquals(0.0, x.getSubMatrix(p, q - 1, 0, x.getColumnDimension() - 1).getNorm());

    }

    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;
    }
}