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Java example source code file (TriDiagonalTransformerTest.java)

This example Java source code file (TriDiagonalTransformerTest.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

nonsquarematrixexception, realmatrix, test, tridiagonaltransformer, tridiagonaltransformertest, util

The TriDiagonalTransformerTest.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.Arrays;

import org.apache.commons.math3.util.FastMath;

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

public class TriDiagonalTransformerTest {

    private double[][] testSquare5 = {
            { 1, 2, 3, 1, 1 },
            { 2, 1, 1, 3, 1 },
            { 3, 1, 1, 1, 2 },
            { 1, 3, 1, 2, 1 },
            { 1, 1, 2, 1, 3 }
    };

    private double[][] testSquare3 = {
            { 1, 3, 4 },
            { 3, 2, 2 },
            { 4, 2, 0 }
    };

    @Test
    public void testNonSquare() {
        try {
            new TriDiagonalTransformer(MatrixUtils.createRealMatrix(new double[3][2]));
            Assert.fail("an exception should have been thrown");
        } catch (NonSquareMatrixException ime) {
            // expected behavior
        }
    }

    @Test
    public void testAEqualQTQt() {
        checkAEqualQTQt(MatrixUtils.createRealMatrix(testSquare5));
        checkAEqualQTQt(MatrixUtils.createRealMatrix(testSquare3));
    }

    private void checkAEqualQTQt(RealMatrix matrix) {
        TriDiagonalTransformer transformer = new TriDiagonalTransformer(matrix);
        RealMatrix q  = transformer.getQ();
        RealMatrix qT = transformer.getQT();
        RealMatrix t  = transformer.getT();
        double norm = q.multiply(t).multiply(qT).subtract(matrix).getNorm();
        Assert.assertEquals(0, norm, 4.0e-15);
    }

    @Test
    public void testNoAccessBelowDiagonal() {
        checkNoAccessBelowDiagonal(testSquare5);
        checkNoAccessBelowDiagonal(testSquare3);
    }

    private void checkNoAccessBelowDiagonal(double[][] data) {
        double[][] modifiedData = new double[data.length][];
        for (int i = 0; i < data.length; ++i) {
            modifiedData[i] = data[i].clone();
            Arrays.fill(modifiedData[i], 0, i, Double.NaN);
        }
        RealMatrix matrix = MatrixUtils.createRealMatrix(modifiedData);
        TriDiagonalTransformer transformer = new TriDiagonalTransformer(matrix);
        RealMatrix q  = transformer.getQ();
        RealMatrix qT = transformer.getQT();
        RealMatrix t  = transformer.getT();
        double norm = q.multiply(t).multiply(qT).subtract(MatrixUtils.createRealMatrix(data)).getNorm();
        Assert.assertEquals(0, norm, 4.0e-15);
    }

    @Test
    public void testQOrthogonal() {
        checkOrthogonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare5)).getQ());
        checkOrthogonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare3)).getQ());
    }

    @Test
    public void testQTOrthogonal() {
        checkOrthogonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare5)).getQT());
        checkOrthogonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare3)).getQT());
    }

    private void checkOrthogonal(RealMatrix m) {
        RealMatrix mTm = m.transpose().multiply(m);
        RealMatrix id  = MatrixUtils.createRealIdentityMatrix(mTm.getRowDimension());
        Assert.assertEquals(0, mTm.subtract(id).getNorm(), 1.0e-15);
    }

    @Test
    public void testTTriDiagonal() {
        checkTriDiagonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare5)).getT());
        checkTriDiagonal(new TriDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare3)).getT());
    }

    private void checkTriDiagonal(RealMatrix m) {
        final int rows = m.getRowDimension();
        final int cols = m.getColumnDimension();
        for (int i = 0; i < rows; ++i) {
            for (int j = 0; j < cols; ++j) {
                if ((i < j - 1) || (i > j + 1)) {
                    Assert.assertEquals(0, m.getEntry(i, j), 1.0e-16);
                }
            }
        }
    }

    @Test
    public void testMatricesValues5() {
        checkMatricesValues(testSquare5,
                            new double[][] {
                                { 1.0,  0.0,                 0.0,                  0.0,                   0.0 },
                                { 0.0, -0.5163977794943222,  0.016748280772542083, 0.839800693771262,     0.16669620021405473 },
                                { 0.0, -0.7745966692414833, -0.4354553000860955,  -0.44989322880603355,  -0.08930153582895772 },
                                { 0.0, -0.2581988897471611,  0.6364346693566014,  -0.30263204032131164,   0.6608313651342882 },
                                { 0.0, -0.2581988897471611,  0.6364346693566009,  -0.027289660803112598, -0.7263191580755246 }
                            },
                            new double[] { 1, 4.4, 1.433099579242636, -0.89537362758743, 2.062274048344794 },
                            new double[] { -FastMath.sqrt(15), -3.0832882879592476, 0.6082710842351517, 1.1786086405912128 });
    }

    @Test
    public void testMatricesValues3() {
        checkMatricesValues(testSquare3,
                            new double[][] {
                                {  1.0,  0.0,  0.0 },
                                {  0.0, -0.6,  0.8 },
                                {  0.0, -0.8, -0.6 },
                            },
                            new double[] { 1, 2.64, -0.64 },
                            new double[] { -5, -1.52 });
    }

    private void checkMatricesValues(double[][] matrix, double[][] qRef,
                                     double[] mainDiagnonal,
                                     double[] secondaryDiagonal) {
        TriDiagonalTransformer transformer =
            new TriDiagonalTransformer(MatrixUtils.createRealMatrix(matrix));

        // check values against known references
        RealMatrix q = transformer.getQ();
        Assert.assertEquals(0, q.subtract(MatrixUtils.createRealMatrix(qRef)).getNorm(), 1.0e-14);

        RealMatrix t = transformer.getT();
        double[][] tData = new double[mainDiagnonal.length][mainDiagnonal.length];
        for (int i = 0; i < mainDiagnonal.length; ++i) {
            tData[i][i] = mainDiagnonal[i];
            if (i > 0) {
                tData[i][i - 1] = secondaryDiagonal[i - 1];
            }
            if (i < secondaryDiagonal.length) {
                tData[i][i + 1] = secondaryDiagonal[i];
            }
        }
        Assert.assertEquals(0, t.subtract(MatrixUtils.createRealMatrix(tData)).getNorm(), 1.0e-14);

        // check the same cached instance is returned the second time
        Assert.assertTrue(q == transformer.getQ());
        Assert.assertTrue(t == transformer.getT());
    }
}

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