Commons Math example source code file (TriDiagonalTransformerTest.java)

This example Commons Math source code file (TriDiagonalTransformerTest.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

exception, exception, invalidmatrixexception, realmatrix, realmatrix, testcase, tridiagonaltransformer, tridiagonaltransformer, tridiagonaltransformertest, tridiagonaltransformertest, util

The Commons Math TriDiagonalTransformerTest.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.Arrays;

import junit.framework.TestCase;

public class TriDiagonalTransformerTest extends TestCase {

    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 }
    };

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

    public void testNonSquare() {
        try {
            new TriDiagonalTransformer(MatrixUtils.createRealMatrix(new double[3][2]));
            fail("an exception should have been thrown");
        } catch (InvalidMatrixException ime) {
            // expected behavior
        } catch (Exception e) {
            fail("wrong exception caught");
        }
    }

    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();
        assertEquals(0, norm, 4.0e-15);
    }

    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();
        assertEquals(0, norm, 4.0e-15);
    }

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

    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());
        assertEquals(0, mTm.subtract(id).getNorm(), 1.0e-15);
    }

    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)) {
                    assertEquals(0, m.getEntry(i, j), 1.0e-16);
                }
            }
        }
    }

    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[] { -Math.sqrt(15), -3.0832882879592476, 0.6082710842351517, 1.1786086405912128 });
    }

    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();
        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];
            }
        }
        assertEquals(0, t.subtract(MatrixUtils.createRealMatrix(tData)).getNorm(), 1.0e-14);

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

    }

}