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Java example source code file (BiDiagonalTransformerTest.java)

This example Java source code file (BiDiagonalTransformerTest.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

bidiagonaltransformer, bidiagonaltransformertest, realmatrix, test

The BiDiagonalTransformerTest.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 org.apache.commons.math3.linear.BiDiagonalTransformer;
import org.apache.commons.math3.linear.MatrixUtils;
import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;

public class BiDiagonalTransformerTest {

    private double[][] testSquare = {
            { 24.0 / 25.0, 43.0 / 25.0 },
            { 57.0 / 25.0, 24.0 / 25.0 }
    };

    private double[][] testNonSquare = {
        {  -540.0 / 625.0,  963.0 / 625.0, -216.0 / 625.0 },
        { -1730.0 / 625.0, -744.0 / 625.0, 1008.0 / 625.0 },
        {  -720.0 / 625.0, 1284.0 / 625.0, -288.0 / 625.0 },
        {  -360.0 / 625.0,  192.0 / 625.0, 1756.0 / 625.0 },
    };

    @Test
    public void testDimensions() {
        checkdimensions(MatrixUtils.createRealMatrix(testSquare));
        checkdimensions(MatrixUtils.createRealMatrix(testNonSquare));
        checkdimensions(MatrixUtils.createRealMatrix(testNonSquare).transpose());
    }

    private void checkdimensions(RealMatrix matrix) {
        final int m = matrix.getRowDimension();
        final int n = matrix.getColumnDimension();
        BiDiagonalTransformer transformer = new BiDiagonalTransformer(matrix);
        Assert.assertEquals(m, transformer.getU().getRowDimension());
        Assert.assertEquals(m, transformer.getU().getColumnDimension());
        Assert.assertEquals(m, transformer.getB().getRowDimension());
        Assert.assertEquals(n, transformer.getB().getColumnDimension());
        Assert.assertEquals(n, transformer.getV().getRowDimension());
        Assert.assertEquals(n, transformer.getV().getColumnDimension());

    }

    @Test
    public void testAEqualUSVt() {
        checkAEqualUSVt(MatrixUtils.createRealMatrix(testSquare));
        checkAEqualUSVt(MatrixUtils.createRealMatrix(testNonSquare));
        checkAEqualUSVt(MatrixUtils.createRealMatrix(testNonSquare).transpose());
    }

    private void checkAEqualUSVt(RealMatrix matrix) {
        BiDiagonalTransformer transformer = new BiDiagonalTransformer(matrix);
        RealMatrix u = transformer.getU();
        RealMatrix b = transformer.getB();
        RealMatrix v = transformer.getV();
        double norm = u.multiply(b).multiply(v.transpose()).subtract(matrix).getNorm();
        Assert.assertEquals(0, norm, 1.0e-14);
    }

    @Test
    public void testUOrthogonal() {
        checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare)).getU());
        checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare)).getU());
        checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare).transpose()).getU());
    }

    @Test
    public void testVOrthogonal() {
        checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare)).getV());
        checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare)).getV());
        checkOrthogonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare).transpose()).getV());
    }

    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-14);
    }

    @Test
    public void testBBiDiagonal() {
        checkBiDiagonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare)).getB());
        checkBiDiagonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare)).getB());
        checkBiDiagonal(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare).transpose()).getB());
    }

    private void checkBiDiagonal(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 (rows < cols) {
                    if ((i < j) || (i > j + 1)) {
                        Assert.assertEquals(0, m.getEntry(i, j), 1.0e-16);
                    }
                } else {
                    if ((i < j - 1) || (i > j)) {
                        Assert.assertEquals(0, m.getEntry(i, j), 1.0e-16);
                    }
                }
            }
        }
    }

    @Test
    public void testSingularMatrix() {
       BiDiagonalTransformer transformer =
            new BiDiagonalTransformer(MatrixUtils.createRealMatrix(new double[][] {
                { 1.0, 2.0, 3.0 },
                { 2.0, 3.0, 4.0 },
                { 3.0, 5.0, 7.0 }
            }));
       final double s3  = FastMath.sqrt(3.0);
       final double s14 = FastMath.sqrt(14.0);
       final double s1553 = FastMath.sqrt(1553.0);
       RealMatrix uRef = MatrixUtils.createRealMatrix(new double[][] {
           {  -1.0 / s14,  5.0 / (s3 * s14),  1.0 / s3 },
           {  -2.0 / s14, -4.0 / (s3 * s14),  1.0 / s3 },
           {  -3.0 / s14,  1.0 / (s3 * s14), -1.0 / s3 }
       });
       RealMatrix bRef = MatrixUtils.createRealMatrix(new double[][] {
           { -s14, s1553 / s14,   0.0 },
           {  0.0, -87 * s3 / (s14 * s1553), -s3 * s14 / s1553 },
           {  0.0, 0.0, 0.0 }
       });
       RealMatrix vRef = MatrixUtils.createRealMatrix(new double[][] {
           { 1.0,   0.0,         0.0        },
           { 0.0,  -23 / s1553,  32 / s1553 },
           { 0.0,  -32 / s1553, -23 / s1553 }
       });

       // check values against known references
       RealMatrix u = transformer.getU();
       Assert.assertEquals(0, u.subtract(uRef).getNorm(), 1.0e-14);
       RealMatrix b = transformer.getB();
       Assert.assertEquals(0, b.subtract(bRef).getNorm(), 1.0e-14);
       RealMatrix v = transformer.getV();
       Assert.assertEquals(0, v.subtract(vRef).getNorm(), 1.0e-14);

       // check the same cached instance is returned the second time
       Assert.assertTrue(u == transformer.getU());
       Assert.assertTrue(b == transformer.getB());
       Assert.assertTrue(v == transformer.getV());

    }

    @Test
    public void testMatricesValues() {
       BiDiagonalTransformer transformer =
            new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare));
       final double s17 = FastMath.sqrt(17.0);
        RealMatrix uRef = MatrixUtils.createRealMatrix(new double[][] {
                {  -8 / (5 * s17), 19 / (5 * s17) },
                { -19 / (5 * s17), -8 / (5 * s17) }
        });
        RealMatrix bRef = MatrixUtils.createRealMatrix(new double[][] {
                { -3 * s17 / 5, 32 * s17 / 85 },
                {      0.0,     -5 * s17 / 17 }
        });
        RealMatrix vRef = MatrixUtils.createRealMatrix(new double[][] {
                { 1.0,  0.0 },
                { 0.0, -1.0 }
        });

        // check values against known references
        RealMatrix u = transformer.getU();
        Assert.assertEquals(0, u.subtract(uRef).getNorm(), 1.0e-14);
        RealMatrix b = transformer.getB();
        Assert.assertEquals(0, b.subtract(bRef).getNorm(), 1.0e-14);
        RealMatrix v = transformer.getV();
        Assert.assertEquals(0, v.subtract(vRef).getNorm(), 1.0e-14);

        // check the same cached instance is returned the second time
        Assert.assertTrue(u == transformer.getU());
        Assert.assertTrue(b == transformer.getB());
        Assert.assertTrue(v == transformer.getV());

    }

    @Test
    public void testUpperOrLower() {
        Assert.assertTrue(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testSquare)).isUpperBiDiagonal());
        Assert.assertTrue(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare)).isUpperBiDiagonal());
        Assert.assertFalse(new BiDiagonalTransformer(MatrixUtils.createRealMatrix(testNonSquare).transpose()).isUpperBiDiagonal());
    }

}

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