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Java example source code file (MatrixUtilsTest.java)

This example Java source code file (MatrixUtilsTest.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

array2drowfieldmatrix, array2drowrealmatrix, arrayrealvector, bigdecimal, bigfraction, blockrealmatrix, expecting, fraction, math, mathillegalargumentexception, notstrictlypositiveexception, nullargumentexception, realmatrix, string, test

The MatrixUtilsTest.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.math.BigDecimal;

import org.apache.commons.math3.TestUtils;
import org.apache.commons.math3.fraction.BigFraction;
import org.apache.commons.math3.fraction.Fraction;
import org.apache.commons.math3.fraction.FractionConversionException;
import org.apache.commons.math3.fraction.FractionField;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.junit.Assert;
import org.junit.Test;

/**
 * Test cases for the {@link MatrixUtils} class.
 *
 */

public final class MatrixUtilsTest {

    protected double[][] testData = { {1d,2d,3d}, {2d,5d,3d}, {1d,0d,8d} };
    protected double[][] testData3x3Singular = { { 1, 4, 7, }, { 2, 5, 8, }, { 3, 6, 9, } };
    protected double[][] testData3x4 = { { 12, -51, 4, 1 }, { 6, 167, -68, 2 }, { -4, 24, -41, 3 } };
    protected double[][] nullMatrix = null;
    protected double[] row = {1,2,3};
    protected BigDecimal[] bigRow =
        {new BigDecimal(1),new BigDecimal(2),new BigDecimal(3)};
    protected String[] stringRow = {"1", "2", "3"};
    protected Fraction[] fractionRow =
        {new Fraction(1),new Fraction(2),new Fraction(3)};
    protected double[][] rowMatrix = {{1,2,3}};
    protected BigDecimal[][] bigRowMatrix =
        {{new BigDecimal(1), new BigDecimal(2), new BigDecimal(3)}};
    protected String[][] stringRowMatrix = {{"1", "2", "3"}};
    protected Fraction[][] fractionRowMatrix =
        {{new Fraction(1), new Fraction(2), new Fraction(3)}};
    protected double[] col = {0,4,6};
    protected BigDecimal[] bigCol =
        {new BigDecimal(0),new BigDecimal(4),new BigDecimal(6)};
    protected String[] stringCol = {"0","4","6"};
    protected Fraction[] fractionCol =
        {new Fraction(0),new Fraction(4),new Fraction(6)};
    protected double[] nullDoubleArray = null;
    protected double[][] colMatrix = {{0},{4},{6}};
    protected BigDecimal[][] bigColMatrix =
        {{new BigDecimal(0)},{new BigDecimal(4)},{new BigDecimal(6)}};
    protected String[][] stringColMatrix = {{"0"}, {"4"}, {"6"}};
    protected Fraction[][] fractionColMatrix =
        {{new Fraction(0)},{new Fraction(4)},{new Fraction(6)}};

    @Test
    public void testCreateRealMatrix() {
        Assert.assertEquals(new BlockRealMatrix(testData),
                MatrixUtils.createRealMatrix(testData));
        try {
            MatrixUtils.createRealMatrix(new double[][] {{1}, {1,2}});  // ragged
            Assert.fail("Expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // expected
        }
        try {
            MatrixUtils.createRealMatrix(new double[][] {{}, {}});  // no columns
            Assert.fail("Expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // expected
        }
        try {
            MatrixUtils.createRealMatrix(null);  // null
            Assert.fail("Expecting NullArgumentException");
        } catch (NullArgumentException ex) {
            // expected
        }
    }

    @Test
    public void testcreateFieldMatrix() {
        Assert.assertEquals(new Array2DRowFieldMatrix<Fraction>(asFraction(testData)),
                     MatrixUtils.createFieldMatrix(asFraction(testData)));
        Assert.assertEquals(new Array2DRowFieldMatrix<Fraction>(FractionField.getInstance(), fractionColMatrix),
                     MatrixUtils.createFieldMatrix(fractionColMatrix));
        try {
            MatrixUtils.createFieldMatrix(asFraction(new double[][] {{1}, {1,2}}));  // ragged
            Assert.fail("Expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // expected
        }
        try {
            MatrixUtils.createFieldMatrix(asFraction(new double[][] {{}, {}}));  // no columns
            Assert.fail("Expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // expected
        }
        try {
            MatrixUtils.createFieldMatrix((Fraction[][])null);  // null
            Assert.fail("Expecting NullArgumentException");
        } catch (NullArgumentException ex) {
            // expected
        }
    }

    @Test
    public void testCreateRowRealMatrix() {
        Assert.assertEquals(MatrixUtils.createRowRealMatrix(row),
                     new BlockRealMatrix(rowMatrix));
        try {
            MatrixUtils.createRowRealMatrix(new double[] {});  // empty
            Assert.fail("Expecting NotStrictlyPositiveException");
        } catch (NotStrictlyPositiveException ex) {
            // expected
        }
        try {
            MatrixUtils.createRowRealMatrix(null);  // null
            Assert.fail("Expecting NullArgumentException");
        } catch (NullArgumentException ex) {
            // expected
        }
    }

    @Test
    public void testCreateRowFieldMatrix() {
        Assert.assertEquals(MatrixUtils.createRowFieldMatrix(asFraction(row)),
                     new Array2DRowFieldMatrix<Fraction>(asFraction(rowMatrix)));
        Assert.assertEquals(MatrixUtils.createRowFieldMatrix(fractionRow),
                     new Array2DRowFieldMatrix<Fraction>(fractionRowMatrix));
        try {
            MatrixUtils.createRowFieldMatrix(new Fraction[] {});  // empty
            Assert.fail("Expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // expected
        }
        try {
            MatrixUtils.createRowFieldMatrix((Fraction[]) null);  // null
            Assert.fail("Expecting NullArgumentException");
        } catch (NullArgumentException ex) {
            // expected
        }
    }

    @Test
    public void testCreateColumnRealMatrix() {
        Assert.assertEquals(MatrixUtils.createColumnRealMatrix(col),
                     new BlockRealMatrix(colMatrix));
        try {
            MatrixUtils.createColumnRealMatrix(new double[] {});  // empty
            Assert.fail("Expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // expected
        }
        try {
            MatrixUtils.createColumnRealMatrix(null);  // null
            Assert.fail("Expecting NullArgumentException");
        } catch (NullArgumentException ex) {
            // expected
        }
    }

    @Test
    public void testCreateColumnFieldMatrix() {
        Assert.assertEquals(MatrixUtils.createColumnFieldMatrix(asFraction(col)),
                     new Array2DRowFieldMatrix<Fraction>(asFraction(colMatrix)));
        Assert.assertEquals(MatrixUtils.createColumnFieldMatrix(fractionCol),
                     new Array2DRowFieldMatrix<Fraction>(fractionColMatrix));

        try {
            MatrixUtils.createColumnFieldMatrix(new Fraction[] {});  // empty
            Assert.fail("Expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // expected
        }
        try {
            MatrixUtils.createColumnFieldMatrix((Fraction[]) null);  // null
            Assert.fail("Expecting NullArgumentException");
        } catch (NullArgumentException ex) {
            // expected
        }
    }

    /**
     * Verifies that the matrix is an identity matrix
     */
    protected void checkIdentityMatrix(RealMatrix m) {
        for (int i = 0; i < m.getRowDimension(); i++) {
            for (int j =0; j < m.getColumnDimension(); j++) {
                if (i == j) {
                    Assert.assertEquals(m.getEntry(i, j), 1d, 0);
                } else {
                    Assert.assertEquals(m.getEntry(i, j), 0d, 0);
                }
            }
        }
    }

    @Test
    public void testCreateIdentityMatrix() {
        checkIdentityMatrix(MatrixUtils.createRealIdentityMatrix(3));
        checkIdentityMatrix(MatrixUtils.createRealIdentityMatrix(2));
        checkIdentityMatrix(MatrixUtils.createRealIdentityMatrix(1));
        try {
            MatrixUtils.createRealIdentityMatrix(0);
            Assert.fail("Expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // expected
        }
    }

    /**
     * Verifies that the matrix is an identity matrix
     */
    protected void checkIdentityFieldMatrix(FieldMatrix<Fraction> m) {
        for (int i = 0; i < m.getRowDimension(); i++) {
            for (int j =0; j < m.getColumnDimension(); j++) {
                if (i == j) {
                    Assert.assertEquals(m.getEntry(i, j), Fraction.ONE);
                } else {
                    Assert.assertEquals(m.getEntry(i, j), Fraction.ZERO);
                }
            }
        }
    }

    @Test
    public void testcreateFieldIdentityMatrix() {
        checkIdentityFieldMatrix(MatrixUtils.createFieldIdentityMatrix(FractionField.getInstance(), 3));
        checkIdentityFieldMatrix(MatrixUtils.createFieldIdentityMatrix(FractionField.getInstance(), 2));
        checkIdentityFieldMatrix(MatrixUtils.createFieldIdentityMatrix(FractionField.getInstance(), 1));
        try {
            MatrixUtils.createRealIdentityMatrix(0);
            Assert.fail("Expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // expected
        }
    }

    @Test
    public void testBigFractionConverter() {
        BigFraction[][] bfData = {
                { new BigFraction(1), new BigFraction(2), new BigFraction(3) },
                { new BigFraction(2), new BigFraction(5), new BigFraction(3) },
                { new BigFraction(1), new BigFraction(0), new BigFraction(8) }
        };
        FieldMatrix<BigFraction> m = new Array2DRowFieldMatrix(bfData, false);
        RealMatrix converted = MatrixUtils.bigFractionMatrixToRealMatrix(m);
        RealMatrix reference = new Array2DRowRealMatrix(testData, false);
        Assert.assertEquals(0.0, converted.subtract(reference).getNorm(), 0.0);
    }

    @Test
    public void testFractionConverter() {
        Fraction[][] fData = {
                { new Fraction(1), new Fraction(2), new Fraction(3) },
                { new Fraction(2), new Fraction(5), new Fraction(3) },
                { new Fraction(1), new Fraction(0), new Fraction(8) }
        };
        FieldMatrix<Fraction> m = new Array2DRowFieldMatrix(fData, false);
        RealMatrix converted = MatrixUtils.fractionMatrixToRealMatrix(m);
        RealMatrix reference = new Array2DRowRealMatrix(testData, false);
        Assert.assertEquals(0.0, converted.subtract(reference).getNorm(), 0.0);
    }

    public static final Fraction[][] asFraction(double[][] data) {
        Fraction d[][] = new Fraction[data.length][];
        try {
            for (int i = 0; i < data.length; ++i) {
                double[] dataI = data[i];
                Fraction[] dI  = new Fraction[dataI.length];
                for (int j = 0; j < dataI.length; ++j) {
                    dI[j] = new Fraction(dataI[j]);
                }
                d[i] = dI;
            }
        } catch (FractionConversionException fce) {
            Assert.fail(fce.getMessage());
        }
        return d;
    }

    public static final Fraction[] asFraction(double[] data) {
        Fraction d[] = new Fraction[data.length];
        try {
            for (int i = 0; i < data.length; ++i) {
                d[i] = new Fraction(data[i]);
            }
        } catch (FractionConversionException fce) {
            Assert.fail(fce.getMessage());
        }
        return d;
    }

    @Test
    public void testSolveLowerTriangularSystem(){
        RealMatrix rm = new Array2DRowRealMatrix(
                new double[][] { {2,0,0,0 }, { 1,1,0,0 }, { 3,3,3,0 }, { 3,3,3,4 } },
                       false);
        RealVector b = new ArrayRealVector(new double[] { 2,3,4,8 }, false);
        MatrixUtils.solveLowerTriangularSystem(rm, b);
        TestUtils.assertEquals( new double[]{1,2,-1.66666666666667, 1.0}  , b.toArray() , 1.0e-12);
    }


    /*
     * Taken from R manual http://stat.ethz.ch/R-manual/R-patched/library/base/html/backsolve.html
     */
    @Test
    public void testSolveUpperTriangularSystem(){
        RealMatrix rm = new Array2DRowRealMatrix(
                new double[][] { {1,2,3 }, { 0,1,1 }, { 0,0,2 } },
                       false);
        RealVector b = new ArrayRealVector(new double[] { 8,4,2 }, false);
        MatrixUtils.solveUpperTriangularSystem(rm, b);
        TestUtils.assertEquals( new double[]{-1,3,1}  , b.toArray() , 1.0e-12);
    }

    /**
     * This test should probably be replaced by one that could show
     * whether this algorithm can sometimes perform better (precision- or
     * performance-wise) than the direct inversion of the whole matrix.
     */
    @Test
    public void testBlockInverse() {
        final double[][] data = {
            { -1, 0, 123, 4 },
            { -56, 78.9, -0.1, -23.4 },
            { 5.67, 8, -9, 1011 },
            { 12, 345, -67.8, 9 },
        };

        final RealMatrix m = new Array2DRowRealMatrix(data);
        final int len = data.length;
        final double tol = 1e-14;

        for (int splitIndex = 0; splitIndex < 3; splitIndex++) {
            final RealMatrix mInv = MatrixUtils.blockInverse(m, splitIndex);
            final RealMatrix id = m.multiply(mInv);

            // Check that we recovered the identity matrix.
            for (int i = 0; i < len; i++) {
                for (int j = 0; j < len; j++) {
                    final double entry = id.getEntry(i, j);
                    if (i == j) {
                        Assert.assertEquals("[" + i + "][" + j + "]",
                                            1, entry, tol);
                    } else {
                        Assert.assertEquals("[" + i + "][" + j + "]",
                                            0, entry, tol);
                    }
                }
            }
        }
    }

    @Test(expected=SingularMatrixException.class)
    public void testBlockInverseNonInvertible() {
        final double[][] data = {
            { -1, 0, 123, 4 },
            { -56, 78.9, -0.1, -23.4 },
            { 5.67, 8, -9, 1011 },
            { 5.67, 8, -9, 1011 },
        };

        MatrixUtils.blockInverse(new Array2DRowRealMatrix(data), 2);
    }

    @Test
    public void testIsSymmetric() {
        final double eps = Math.ulp(1d);

        final double[][] dataSym = {
            { 1, 2, 3 },
            { 2, 2, 5 },
            { 3, 5, 6 },
        };
        Assert.assertTrue(MatrixUtils.isSymmetric(MatrixUtils.createRealMatrix(dataSym), eps));

        final double[][] dataNonSym = {
            { 1, 2, -3 },
            { 2, 2, 5 },
            { 3, 5, 6 },
        };
        Assert.assertFalse(MatrixUtils.isSymmetric(MatrixUtils.createRealMatrix(dataNonSym), eps));
    }

    @Test
    public void testIsSymmetricTolerance() {
        final double eps = 1e-4;

        final double[][] dataSym1 = {
            { 1,   1, 1.00009 },
            { 1,   1, 1       },
            { 1.0, 1, 1       },
        };
        Assert.assertTrue(MatrixUtils.isSymmetric(MatrixUtils.createRealMatrix(dataSym1), eps));
        final double[][] dataSym2 = {
            { 1,   1, 0.99990 },
            { 1,   1, 1       },
            { 1.0, 1, 1       },
        };
        Assert.assertTrue(MatrixUtils.isSymmetric(MatrixUtils.createRealMatrix(dataSym2), eps));

        final double[][] dataNonSym1 = {
            { 1,   1, 1.00011 },
            { 1,   1, 1       },
            { 1.0, 1, 1       },
        };
        Assert.assertFalse(MatrixUtils.isSymmetric(MatrixUtils.createRealMatrix(dataNonSym1), eps));
        final double[][] dataNonSym2 = {
            { 1,   1, 0.99989 },
            { 1,   1, 1       },
            { 1.0, 1, 1       },
        };
        Assert.assertFalse(MatrixUtils.isSymmetric(MatrixUtils.createRealMatrix(dataNonSym2), eps));
    }

    @Test
    public void testCheckSymmetric1() {
        final double[][] dataSym = {
            { 1, 2, 3 },
            { 2, 2, 5 },
            { 3, 5, 6 },
        };
        MatrixUtils.checkSymmetric(MatrixUtils.createRealMatrix(dataSym), Math.ulp(1d));
    }

    @Test(expected=NonSymmetricMatrixException.class)
    public void testCheckSymmetric2() {
        final double[][] dataNonSym = {
            { 1, 2, -3 },
            { 2, 2, 5 },
            { 3, 5, 6 },
        };
        MatrixUtils.checkSymmetric(MatrixUtils.createRealMatrix(dataNonSym), Math.ulp(1d));
    }

    @Test(expected=SingularMatrixException.class)
    public void testInverseSingular() {
        RealMatrix m = MatrixUtils.createRealMatrix(testData3x3Singular);
        MatrixUtils.inverse(m);
    }

    @Test(expected=NonSquareMatrixException.class)
    public void testInverseNonSquare() {
        RealMatrix m = MatrixUtils.createRealMatrix(testData3x4);
        MatrixUtils.inverse(m);
    }

    @Test
    public void testInverseDiagonalMatrix() {
        final double[] data = { 1, 2, 3 };
        final RealMatrix m = new DiagonalMatrix(data);
        final RealMatrix inverse = MatrixUtils.inverse(m);

        final RealMatrix result = m.multiply(inverse);
        TestUtils.assertEquals("MatrixUtils.inverse() returns wrong result",
                MatrixUtils.createRealIdentityMatrix(data.length), result, Math.ulp(1d));
    }

    @Test
    public void testInverseRealMatrix() {
        RealMatrix m = MatrixUtils.createRealMatrix(testData);
        final RealMatrix inverse = MatrixUtils.inverse(m);

        final RealMatrix result = m.multiply(inverse);
        TestUtils.assertEquals("MatrixUtils.inverse() returns wrong result",
                MatrixUtils.createRealIdentityMatrix(testData.length), result, 1e-12);
    }

}

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