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Java example source code file (Array2DRowRealMatrixTest.java)

This example Java source code file (Array2DRowRealMatrixTest.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.

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Java - Java tags/keywords

array2drowrealmatrix, arrayrealvector, expecting, getvisitor, mathillegalargumentexception, matrixdimensionmismatchexception, nodataexception, nonsquarematrixexception, numberistoosmallexception, outofrangeexception, realmatrix, realvector, setvisitor, test

The Array2DRowRealMatrixTest.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.junit.Test;
import org.junit.Assert;

import org.apache.commons.math3.TestUtils;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.exception.NoDataException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.MathIllegalStateException;

/**
 * Test cases for the {@link Array2DRowRealMatrix} class.
 *
 */

public final class Array2DRowRealMatrixTest {

    // 3 x 3 identity matrix
    protected double[][] id = { {1d,0d,0d}, {0d,1d,0d}, {0d,0d,1d} };

    // Test data for group operations
    protected double[][] testData = { {1d,2d,3d}, {2d,5d,3d}, {1d,0d,8d} };
    protected double[][] testDataLU = {{2d, 5d, 3d}, {.5d, -2.5d, 6.5d}, {0.5d, 0.2d, .2d}};
    protected double[][] testDataPlus2 = { {3d,4d,5d}, {4d,7d,5d}, {3d,2d,10d} };
    protected double[][] testDataMinus = { {-1d,-2d,-3d}, {-2d,-5d,-3d},
       {-1d,0d,-8d} };
    protected double[] testDataRow1 = {1d,2d,3d};
    protected double[] testDataCol3 = {3d,3d,8d};
    protected double[][] testDataInv =
        { {-40d,16d,9d}, {13d,-5d,-3d}, {5d,-2d,-1d} };
    protected double[] preMultTest = {8,12,33};
    protected double[][] testData2 ={ {1d,2d,3d}, {2d,5d,3d}};
    protected double[][] testData2T = { {1d,2d}, {2d,5d}, {3d,3d}};
    protected double[][] testDataPlusInv =
        { {-39d,18d,12d}, {15d,0d,0d}, {6d,-2d,7d} };

    // lu decomposition tests
    protected double[][] luData = { {2d,3d,3d}, {0d,5d,7d}, {6d,9d,8d} };
    protected double[][] luDataLUDecomposition = { {6d,9d,8d}, {0d,5d,7d},
            {0.33333333333333,0d,0.33333333333333} };

    // singular matrices
    protected double[][] singular = { {2d,3d}, {2d,3d} };
    protected double[][] bigSingular = {{1d,2d,3d,4d}, {2d,5d,3d,4d},
        {7d,3d,256d,1930d}, {3d,7d,6d,8d}}; // 4th row = 1st + 2nd
    protected double[][] detData = { {1d,2d,3d}, {4d,5d,6d}, {7d,8d,10d} };
    protected double[][] detData2 = { {1d, 3d}, {2d, 4d}};

    // vectors
    protected double[] testVector = {1,2,3};
    protected double[] testVector2 = {1,2,3,4};

    // submatrix accessor tests
    protected double[][] subTestData = {{1, 2, 3, 4}, {1.5, 2.5, 3.5, 4.5},
            {2, 4, 6, 8}, {4, 5, 6, 7}};
    // array selections
    protected double[][] subRows02Cols13 = { {2, 4}, {4, 8}};
    protected double[][] subRows03Cols12 = { {2, 3}, {5, 6}};
    protected double[][] subRows03Cols123 = { {2, 3, 4} , {5, 6, 7}};
    // effective permutations
    protected double[][] subRows20Cols123 = { {4, 6, 8} , {2, 3, 4}};
    protected double[][] subRows31Cols31 = {{7, 5}, {4.5, 2.5}};
    // contiguous ranges
    protected double[][] subRows01Cols23 = {{3,4} , {3.5, 4.5}};
    protected double[][] subRows23Cols00 = {{2} , {4}};
    protected double[][] subRows00Cols33 = {{4}};
    // row matrices
    protected double[][] subRow0 = {{1,2,3,4}};
    protected double[][] subRow3 = {{4,5,6,7}};
    // column matrices
    protected double[][] subColumn1 = {{2}, {2.5}, {4}, {5}};
    protected double[][] subColumn3 = {{4}, {4.5}, {8}, {7}};

    // tolerances
    protected double entryTolerance = 10E-16;
    protected double normTolerance = 10E-14;
    protected double powerTolerance = 10E-16;

    /** test dimensions */
    @Test
    public void testDimensions() {
        Array2DRowRealMatrix m = new Array2DRowRealMatrix(testData);
        Array2DRowRealMatrix m2 = new Array2DRowRealMatrix(testData2);
        Assert.assertEquals("testData row dimension",3,m.getRowDimension());
        Assert.assertEquals("testData column dimension",3,m.getColumnDimension());
        Assert.assertTrue("testData is square",m.isSquare());
        Assert.assertEquals("testData2 row dimension",m2.getRowDimension(),2);
        Assert.assertEquals("testData2 column dimension",m2.getColumnDimension(),3);
        Assert.assertTrue("testData2 is not square",!m2.isSquare());
    }

    /** test copy functions */
    @Test
    public void testCopyFunctions() {
        Array2DRowRealMatrix m1 = new Array2DRowRealMatrix(testData);
        Array2DRowRealMatrix m2 = new Array2DRowRealMatrix(m1.getData());
        Assert.assertEquals(m2,m1);
        Array2DRowRealMatrix m3 = new Array2DRowRealMatrix(testData);
        Array2DRowRealMatrix m4 = new Array2DRowRealMatrix(m3.getData(), false);
        Assert.assertEquals(m4,m3);
    }

    /** test add */
    @Test
    public void testAdd() {
        Array2DRowRealMatrix m = new Array2DRowRealMatrix(testData);
        Array2DRowRealMatrix mInv = new Array2DRowRealMatrix(testDataInv);
        RealMatrix mPlusMInv = m.add(mInv);
        double[][] sumEntries = mPlusMInv.getData();
        for (int row = 0; row < m.getRowDimension(); row++) {
            for (int col = 0; col < m.getColumnDimension(); col++) {
                Assert.assertEquals("sum entry entry",
                    testDataPlusInv[row][col],sumEntries[row][col],
                        entryTolerance);
            }
        }
    }

    /** test add failure */
    @Test
    public void testAddFail() {
        Array2DRowRealMatrix m = new Array2DRowRealMatrix(testData);
        Array2DRowRealMatrix m2 = new Array2DRowRealMatrix(testData2);
        try {
            m.add(m2);
            Assert.fail("MathIllegalArgumentException expected");
        } catch (MathIllegalArgumentException ex) {
            // ignored
        }
    }

    /** test norm */
    @Test
    public void testNorm() {
        Array2DRowRealMatrix m = new Array2DRowRealMatrix(testData);
        Array2DRowRealMatrix m2 = new Array2DRowRealMatrix(testData2);
        Assert.assertEquals("testData norm",14d,m.getNorm(),entryTolerance);
        Assert.assertEquals("testData2 norm",7d,m2.getNorm(),entryTolerance);
    }

    /** test Frobenius norm */
    @Test
    public void testFrobeniusNorm() {
        Array2DRowRealMatrix m = new Array2DRowRealMatrix(testData);
        Array2DRowRealMatrix m2 = new Array2DRowRealMatrix(testData2);
        Assert.assertEquals("testData Frobenius norm", FastMath.sqrt(117.0), m.getFrobeniusNorm(), entryTolerance);
        Assert.assertEquals("testData2 Frobenius norm", FastMath.sqrt(52.0), m2.getFrobeniusNorm(), entryTolerance);
    }

     /** test m-n = m + -n */
    @Test
    public void testPlusMinus() {
        Array2DRowRealMatrix m = new Array2DRowRealMatrix(testData);
        Array2DRowRealMatrix m2 = new Array2DRowRealMatrix(testDataInv);
        TestUtils.assertEquals("m-n = m + -n",m.subtract(m2),
            m2.scalarMultiply(-1d).add(m),entryTolerance);
        try {
            m.subtract(new Array2DRowRealMatrix(testData2));
            Assert.fail("Expecting illegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // ignored
        }
    }

    /** test multiply */
    @Test
    public void testMultiply() {
        Array2DRowRealMatrix m = new Array2DRowRealMatrix(testData);
        Array2DRowRealMatrix mInv = new Array2DRowRealMatrix(testDataInv);
        Array2DRowRealMatrix identity = new Array2DRowRealMatrix(id);
        Array2DRowRealMatrix m2 = new Array2DRowRealMatrix(testData2);
        TestUtils.assertEquals("inverse multiply",m.multiply(mInv),
            identity,entryTolerance);
        TestUtils.assertEquals("inverse multiply",mInv.multiply(m),
            identity,entryTolerance);
        TestUtils.assertEquals("identity multiply",m.multiply(identity),
            m,entryTolerance);
        TestUtils.assertEquals("identity multiply",identity.multiply(mInv),
            mInv,entryTolerance);
        TestUtils.assertEquals("identity multiply",m2.multiply(identity),
            m2,entryTolerance);
        try {
            m.multiply(new Array2DRowRealMatrix(bigSingular));
            Assert.fail("Expecting illegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // ignored
        }
    }

    //Additional Test for Array2DRowRealMatrixTest.testMultiply

    private double[][] d3 = new double[][] {{1,2,3,4},{5,6,7,8}};
    private double[][] d4 = new double[][] {{1},{2},{3},{4}};
    private double[][] d5 = new double[][] {{30},{70}};

    @Test
    public void testMultiply2() {
       RealMatrix m3 = new Array2DRowRealMatrix(d3);
       RealMatrix m4 = new Array2DRowRealMatrix(d4);
       RealMatrix m5 = new Array2DRowRealMatrix(d5);
       TestUtils.assertEquals("m3*m4=m5", m3.multiply(m4), m5, entryTolerance);
   }

    @Test
    public void testPower() {
        Array2DRowRealMatrix m = new Array2DRowRealMatrix(testData);
        Array2DRowRealMatrix mInv = new Array2DRowRealMatrix(testDataInv);
        Array2DRowRealMatrix mPlusInv = new Array2DRowRealMatrix(testDataPlusInv);
        Array2DRowRealMatrix identity = new Array2DRowRealMatrix(id);

        TestUtils.assertEquals("m^0", m.power(0),
            identity, entryTolerance);
        TestUtils.assertEquals("mInv^0", mInv.power(0),
                identity, entryTolerance);
        TestUtils.assertEquals("mPlusInv^0", mPlusInv.power(0),
                identity, entryTolerance);

        TestUtils.assertEquals("m^1", m.power(1),
                m, entryTolerance);
        TestUtils.assertEquals("mInv^1", mInv.power(1),
                mInv, entryTolerance);
        TestUtils.assertEquals("mPlusInv^1", mPlusInv.power(1),
                mPlusInv, entryTolerance);

        RealMatrix C1 = m.copy();
        RealMatrix C2 = mInv.copy();
        RealMatrix C3 = mPlusInv.copy();

        for (int i = 2; i <= 10; ++i) {
            C1 = C1.multiply(m);
            C2 = C2.multiply(mInv);
            C3 = C3.multiply(mPlusInv);

            TestUtils.assertEquals("m^" + i, m.power(i),
                    C1, entryTolerance);
            TestUtils.assertEquals("mInv^" + i, mInv.power(i),
                    C2, entryTolerance);
            TestUtils.assertEquals("mPlusInv^" + i, mPlusInv.power(i),
                    C3, entryTolerance);
        }

        try {
            Array2DRowRealMatrix mNotSquare = new Array2DRowRealMatrix(testData2T);
            mNotSquare.power(2);
            Assert.fail("Expecting NonSquareMatrixException");
        } catch (NonSquareMatrixException ex) {
            // ignored
        }

        try {
            m.power(-1);
            Assert.fail("Expecting IllegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
    }

    /** test trace */
    @Test
    public void testTrace() {
        RealMatrix m = new Array2DRowRealMatrix(id);
        Assert.assertEquals("identity trace",3d,m.getTrace(),entryTolerance);
        m = new Array2DRowRealMatrix(testData2);
        try {
            m.getTrace();
            Assert.fail("Expecting NonSquareMatrixException");
        } catch (NonSquareMatrixException ex) {
            // ignored
        }
    }

    /** test sclarAdd */
    @Test
    public void testScalarAdd() {
        RealMatrix m = new Array2DRowRealMatrix(testData);
        TestUtils.assertEquals("scalar add",new Array2DRowRealMatrix(testDataPlus2),
            m.scalarAdd(2d),entryTolerance);
    }

    /** test operate */
    @Test
    public void testOperate() {
        RealMatrix m = new Array2DRowRealMatrix(id);
        TestUtils.assertEquals("identity operate", testVector,
                    m.operate(testVector), entryTolerance);
        TestUtils.assertEquals("identity operate", testVector,
                    m.operate(new ArrayRealVector(testVector)).toArray(), entryTolerance);
        m = new Array2DRowRealMatrix(bigSingular);
        try {
            m.operate(testVector);
            Assert.fail("Expecting illegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // ignored
        }
    }

    /** test issue MATH-209 */
    @Test
    public void testMath209() {
        RealMatrix a = new Array2DRowRealMatrix(new double[][] {
                { 1, 2 }, { 3, 4 }, { 5, 6 }
        }, false);
        double[] b = a.operate(new double[] { 1, 1 });
        Assert.assertEquals(a.getRowDimension(), b.length);
        Assert.assertEquals( 3.0, b[0], 1.0e-12);
        Assert.assertEquals( 7.0, b[1], 1.0e-12);
        Assert.assertEquals(11.0, b[2], 1.0e-12);
    }

    /** test transpose */
    @Test
    public void testTranspose() {
        RealMatrix m = new Array2DRowRealMatrix(testData);
        RealMatrix mIT = new LUDecomposition(m).getSolver().getInverse().transpose();
        RealMatrix mTI = new LUDecomposition(m.transpose()).getSolver().getInverse();
        TestUtils.assertEquals("inverse-transpose", mIT, mTI, normTolerance);
        m = new Array2DRowRealMatrix(testData2);
        RealMatrix mt = new Array2DRowRealMatrix(testData2T);
        TestUtils.assertEquals("transpose",mt,m.transpose(),normTolerance);
    }

    /** test preMultiply by vector */
    @Test
    public void testPremultiplyVector() {
        RealMatrix m = new Array2DRowRealMatrix(testData);
        TestUtils.assertEquals("premultiply", m.preMultiply(testVector),
                    preMultTest, normTolerance);
        TestUtils.assertEquals("premultiply", m.preMultiply(new ArrayRealVector(testVector).toArray()),
                    preMultTest, normTolerance);
        m = new Array2DRowRealMatrix(bigSingular);
        try {
            m.preMultiply(testVector);
            Assert.fail("expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // ignored
        }
    }

    @Test
    public void testPremultiply() {
        RealMatrix m3 = new Array2DRowRealMatrix(d3);
        RealMatrix m4 = new Array2DRowRealMatrix(d4);
        RealMatrix m5 = new Array2DRowRealMatrix(d5);
        TestUtils.assertEquals("m3*m4=m5", m4.preMultiply(m3), m5, entryTolerance);

        Array2DRowRealMatrix m = new Array2DRowRealMatrix(testData);
        Array2DRowRealMatrix mInv = new Array2DRowRealMatrix(testDataInv);
        Array2DRowRealMatrix identity = new Array2DRowRealMatrix(id);
        TestUtils.assertEquals("inverse multiply",m.preMultiply(mInv),
                identity,entryTolerance);
        TestUtils.assertEquals("inverse multiply",mInv.preMultiply(m),
                identity,entryTolerance);
        TestUtils.assertEquals("identity multiply",m.preMultiply(identity),
                m,entryTolerance);
        TestUtils.assertEquals("identity multiply",identity.preMultiply(mInv),
                mInv,entryTolerance);
        try {
            m.preMultiply(new Array2DRowRealMatrix(bigSingular));
            Assert.fail("Expecting illegalArgumentException");
        } catch (MathIllegalArgumentException ex) {
            // ignored
        }
    }

    @Test
    public void testGetVectors() {
        RealMatrix m = new Array2DRowRealMatrix(testData);
        TestUtils.assertEquals("get row",m.getRow(0),testDataRow1,entryTolerance);
        TestUtils.assertEquals("get col",m.getColumn(2),testDataCol3,entryTolerance);
        try {
            m.getRow(10);
            Assert.fail("expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // ignored
        }
        try {
            m.getColumn(-1);
            Assert.fail("expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // ignored
        }
    }

    @Test
    public void testGetEntry() {
        RealMatrix m = new Array2DRowRealMatrix(testData);
        Assert.assertEquals("get entry",m.getEntry(0,1),2d,entryTolerance);
        try {
            m.getEntry(10, 4);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
    }

    /** test examples in user guide */
    @Test
    public void testExamples() {
        // Create a real matrix with two rows and three columns
        double[][] matrixData = { {1d,2d,3d}, {2d,5d,3d}};
        RealMatrix m = new Array2DRowRealMatrix(matrixData);
        // One more with three rows, two columns
        double[][] matrixData2 = { {1d,2d}, {2d,5d}, {1d, 7d}};
        RealMatrix n = new Array2DRowRealMatrix(matrixData2);
        // Now multiply m by n
        RealMatrix p = m.multiply(n);
        Assert.assertEquals(2, p.getRowDimension());
        Assert.assertEquals(2, p.getColumnDimension());
        // Invert p
        RealMatrix pInverse = new LUDecomposition(p).getSolver().getInverse();
        Assert.assertEquals(2, pInverse.getRowDimension());
        Assert.assertEquals(2, pInverse.getColumnDimension());

        // Solve example
        double[][] coefficientsData = {{2, 3, -2}, {-1, 7, 6}, {4, -3, -5}};
        RealMatrix coefficients = new Array2DRowRealMatrix(coefficientsData);
        RealVector constants = new ArrayRealVector(new double[]{1, -2, 1}, false);
        RealVector solution = new LUDecomposition(coefficients).getSolver().solve(constants);
        final double cst0 = constants.getEntry(0);
        final double cst1 = constants.getEntry(1);
        final double cst2 = constants.getEntry(2);
        final double sol0 = solution.getEntry(0);
        final double sol1 = solution.getEntry(1);
        final double sol2 = solution.getEntry(2);
        Assert.assertEquals(2 * sol0 + 3 * sol1 -2 * sol2, cst0, 1E-12);
        Assert.assertEquals(-1 * sol0 + 7 * sol1 + 6 * sol2, cst1, 1E-12);
        Assert.assertEquals(4 * sol0 - 3 * sol1 -5 * sol2, cst2, 1E-12);
    }

    // test submatrix accessors
    @Test
    public void testGetSubMatrix() {
        RealMatrix m = new Array2DRowRealMatrix(subTestData);
        checkGetSubMatrix(m, subRows23Cols00,  2 , 3 , 0, 0, false);
        checkGetSubMatrix(m, subRows00Cols33,  0 , 0 , 3, 3, false);
        checkGetSubMatrix(m, subRows01Cols23,  0 , 1 , 2, 3, false);
        checkGetSubMatrix(m, subRows02Cols13,  new int[] { 0, 2 }, new int[] { 1, 3 },    false);
        checkGetSubMatrix(m, subRows03Cols12,  new int[] { 0, 3 }, new int[] { 1, 2 },    false);
        checkGetSubMatrix(m, subRows03Cols123, new int[] { 0, 3 }, new int[] { 1, 2, 3 }, false);
        checkGetSubMatrix(m, subRows20Cols123, new int[] { 2, 0 }, new int[] { 1, 2, 3 }, false);
        checkGetSubMatrix(m, subRows31Cols31,  new int[] { 3, 1 }, new int[] { 3, 1 },    false);
        checkGetSubMatrix(m, subRows31Cols31,  new int[] { 3, 1 }, new int[] { 3, 1 },    false);
        checkGetSubMatrix(m, null,  1, 0, 2, 4, true);
        checkGetSubMatrix(m, null, -1, 1, 2, 2, true);
        checkGetSubMatrix(m, null,  1, 0, 2, 2, true);
        checkGetSubMatrix(m, null,  1, 0, 2, 4, true);
        checkGetSubMatrix(m, null, new int[] {},    new int[] { 0 }, true);
        checkGetSubMatrix(m, null, new int[] { 0 }, new int[] { 4 }, true);
    }

    private void checkGetSubMatrix(RealMatrix m, double[][] reference,
                                   int startRow, int endRow, int startColumn, int endColumn,
                                   boolean mustFail) {
        try {
            RealMatrix sub = m.getSubMatrix(startRow, endRow, startColumn, endColumn);
            Assert.assertEquals(new Array2DRowRealMatrix(reference), sub);
            if (mustFail) {
                Assert.fail("Expecting OutOfRangeException or NumberIsTooSmallException or NoDataException");
            }
        } catch (OutOfRangeException e) {
            if (!mustFail) {
                throw e;
            }
        } catch (NumberIsTooSmallException e) {
            if (!mustFail) {
                throw e;
            }
        } catch (NoDataException e) {
            if (!mustFail) {
                throw e;
            }
        }
    }

    private void checkGetSubMatrix(RealMatrix m, double[][] reference,
                                   int[] selectedRows, int[] selectedColumns,
                                   boolean mustFail) {
        try {
            RealMatrix sub = m.getSubMatrix(selectedRows, selectedColumns);
            Assert.assertEquals(new Array2DRowRealMatrix(reference), sub);
            if (mustFail) {
                Assert.fail("Expecting OutOfRangeException or NumberIsTooSmallException or NoDataException");
            }
        } catch (OutOfRangeException e) {
            if (!mustFail) {
                throw e;
            }
        } catch (NumberIsTooSmallException e) {
            if (!mustFail) {
                throw e;
            }
        } catch (NoDataException e) {
            if (!mustFail) {
                throw e;
            }
        }
    }

    @Test
    public void testCopySubMatrix() {
        RealMatrix m = new Array2DRowRealMatrix(subTestData);
        checkCopy(m, subRows23Cols00,  2 , 3 , 0, 0, false);
        checkCopy(m, subRows00Cols33,  0 , 0 , 3, 3, false);
        checkCopy(m, subRows01Cols23,  0 , 1 , 2, 3, false);
        checkCopy(m, subRows02Cols13,  new int[] { 0, 2 }, new int[] { 1, 3 },    false);
        checkCopy(m, subRows03Cols12,  new int[] { 0, 3 }, new int[] { 1, 2 },    false);
        checkCopy(m, subRows03Cols123, new int[] { 0, 3 }, new int[] { 1, 2, 3 }, false);
        checkCopy(m, subRows20Cols123, new int[] { 2, 0 }, new int[] { 1, 2, 3 }, false);
        checkCopy(m, subRows31Cols31,  new int[] { 3, 1 }, new int[] { 3, 1 },    false);
        checkCopy(m, subRows31Cols31,  new int[] { 3, 1 }, new int[] { 3, 1 },    false);

        checkCopy(m, null,  1, 0, 2, 4, true);
        checkCopy(m, null, -1, 1, 2, 2, true);
        checkCopy(m, null,  1, 0, 2, 2, true);
        checkCopy(m, null,  1, 0, 2, 4, true);
        checkCopy(m, null, new int[] {},    new int[] { 0 }, true);
        checkCopy(m, null, new int[] { 0 }, new int[] { 4 }, true);

        // rectangular check
        double[][] copy = new double[][] { { 0, 0, 0 }, { 0, 0 } };
        checkCopy(m, copy, 0, 1, 0, 2, true);
        checkCopy(m, copy, new int[] { 0, 1 }, new int[] { 0, 1, 2 }, true);
    }

    private void checkCopy(RealMatrix m, double[][] reference,
                           int startRow, int endRow, int startColumn, int endColumn,
                           boolean mustFail) {
        try {
            double[][] sub = (reference == null) ?
                             new double[1][1] : createIdenticalCopy(reference);
            m.copySubMatrix(startRow, endRow, startColumn, endColumn, sub);
            Assert.assertEquals(new Array2DRowRealMatrix(reference), new Array2DRowRealMatrix(sub));
            if (mustFail) {
                Assert.fail("Expecting OutOfRangeException or NumberIsTooSmallException or NoDataException");
            }
        } catch (OutOfRangeException e) {
            if (!mustFail) {
                throw e;
            }
        } catch (NumberIsTooSmallException e) {
            if (!mustFail) {
                throw e;
            }
        } catch (NoDataException e) {
            if (!mustFail) {
                throw e;
            }
        } catch (MatrixDimensionMismatchException e) {
            if (!mustFail) {
                throw e;
            }
        }
    }

    private void checkCopy(RealMatrix m, double[][] reference,
                           int[] selectedRows, int[] selectedColumns,
                           boolean mustFail) {
        try {
            double[][] sub = (reference == null) ?
                    new double[1][1] : createIdenticalCopy(reference);
            m.copySubMatrix(selectedRows, selectedColumns, sub);
            Assert.assertEquals(new Array2DRowRealMatrix(reference), new Array2DRowRealMatrix(sub));
            if (mustFail) {
                Assert.fail("Expecting OutOfRangeException or NumberIsTooSmallException or NoDataException");
            }
        } catch (OutOfRangeException e) {
            if (!mustFail) {
                throw e;
            }
        } catch (NumberIsTooSmallException e) {
            if (!mustFail) {
                throw e;
            }
        } catch (NoDataException e) {
            if (!mustFail) {
                throw e;
            }
        } catch (MatrixDimensionMismatchException e) {
            if (!mustFail) {
                throw e;
            }
        }
    }

    private double[][] createIdenticalCopy(final double[][] matrix) {
        final double[][] matrixCopy = new double[matrix.length][];
        for (int i = 0; i < matrixCopy.length; i++) {
            matrixCopy[i] = new double[matrix[i].length];
        }
        return matrixCopy;
    }

    @Test
    public void testGetRowMatrix() {
        RealMatrix m = new Array2DRowRealMatrix(subTestData);
        RealMatrix mRow0 = new Array2DRowRealMatrix(subRow0);
        RealMatrix mRow3 = new Array2DRowRealMatrix(subRow3);
        Assert.assertEquals("Row0", mRow0,
                m.getRowMatrix(0));
        Assert.assertEquals("Row3", mRow3,
                m.getRowMatrix(3));
        try {
            m.getRowMatrix(-1);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
        try {
            m.getRowMatrix(4);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
    }

    @Test
    public void testSetRowMatrix() {
        RealMatrix m = new Array2DRowRealMatrix(subTestData);
        RealMatrix mRow3 = new Array2DRowRealMatrix(subRow3);
        Assert.assertNotSame(mRow3, m.getRowMatrix(0));
        m.setRowMatrix(0, mRow3);
        Assert.assertEquals(mRow3, m.getRowMatrix(0));
        try {
            m.setRowMatrix(-1, mRow3);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
        try {
            m.setRowMatrix(0, m);
            Assert.fail("Expecting MatrixDimensionMismatchException");
        } catch (MatrixDimensionMismatchException ex) {
            // expected
        }
    }

    @Test
    public void testGetColumnMatrix() {
        RealMatrix m = new Array2DRowRealMatrix(subTestData);
        RealMatrix mColumn1 = new Array2DRowRealMatrix(subColumn1);
        RealMatrix mColumn3 = new Array2DRowRealMatrix(subColumn3);
        Assert.assertEquals("Column1", mColumn1,
                m.getColumnMatrix(1));
        Assert.assertEquals("Column3", mColumn3,
                m.getColumnMatrix(3));
        try {
            m.getColumnMatrix(-1);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
        try {
            m.getColumnMatrix(4);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
    }

    @Test
    public void testSetColumnMatrix() {
        RealMatrix m = new Array2DRowRealMatrix(subTestData);
        RealMatrix mColumn3 = new Array2DRowRealMatrix(subColumn3);
        Assert.assertNotSame(mColumn3, m.getColumnMatrix(1));
        m.setColumnMatrix(1, mColumn3);
        Assert.assertEquals(mColumn3, m.getColumnMatrix(1));
        try {
            m.setColumnMatrix(-1, mColumn3);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
        try {
            m.setColumnMatrix(0, m);
            Assert.fail("Expecting MatrixDimensionMismatchException");
        } catch (MatrixDimensionMismatchException ex) {
            // expected
        }
    }

    @Test
    public void testGetRowVector() {
        RealMatrix m = new Array2DRowRealMatrix(subTestData);
        RealVector mRow0 = new ArrayRealVector(subRow0[0]);
        RealVector mRow3 = new ArrayRealVector(subRow3[0]);
        Assert.assertEquals("Row0", mRow0, m.getRowVector(0));
        Assert.assertEquals("Row3", mRow3, m.getRowVector(3));
        try {
            m.getRowVector(-1);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
        try {
            m.getRowVector(4);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
    }

    @Test
    public void testSetRowVector() {
        RealMatrix m = new Array2DRowRealMatrix(subTestData);
        RealVector mRow3 = new ArrayRealVector(subRow3[0]);
        Assert.assertNotSame(mRow3, m.getRowMatrix(0));
        m.setRowVector(0, mRow3);
        Assert.assertEquals(mRow3, m.getRowVector(0));
        try {
            m.setRowVector(-1, mRow3);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
        try {
            m.setRowVector(0, new ArrayRealVector(5));
            Assert.fail("Expecting MatrixDimensionMismatchException");
        } catch (MatrixDimensionMismatchException ex) {
            // expected
        }
    }

    @Test
    public void testGetColumnVector() {
        RealMatrix m = new Array2DRowRealMatrix(subTestData);
        RealVector mColumn1 = columnToVector(subColumn1);
        RealVector mColumn3 = columnToVector(subColumn3);
        Assert.assertEquals("Column1", mColumn1, m.getColumnVector(1));
        Assert.assertEquals("Column3", mColumn3, m.getColumnVector(3));
        try {
            m.getColumnVector(-1);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
        try {
            m.getColumnVector(4);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
    }

    @Test
    public void testSetColumnVector() {
        RealMatrix m = new Array2DRowRealMatrix(subTestData);
        RealVector mColumn3 = columnToVector(subColumn3);
        Assert.assertNotSame(mColumn3, m.getColumnVector(1));
        m.setColumnVector(1, mColumn3);
        Assert.assertEquals(mColumn3, m.getColumnVector(1));
        try {
            m.setColumnVector(-1, mColumn3);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
        try {
            m.setColumnVector(0, new ArrayRealVector(5));
            Assert.fail("Expecting MatrixDimensionMismatchException");
        } catch (MatrixDimensionMismatchException ex) {
            // expected
        }
    }

    private RealVector columnToVector(double[][] column) {
        double[] data = new double[column.length];
        for (int i = 0; i < data.length; ++i) {
            data[i] = column[i][0];
        }
        return new ArrayRealVector(data, false);
    }

    @Test
    public void testGetRow() {
        RealMatrix m = new Array2DRowRealMatrix(subTestData);
        checkArrays(subRow0[0], m.getRow(0));
        checkArrays(subRow3[0], m.getRow(3));
        try {
            m.getRow(-1);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
        try {
            m.getRow(4);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
    }

    @Test
    public void testSetRow() {
        RealMatrix m = new Array2DRowRealMatrix(subTestData);
        Assert.assertTrue(subRow3[0][0] != m.getRow(0)[0]);
        m.setRow(0, subRow3[0]);
        checkArrays(subRow3[0], m.getRow(0));
        try {
            m.setRow(-1, subRow3[0]);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
        try {
            m.setRow(0, new double[5]);
            Assert.fail("Expecting MatrixDimensionMismatchException");
        } catch (MatrixDimensionMismatchException ex) {
            // expected
        }
    }

    @Test
    public void testGetColumn() {
        RealMatrix m = new Array2DRowRealMatrix(subTestData);
        double[] mColumn1 = columnToArray(subColumn1);
        double[] mColumn3 = columnToArray(subColumn3);
        checkArrays(mColumn1, m.getColumn(1));
        checkArrays(mColumn3, m.getColumn(3));
        try {
            m.getColumn(-1);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
        try {
            m.getColumn(4);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
    }

    @Test
    public void testSetColumn() {
        RealMatrix m = new Array2DRowRealMatrix(subTestData);
        double[] mColumn3 = columnToArray(subColumn3);
        Assert.assertTrue(mColumn3[0] != m.getColumn(1)[0]);
        m.setColumn(1, mColumn3);
        checkArrays(mColumn3, m.getColumn(1));
        try {
            m.setColumn(-1, mColumn3);
            Assert.fail("Expecting OutOfRangeException");
        } catch (OutOfRangeException ex) {
            // expected
        }
        try {
            m.setColumn(0, new double[5]);
            Assert.fail("Expecting MatrixDimensionMismatchException");
        } catch (MatrixDimensionMismatchException ex) {
            // expected
        }
    }

    private double[] columnToArray(double[][] column) {
        double[] data = new double[column.length];
        for (int i = 0; i < data.length; ++i) {
            data[i] = column[i][0];
        }
        return data;
    }

    private void checkArrays(double[] expected, double[] actual) {
        Assert.assertEquals(expected.length, actual.length);
        for (int i = 0; i < expected.length; ++i) {
            Assert.assertEquals(expected[i], actual[i], 0);
        }
    }

    @Test
    public void testEqualsAndHashCode() {
        Array2DRowRealMatrix m = new Array2DRowRealMatrix(testData);
        Array2DRowRealMatrix m1 = (Array2DRowRealMatrix) m.copy();
        Array2DRowRealMatrix mt = (Array2DRowRealMatrix) m.transpose();
        Assert.assertTrue(m.hashCode() != mt.hashCode());
        Assert.assertEquals(m.hashCode(), m1.hashCode());
        Assert.assertEquals(m, m);
        Assert.assertEquals(m, m1);
        Assert.assertFalse(m.equals(null));
        Assert.assertFalse(m.equals(mt));
        Assert.assertFalse(m.equals(new Array2DRowRealMatrix(bigSingular)));
    }

    @Test
    public void testToString() {
        Array2DRowRealMatrix m = new Array2DRowRealMatrix(testData);
        Assert.assertEquals("Array2DRowRealMatrix{{1.0,2.0,3.0},{2.0,5.0,3.0},{1.0,0.0,8.0}}",
                m.toString());
        m = new Array2DRowRealMatrix();
        Assert.assertEquals("Array2DRowRealMatrix{}",
                m.toString());
    }

    @Test
    public void testSetSubMatrix() {
        Array2DRowRealMatrix m = new Array2DRowRealMatrix(testData);
        m.setSubMatrix(detData2,1,1);
        RealMatrix expected = MatrixUtils.createRealMatrix
            (new double[][] {{1.0,2.0,3.0},{2.0,1.0,3.0},{1.0,2.0,4.0}});
        Assert.assertEquals(expected, m);

        m.setSubMatrix(detData2,0,0);
        expected = MatrixUtils.createRealMatrix
            (new double[][] {{1.0,3.0,3.0},{2.0,4.0,3.0},{1.0,2.0,4.0}});
        Assert.assertEquals(expected, m);

        m.setSubMatrix(testDataPlus2,0,0);
        expected = MatrixUtils.createRealMatrix
            (new double[][] {{3.0,4.0,5.0},{4.0,7.0,5.0},{3.0,2.0,10.0}});
        Assert.assertEquals(expected, m);

        // dimension overflow
        try {
            m.setSubMatrix(testData,1,1);
            Assert.fail("expecting OutOfRangeException");
        } catch (OutOfRangeException e) {
            // expected
        }
        // dimension underflow
        try {
            m.setSubMatrix(testData,-1,1);
            Assert.fail("expecting OutOfRangeException");
        } catch (OutOfRangeException e) {
            // expected
        }
        try {
            m.setSubMatrix(testData,1,-1);
            Assert.fail("expecting OutOfRangeException");
        } catch (OutOfRangeException e) {
            // expected
        }

        // null
        try {
            m.setSubMatrix(null,1,1);
            Assert.fail("expecting NullArgumentException");
        } catch (NullArgumentException e) {
            // expected
        }
        Array2DRowRealMatrix m2 = new Array2DRowRealMatrix();
        try {
            m2.setSubMatrix(testData,0,1);
            Assert.fail("expecting MathIllegalStateException");
        } catch (MathIllegalStateException e) {
            // expected
        }
        try {
            m2.setSubMatrix(testData,1,0);
            Assert.fail("expecting MathIllegalStateException");
        } catch (MathIllegalStateException e) {
            // expected
        }

        // ragged
        try {
            m.setSubMatrix(new double[][] {{1}, {2, 3}}, 0, 0);
            Assert.fail("expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException e) {
            // expected
        }

        // empty
        try {
            m.setSubMatrix(new double[][] {{}}, 0, 0);
            Assert.fail("expecting MathIllegalArgumentException");
        } catch (MathIllegalArgumentException e) {
            // expected
        }
    }

    @Test
    public void testWalk() {
        int rows    = 150;
        int columns = 75;

        RealMatrix m = new Array2DRowRealMatrix(rows, columns);
        m.walkInRowOrder(new SetVisitor());
        GetVisitor getVisitor = new GetVisitor();
        m.walkInOptimizedOrder(getVisitor);
        Assert.assertEquals(rows * columns, getVisitor.getCount());

        m = new Array2DRowRealMatrix(rows, columns);
        m.walkInRowOrder(new SetVisitor(), 1, rows - 2, 1, columns - 2);
        getVisitor = new GetVisitor();
        m.walkInOptimizedOrder(getVisitor, 1, rows - 2, 1, columns - 2);
        Assert.assertEquals((rows - 2) * (columns - 2), getVisitor.getCount());
        for (int i = 0; i < rows; ++i) {
            Assert.assertEquals(0.0, m.getEntry(i, 0), 0);
            Assert.assertEquals(0.0, m.getEntry(i, columns - 1), 0);
        }
        for (int j = 0; j < columns; ++j) {
            Assert.assertEquals(0.0, m.getEntry(0, j), 0);
            Assert.assertEquals(0.0, m.getEntry(rows - 1, j), 0);
        }

        m = new Array2DRowRealMatrix(rows, columns);
        m.walkInColumnOrder(new SetVisitor());
        getVisitor = new GetVisitor();
        m.walkInOptimizedOrder(getVisitor);
        Assert.assertEquals(rows * columns, getVisitor.getCount());

        m = new Array2DRowRealMatrix(rows, columns);
        m.walkInColumnOrder(new SetVisitor(), 1, rows - 2, 1, columns - 2);
        getVisitor = new GetVisitor();
        m.walkInOptimizedOrder(getVisitor, 1, rows - 2, 1, columns - 2);
        Assert.assertEquals((rows - 2) * (columns - 2), getVisitor.getCount());
        for (int i = 0; i < rows; ++i) {
            Assert.assertEquals(0.0, m.getEntry(i, 0), 0);
            Assert.assertEquals(0.0, m.getEntry(i, columns - 1), 0);
        }
        for (int j = 0; j < columns; ++j) {
            Assert.assertEquals(0.0, m.getEntry(0, j), 0);
            Assert.assertEquals(0.0, m.getEntry(rows - 1, j), 0);
        }

        m = new Array2DRowRealMatrix(rows, columns);
        m.walkInOptimizedOrder(new SetVisitor());
        getVisitor = new GetVisitor();
        m.walkInRowOrder(getVisitor);
        Assert.assertEquals(rows * columns, getVisitor.getCount());

        m = new Array2DRowRealMatrix(rows, columns);
        m.walkInOptimizedOrder(new SetVisitor(), 1, rows - 2, 1, columns - 2);
        getVisitor = new GetVisitor();
        m.walkInRowOrder(getVisitor, 1, rows - 2, 1, columns - 2);
        Assert.assertEquals((rows - 2) * (columns - 2), getVisitor.getCount());
        for (int i = 0; i < rows; ++i) {
            Assert.assertEquals(0.0, m.getEntry(i, 0), 0);
            Assert.assertEquals(0.0, m.getEntry(i, columns - 1), 0);
        }
        for (int j = 0; j < columns; ++j) {
            Assert.assertEquals(0.0, m.getEntry(0, j), 0);
            Assert.assertEquals(0.0, m.getEntry(rows - 1, j), 0);
        }

        m = new Array2DRowRealMatrix(rows, columns);
        m.walkInOptimizedOrder(new SetVisitor());
        getVisitor = new GetVisitor();
        m.walkInColumnOrder(getVisitor);
        Assert.assertEquals(rows * columns, getVisitor.getCount());

        m = new Array2DRowRealMatrix(rows, columns);
        m.walkInOptimizedOrder(new SetVisitor(), 1, rows - 2, 1, columns - 2);
        getVisitor = new GetVisitor();
        m.walkInColumnOrder(getVisitor, 1, rows - 2, 1, columns - 2);
        Assert.assertEquals((rows - 2) * (columns - 2), getVisitor.getCount());
        for (int i = 0; i < rows; ++i) {
            Assert.assertEquals(0.0, m.getEntry(i, 0), 0);
            Assert.assertEquals(0.0, m.getEntry(i, columns - 1), 0);
        }
        for (int j = 0; j < columns; ++j) {
            Assert.assertEquals(0.0, m.getEntry(0, j), 0);
            Assert.assertEquals(0.0, m.getEntry(rows - 1, j), 0);
        }
    }

    @Test
    public void testSerial()  {
        Array2DRowRealMatrix m = new Array2DRowRealMatrix(testData);
        Assert.assertEquals(m,TestUtils.serializeAndRecover(m));
    }


    private static class SetVisitor extends DefaultRealMatrixChangingVisitor {
        @Override
        public double visit(int i, int j, double value) {
            return i + j / 1024.0;
        }
    }

    private static class GetVisitor extends DefaultRealMatrixPreservingVisitor {
        private int count = 0;
        @Override
        public void visit(int i, int j, double value) {
            ++count;
            Assert.assertEquals(i + j / 1024.0, value, 0.0);
        }
        public int getCount() {
            return count;
        }
    }

    //--------------- -----------------Protected methods

    /** extracts the l  and u matrices from compact lu representation */
    protected void splitLU(RealMatrix lu, double[][] lowerData, double[][] upperData) {
        if (!lu.isSquare()) {
            throw new NonSquareMatrixException(lu.getRowDimension(), lu.getColumnDimension());
        }
        if (lowerData.length != lowerData[0].length) {
            throw new DimensionMismatchException(lowerData.length, lowerData[0].length);
        }
        if (upperData.length != upperData[0].length) {
            throw new DimensionMismatchException(upperData.length, upperData[0].length);
        }
        if (lowerData.length != upperData.length) {
            throw new DimensionMismatchException(lowerData.length, upperData.length);
        }
        if (lowerData.length != lu.getRowDimension()) {
            throw new DimensionMismatchException(lowerData.length, lu.getRowDimension());
        }

        int n = lu.getRowDimension();
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (j < i) {
                    lowerData[i][j] = lu.getEntry(i, j);
                    upperData[i][j] = 0d;
                } else if (i == j) {
                    lowerData[i][j] = 1d;
                    upperData[i][j] = lu.getEntry(i, j);
                } else {
                    lowerData[i][j] = 0d;
                    upperData[i][j] = lu.getEntry(i, j);
                }
            }
        }
    }

    /** Returns the result of applying the given row permutation to the matrix */
    protected RealMatrix permuteRows(RealMatrix matrix, int[] permutation) {
        if (!matrix.isSquare()) {
            throw new NonSquareMatrixException(matrix.getRowDimension(),
                                               matrix.getColumnDimension());
        }
        if (matrix.getRowDimension() != permutation.length) {
            throw new DimensionMismatchException(matrix.getRowDimension(), permutation.length);
        }

        int n = matrix.getRowDimension();
        int m = matrix.getColumnDimension();
        double out[][] = new double[m][n];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                out[i][j] = matrix.getEntry(permutation[i], j);
            }
        }
        return new Array2DRowRealMatrix(out);
    }

//    /** Useful for debugging */
//    private void dumpMatrix(RealMatrix m) {
//          for (int i = 0; i < m.getRowDimension(); i++) {
//              String os = "";
//              for (int j = 0; j < m.getColumnDimension(); j++) {
//                  os += m.getEntry(i, j) + " ";
//              }
//              System.out.println(os);
//          }
//    }
}

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