Commons Math example source code file (SparseRealMatrixTest.java)

This example Commons Math source code file (SparseRealMatrixTest.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

arrayrealvector, column1, column3, expecting, expecting, illegalargumentexception, matrixindexexception, matrixindexexception, nonsquarematrixexception, openmaprealmatrix, openmaprealmatrix, realmatrix, realmatrix, realvector

The Commons Math SparseRealMatrixTest.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 junit.framework.TestCase;

import org.apache.commons.math.TestUtils;

/**
 * Test cases for the {@link OpenMapRealMatrix} class.
 *
 * @version $Revision: 902201 $ $Date: 2008-11-07 06:48:13 -0800 (Fri, 07 Nov
 *          2008) $
 */
public final class SparseRealMatrixTest extends TestCase {

    // 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;

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

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

    /** test copy functions */
    public void testCopyFunctions() {
        OpenMapRealMatrix m1 = createSparseMatrix(testData);
        RealMatrix m2 = m1.copy();
        assertEquals(m1.getClass(), m2.getClass());
        assertEquals((m2), m1);
        OpenMapRealMatrix m3 = createSparseMatrix(testData);
        RealMatrix m4 = m3.copy();
        assertEquals(m3.getClass(), m4.getClass());
        assertEquals((m4), m3);
    }

    /** test add */
    public void testAdd() {
        OpenMapRealMatrix m = createSparseMatrix(testData);
        OpenMapRealMatrix mInv = createSparseMatrix(testDataInv);
        OpenMapRealMatrix mDataPlusInv = createSparseMatrix(testDataPlusInv);
        RealMatrix mPlusMInv = m.add(mInv);
        for (int row = 0; row < m.getRowDimension(); row++) {
            for (int col = 0; col < m.getColumnDimension(); col++) {
                assertEquals("sum entry entry",
                    mDataPlusInv.getEntry(row, col), mPlusMInv.getEntry(row, col),
                    entryTolerance);
            }
        }
    }

    /** test add failure */
    public void testAddFail() {
        OpenMapRealMatrix m = createSparseMatrix(testData);
        OpenMapRealMatrix m2 = createSparseMatrix(testData2);
        try {
            m.add(m2);
            fail("IllegalArgumentException expected");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
    }

    /** test norm */
    public void testNorm() {
        OpenMapRealMatrix m = createSparseMatrix(testData);
        OpenMapRealMatrix m2 = createSparseMatrix(testData2);
        assertEquals("testData norm", 14d, m.getNorm(), entryTolerance);
        assertEquals("testData2 norm", 7d, m2.getNorm(), entryTolerance);
    }

    /** test m-n = m + -n */
    public void testPlusMinus() {
        OpenMapRealMatrix m = createSparseMatrix(testData);
        OpenMapRealMatrix n = createSparseMatrix(testDataInv);
        assertClose("m-n = m + -n", m.subtract(n),
            n.scalarMultiply(-1d).add(m), entryTolerance);
        try {
            m.subtract(createSparseMatrix(testData2));
            fail("Expecting illegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
    }

    /** test multiply */
    public void testMultiply() {
        OpenMapRealMatrix m = createSparseMatrix(testData);
        OpenMapRealMatrix mInv = createSparseMatrix(testDataInv);
        OpenMapRealMatrix identity = createSparseMatrix(id);
        OpenMapRealMatrix m2 = createSparseMatrix(testData2);
        assertClose("inverse multiply", m.multiply(mInv), identity,
                entryTolerance);
        assertClose("inverse multiply", m.multiply(new BlockRealMatrix(testDataInv)), identity,
                    entryTolerance);
        assertClose("inverse multiply", mInv.multiply(m), identity,
                entryTolerance);
        assertClose("identity multiply", m.multiply(identity), m,
                entryTolerance);
        assertClose("identity multiply", identity.multiply(mInv), mInv,
                entryTolerance);
        assertClose("identity multiply", m2.multiply(identity), m2,
                entryTolerance);
        try {
            m.multiply(createSparseMatrix(bigSingular));
            fail("Expecting illegalArgumentException");
        } catch (IllegalArgumentException 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 } };

    public void testMultiply2() {
        RealMatrix m3 = createSparseMatrix(d3);
        RealMatrix m4 = createSparseMatrix(d4);
        RealMatrix m5 = createSparseMatrix(d5);
        assertClose("m3*m4=m5", m3.multiply(m4), m5, entryTolerance);
    }

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

    /** test sclarAdd */
    public void testScalarAdd() {
        RealMatrix m = createSparseMatrix(testData);
        assertClose("scalar add", createSparseMatrix(testDataPlus2),
            m.scalarAdd(2d), entryTolerance);
    }

    /** test operate */
    public void testOperate() {
        RealMatrix m = createSparseMatrix(id);
        assertClose("identity operate", testVector, m.operate(testVector),
                entryTolerance);
        assertClose("identity operate", testVector, m.operate(
                new ArrayRealVector(testVector)).getData(), entryTolerance);
        m = createSparseMatrix(bigSingular);
        try {
            m.operate(testVector);
            fail("Expecting illegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
    }

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

    /** test transpose */
    public void testTranspose() {

        RealMatrix m = createSparseMatrix(testData);
        RealMatrix mIT = new LUDecompositionImpl(m).getSolver().getInverse().transpose();
        RealMatrix mTI = new LUDecompositionImpl(m.transpose()).getSolver().getInverse();
        assertClose("inverse-transpose", mIT, mTI, normTolerance);
        m = createSparseMatrix(testData2);
        RealMatrix mt = createSparseMatrix(testData2T);
        assertClose("transpose",mt,m.transpose(),normTolerance);
    }

    /** test preMultiply by vector */
    public void testPremultiplyVector() {
        RealMatrix m = createSparseMatrix(testData);
        assertClose("premultiply", m.preMultiply(testVector), preMultTest,
            normTolerance);
        assertClose("premultiply", m.preMultiply(
            new ArrayRealVector(testVector).getData()), preMultTest, normTolerance);
        m = createSparseMatrix(bigSingular);
        try {
            m.preMultiply(testVector);
            fail("expecting IllegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
    }

    public void testPremultiply() {
        RealMatrix m3 = createSparseMatrix(d3);
        RealMatrix m4 = createSparseMatrix(d4);
        RealMatrix m5 = createSparseMatrix(d5);
        assertClose("m3*m4=m5", m4.preMultiply(m3), m5, entryTolerance);

        OpenMapRealMatrix m = createSparseMatrix(testData);
        OpenMapRealMatrix mInv = createSparseMatrix(testDataInv);
        OpenMapRealMatrix identity = createSparseMatrix(id);
        assertClose("inverse multiply", m.preMultiply(mInv), identity,
                entryTolerance);
        assertClose("inverse multiply", mInv.preMultiply(m), identity,
                entryTolerance);
        assertClose("identity multiply", m.preMultiply(identity), m,
                entryTolerance);
        assertClose("identity multiply", identity.preMultiply(mInv), mInv,
                entryTolerance);
        try {
            m.preMultiply(createSparseMatrix(bigSingular));
            fail("Expecting illegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
    }

    public void testGetVectors() {
        RealMatrix m = createSparseMatrix(testData);
        assertClose("get row", m.getRow(0), testDataRow1, entryTolerance);
        assertClose("get col", m.getColumn(2), testDataCol3, entryTolerance);
        try {
            m.getRow(10);
            fail("expecting MatrixIndexException");
        } catch (MatrixIndexException ex) {
            // ignored
        }
        try {
            m.getColumn(-1);
            fail("expecting MatrixIndexException");
        } catch (MatrixIndexException ex) {
            // ignored
        }
    }

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

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

        // Solve example
        double[][] coefficientsData = { { 2, 3, -2 }, { -1, 7, 6 },
                { 4, -3, -5 } };
        RealMatrix coefficients = createSparseMatrix(coefficientsData);
        double[] constants = { 1, -2, 1 };
        double[] solution = new LUDecompositionImpl(coefficients).getSolver().solve(constants);
        assertEquals(2 * solution[0] + 3 * solution[1] - 2 * solution[2],
                constants[0], 1E-12);
        assertEquals(-1 * solution[0] + 7 * solution[1] + 6 * solution[2],
                constants[1], 1E-12);
        assertEquals(4 * solution[0] - 3 * solution[1] - 5 * solution[2],
                constants[2], 1E-12);

    }

    // test submatrix accessors
    public void testSubMatrix() {
        RealMatrix m = createSparseMatrix(subTestData);
        RealMatrix mRows23Cols00 = createSparseMatrix(subRows23Cols00);
        RealMatrix mRows00Cols33 = createSparseMatrix(subRows00Cols33);
        RealMatrix mRows01Cols23 = createSparseMatrix(subRows01Cols23);
        RealMatrix mRows02Cols13 = createSparseMatrix(subRows02Cols13);
        RealMatrix mRows03Cols12 = createSparseMatrix(subRows03Cols12);
        RealMatrix mRows03Cols123 = createSparseMatrix(subRows03Cols123);
        RealMatrix mRows20Cols123 = createSparseMatrix(subRows20Cols123);
        RealMatrix mRows31Cols31 = createSparseMatrix(subRows31Cols31);
        assertEquals("Rows23Cols00", mRows23Cols00, m.getSubMatrix(2, 3, 0, 0));
        assertEquals("Rows00Cols33", mRows00Cols33, m.getSubMatrix(0, 0, 3, 3));
        assertEquals("Rows01Cols23", mRows01Cols23, m.getSubMatrix(0, 1, 2, 3));
        assertEquals("Rows02Cols13", mRows02Cols13,
            m.getSubMatrix(new int[] { 0, 2 }, new int[] { 1, 3 }));
        assertEquals("Rows03Cols12", mRows03Cols12,
            m.getSubMatrix(new int[] { 0, 3 }, new int[] { 1, 2 }));
        assertEquals("Rows03Cols123", mRows03Cols123,
            m.getSubMatrix(new int[] { 0, 3 }, new int[] { 1, 2, 3 }));
        assertEquals("Rows20Cols123", mRows20Cols123,
            m.getSubMatrix(new int[] { 2, 0 }, new int[] { 1, 2, 3 }));
        assertEquals("Rows31Cols31", mRows31Cols31,
            m.getSubMatrix(new int[] { 3, 1 }, new int[] { 3, 1 }));
        assertEquals("Rows31Cols31", mRows31Cols31,
            m.getSubMatrix(new int[] { 3, 1 }, new int[] { 3, 1 }));

        try {
            m.getSubMatrix(1, 0, 2, 4);
            fail("Expecting MatrixIndexException");
        } catch (MatrixIndexException ex) {
            // expected
        }
        try {
            m.getSubMatrix(-1, 1, 2, 2);
            fail("Expecting MatrixIndexException");
        } catch (MatrixIndexException ex) {
            // expected
        }
        try {
            m.getSubMatrix(1, 0, 2, 2);
            fail("Expecting MatrixIndexException");
        } catch (MatrixIndexException ex) {
            // expected
        }
        try {
            m.getSubMatrix(1, 0, 2, 4);
            fail("Expecting MatrixIndexException");
        } catch (MatrixIndexException ex) {
            // expected
        }
        try {
            m.getSubMatrix(new int[] {}, new int[] { 0 });
            fail("Expecting MatrixIndexException");
        } catch (MatrixIndexException ex) {
            // expected
        }
        try {
            m.getSubMatrix(new int[] { 0 }, new int[] { 4 });
            fail("Expecting MatrixIndexException");
        } catch (MatrixIndexException ex) {
            // expected
        }
    }

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

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

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

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

    public void testEqualsAndHashCode() {
        OpenMapRealMatrix m = createSparseMatrix(testData);
        OpenMapRealMatrix m1 = m.copy();
        OpenMapRealMatrix mt = (OpenMapRealMatrix) m.transpose();
        assertTrue(m.hashCode() != mt.hashCode());
        assertEquals(m.hashCode(), m1.hashCode());
        assertEquals(m, m);
        assertEquals(m, m1);
        assertFalse(m.equals(null));
        assertFalse(m.equals(mt));
        assertFalse(m.equals(createSparseMatrix(bigSingular)));
    }

    public void testToString() {
        OpenMapRealMatrix m = createSparseMatrix(testData);
        assertEquals("OpenMapRealMatrix{{1.0,2.0,3.0},{2.0,5.0,3.0},{1.0,0.0,8.0}}",
            m.toString());
        m = new OpenMapRealMatrix(1, 1);
        assertEquals("OpenMapRealMatrix{{0.0}}", m.toString());
    }

    public void testSetSubMatrix() throws Exception {
        OpenMapRealMatrix m = createSparseMatrix(testData);
        m.setSubMatrix(detData2, 1, 1);
        RealMatrix expected = createSparseMatrix(new double[][] {
                { 1.0, 2.0, 3.0 }, { 2.0, 1.0, 3.0 }, { 1.0, 2.0, 4.0 } });
        assertEquals(expected, m);

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

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

        // javadoc example
        OpenMapRealMatrix matrix =
            createSparseMatrix(new double[][] {
        { 1, 2, 3, 4 }, { 5, 6, 7, 8 }, { 9, 0, 1, 2 } });
        matrix.setSubMatrix(new double[][] { { 3, 4 }, { 5, 6 } }, 1, 1);
        expected = createSparseMatrix(new double[][] {
                { 1, 2, 3, 4 }, { 5, 3, 4, 8 }, { 9, 5, 6, 2 } });
        assertEquals(expected, matrix);

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

        // null
        try {
            m.setSubMatrix(null, 1, 1);
            fail("expecting NullPointerException");
        } catch (NullPointerException e) {
            // expected
        }
        try {
            new OpenMapRealMatrix(0, 0);
            fail("expecting IllegalArgumentException");
        } catch (IllegalArgumentException e) {
            // expected
        }

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

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

    }

    public void testSerial()  {
        OpenMapRealMatrix m = createSparseMatrix(testData);
        assertEquals(m,TestUtils.serializeAndRecover(m));
    }

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

    /** verifies that two matrices are close (1-norm) */
    protected void assertClose(String msg, RealMatrix m, RealMatrix n,
            double tolerance) {
        assertTrue(msg, m.subtract(n).getNorm() < tolerance);
    }

    /** verifies that two vectors are close (sup norm) */
    protected void assertClose(String msg, double[] m, double[] n,
            double tolerance) {
        if (m.length != n.length) {
            fail("vectors not same length");
        }
        for (int i = 0; i < m.length; i++) {
            assertEquals(msg + " " + i + " elements differ", m[i], n[i],
                    tolerance);
        }
    }

    private OpenMapRealMatrix createSparseMatrix(double[][] data) {
        OpenMapRealMatrix matrix = new OpenMapRealMatrix(data.length, data[0].length);
        for (int row = 0; row < data.length; row++) {
            for (int col = 0; col < data[row].length; col++) {
                matrix.setEntry(row, col, data[row][col]);
            }
        }
        return matrix;
    }


}