Commons Math example source code file (SparseFieldMatrixTest.java)

This example Commons Math source code file (SparseFieldMatrixTest.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

arrayfieldvector, column3, expecting, fieldmatrix, fieldmatrix, fieldvector, fraction, fraction, illegalargumentexception, matrixindexexception, matrixindexexception, nonsquarematrixexception, sparsefieldmatrix, sparsefieldmatrix

The Commons Math SparseFieldMatrixTest.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.Field;
import org.apache.commons.math.fraction.Fraction;
import org.apache.commons.math.fraction.FractionConversionException;
import org.apache.commons.math.fraction.FractionField;

/**
 * Test cases for the {@link SparseFieldMatrix} class.
 *
 * @version $Revision: 902201 $ $Date: 2010-01-22 13:18:16 -0500 (Fri, 22 Jan 2010) $
 */
public class SparseFieldMatrixTest extends TestCase {
    // 3 x 3 identity matrix
    protected Fraction[][] id = { {new Fraction(1), new Fraction(0), new Fraction(0) }, { new Fraction(0), new Fraction(1), new Fraction(0) }, { new Fraction(0), new Fraction(0), new Fraction(1) } };
    // Test data for group operations
    protected Fraction[][] testData = { { 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) } };
    protected Fraction[][] testDataLU = null;
    protected Fraction[][] testDataPlus2 = { { new Fraction(3), new Fraction(4), new Fraction(5) }, { new Fraction(4), new Fraction(7), new Fraction(5) },
            { new Fraction(3), new Fraction(2), new Fraction(10) } };
    protected Fraction[][] testDataMinus = { { 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) } };
    protected Fraction[] testDataRow1 = { new Fraction(1), new Fraction(2), new Fraction(3) };
    protected Fraction[] testDataCol3 = { new Fraction(3), new Fraction(3), new Fraction(8) };
    protected Fraction[][] testDataInv = { { new Fraction(-40), new Fraction(16), new Fraction(9) }, { new Fraction(13), new Fraction(-5), new Fraction(-3) },
            { new Fraction(5), new Fraction(-2), new Fraction(-1) } };
    protected Fraction[] preMultTest = { new Fraction(8), new Fraction(12), new Fraction(33) };
    protected Fraction[][] testData2 = { { new Fraction(1), new Fraction(2), new Fraction(3) }, { new Fraction(2), new Fraction(5), new Fraction(3) } };
    protected Fraction[][] testData2T = { { new Fraction(1), new Fraction(2) }, { new Fraction(2), new Fraction(5) }, { new Fraction(3), new Fraction(3) } };
    protected Fraction[][] testDataPlusInv = { { new Fraction(-39), new Fraction(18), new Fraction(12) },
            { new Fraction(15), new Fraction(0), new Fraction(0) }, { new Fraction(6), new Fraction(-2), new Fraction(7) } };

    // lu decomposition tests
    protected Fraction[][] luData = { { new Fraction(2), new Fraction(3), new Fraction(3) }, { new Fraction(0), new Fraction(5), new Fraction(7) }, { new Fraction(6), new Fraction(9), new Fraction(8) } };
    protected Fraction[][] luDataLUDecomposition = null;

    // singular matrices
    protected Fraction[][] singular = { { new Fraction(2), new Fraction(3) }, { new Fraction(2), new Fraction(3) } };
    protected Fraction[][] bigSingular = { { new Fraction(1), new Fraction(2), new Fraction(3), new Fraction(4) },
            { new Fraction(2), new Fraction(5), new Fraction(3), new Fraction(4) }, { new Fraction(7), new Fraction(3), new Fraction(256), new Fraction(1930) }, { new Fraction(3), new Fraction(7), new Fraction(6), new Fraction(8) } }; // 4th

    // row
    // =
    // 1st
    // +
    // 2nd
    protected Fraction[][] detData = { { new Fraction(1), new Fraction(2), new Fraction(3) }, { new Fraction(4), new Fraction(5), new Fraction(6) },
            { new Fraction(7), new Fraction(8), new Fraction(10) } };
    protected Fraction[][] detData2 = { { new Fraction(1), new Fraction(3) }, { new Fraction(2), new Fraction(4) } };

    // vectors
    protected Fraction[] testVector = { new Fraction(1), new Fraction(2), new Fraction(3) };
    protected Fraction[] testVector2 = { new Fraction(1), new Fraction(2), new Fraction(3), new Fraction(4) };

    // submatrix accessor tests
    protected Fraction[][] subTestData = null;

    // array selections
    protected Fraction[][] subRows02Cols13 = { {new Fraction(2), new Fraction(4) }, { new Fraction(4), new Fraction(8) } };
    protected Fraction[][] subRows03Cols12 = { { new Fraction(2), new Fraction(3) }, { new Fraction(5), new Fraction(6) } };
    protected Fraction[][] subRows03Cols123 = { { new Fraction(2), new Fraction(3), new Fraction(4) }, { new Fraction(5), new Fraction(6), new Fraction(7) } };

    // effective permutations
    protected Fraction[][] subRows20Cols123 = { { new Fraction(4), new Fraction(6), new Fraction(8) }, { new Fraction(2), new Fraction(3), new Fraction(4) } };
    protected Fraction[][] subRows31Cols31 = null;

    // contiguous ranges
    protected Fraction[][] subRows01Cols23 = null;
    protected Fraction[][] subRows23Cols00 = { { new Fraction(2) }, { new Fraction(4) } };
    protected Fraction[][] subRows00Cols33 = { { new Fraction(4) } };

    // row matrices
    protected Fraction[][] subRow0 = { { new Fraction(1), new Fraction(2), new Fraction(3), new Fraction(4) } };
    protected Fraction[][] subRow3 = { { new Fraction(4), new Fraction(5), new Fraction(6), new Fraction(7) } };

    // column matrices
    protected Fraction[][] subColumn1 = null;
    protected Fraction[][] subColumn3 = null;

    // tolerances
    protected double entryTolerance = 10E-16;
    protected double normTolerance = 10E-14;
    protected Field<Fraction> field = FractionField.getInstance();

    public SparseFieldMatrixTest(String name) {
        super(name);
        setupFractionArrays();
    }

    private void setupFractionArrays() {
        try {
            testDataLU = new Fraction[][]{ { new Fraction(2), new Fraction(5), new Fraction(3) }, { new Fraction(.5d), new Fraction(-2.5d), new Fraction(6.5d) },
                    { new Fraction(0.5d), new Fraction(0.2d), new Fraction(.2d) } };
            luDataLUDecomposition = new Fraction[][]{ { new Fraction(6), new Fraction(9), new Fraction(8) },
                { new Fraction(0), new Fraction(5), new Fraction(7) }, { new Fraction(0.33333333333333), new Fraction(0), new Fraction(0.33333333333333) } };
            subTestData = new Fraction [][]{ { new Fraction(1), new Fraction(2), new Fraction(3), new Fraction(4) },
                    { new Fraction(1.5), new Fraction(2.5), new Fraction(3.5), new Fraction(4.5) }, { new Fraction(2), new Fraction(4), new Fraction(6), new Fraction(8) }, { new Fraction(4), new Fraction(5), new Fraction(6), new Fraction(7) } };
            subRows31Cols31 = new Fraction[][]{ { new Fraction(7), new Fraction(5) }, { new Fraction(4.5), new Fraction(2.5) } };
            subRows01Cols23 = new Fraction[][]{ { new Fraction(3), new Fraction(4) }, { new Fraction(3.5), new Fraction(4.5) } };
            subColumn1 = new Fraction [][]{ { new Fraction(2) }, { new Fraction(2.5) }, { new Fraction(4) }, { new Fraction(5) } };
            subColumn3 = new Fraction[][]{ { new Fraction(4) }, { new Fraction(4.5) }, { new Fraction(8) }, { new Fraction(7) } };
        } catch (FractionConversionException e) {
            // ignore, can't happen
        }


    }

    /** test dimensions */
    public void testDimensions() {
        SparseFieldMatrix<Fraction> m = createSparseMatrix(testData);
        SparseFieldMatrix<Fraction> 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() {
        SparseFieldMatrix<Fraction> m1 = createSparseMatrix(testData);
        FieldMatrix<Fraction> m2 = m1.copy();
        assertEquals(m1.getClass(), m2.getClass());
        assertEquals((m2), m1);
        SparseFieldMatrix<Fraction> m3 = createSparseMatrix(testData);
        FieldMatrix<Fraction> m4 = m3.copy();
        assertEquals(m3.getClass(), m4.getClass());
        assertEquals((m4), m3);
    }

    /** test add */
    public void testAdd() {
        SparseFieldMatrix<Fraction> m = createSparseMatrix(testData);
        SparseFieldMatrix<Fraction> mInv = createSparseMatrix(testDataInv);
        SparseFieldMatrix<Fraction> mDataPlusInv = createSparseMatrix(testDataPlusInv);
        FieldMatrix<Fraction> 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).doubleValue(), mPlusMInv.getEntry(row, col).doubleValue(),
                    entryTolerance);
            }
        }
    }

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


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

    /** test multiply */
    public void testMultiply() {
        SparseFieldMatrix<Fraction> m = createSparseMatrix(testData);
        SparseFieldMatrix<Fraction> mInv = createSparseMatrix(testDataInv);
        SparseFieldMatrix<Fraction> identity = createSparseMatrix(id);
        SparseFieldMatrix<Fraction> m2 = createSparseMatrix(testData2);
        assertClose("inverse multiply", m.multiply(mInv), identity,
                entryTolerance);
        assertClose("inverse multiply", m.multiply(new Array2DRowFieldMatrix<Fraction>(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 Fraction[][] d3 = new Fraction[][] { { new Fraction(1), new Fraction(2), new Fraction(3), new Fraction(4) }, { new Fraction(5), new Fraction(6), new Fraction(7), new Fraction(8) } };
    private Fraction[][] d4 = new Fraction[][] { { new Fraction(1) }, { new Fraction(2) }, { new Fraction(3) }, { new Fraction(4) } };
    private Fraction[][] d5 = new Fraction[][] { { new Fraction(30) }, { new Fraction(70) } };

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

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

    /** test sclarAdd */
    public void testScalarAdd() {
        FieldMatrix<Fraction> m = createSparseMatrix(testData);
        assertClose("scalar add", createSparseMatrix(testDataPlus2),
            m.scalarAdd(new Fraction(2)), entryTolerance);
    }

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

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

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

        FieldMatrix<Fraction> m = createSparseMatrix(testData);
        FieldMatrix<Fraction> mIT = new FieldLUDecompositionImpl(m).getSolver().getInverse().transpose();
        FieldMatrix<Fraction> mTI = new FieldLUDecompositionImpl(m.transpose()).getSolver().getInverse();
        assertClose("inverse-transpose", mIT, mTI, normTolerance);
        m = createSparseMatrix(testData2);
        FieldMatrix<Fraction> mt = createSparseMatrix(testData2T);
        assertClose("transpose",mt,m.transpose(),normTolerance);
    }

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

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

        SparseFieldMatrix<Fraction> m = createSparseMatrix(testData);
        SparseFieldMatrix<Fraction> mInv = createSparseMatrix(testDataInv);
        SparseFieldMatrix<Fraction> 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() {
        FieldMatrix<Fraction> 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() {
        FieldMatrix<Fraction> m = createSparseMatrix(testData);
        assertEquals("get entry", m.getEntry(0, 1).doubleValue(), 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
        Fraction[][] matrixData = { { new Fraction(1), new Fraction(2), new Fraction(3) }, { new Fraction(2), new Fraction(5), new Fraction(3) } };
        FieldMatrix<Fraction> m = createSparseMatrix(matrixData);
        // One more with three rows, two columns
        Fraction[][] matrixData2 = { { new Fraction(1), new Fraction(2) }, { new Fraction(2), new Fraction(5) }, { new Fraction(1), new Fraction(7) } };
        FieldMatrix<Fraction> n = createSparseMatrix(matrixData2);
        // Now multiply m by n
        FieldMatrix<Fraction> p = m.multiply(n);
        assertEquals(2, p.getRowDimension());
        assertEquals(2, p.getColumnDimension());
        // Invert p
        FieldMatrix<Fraction> pInverse = new FieldLUDecompositionImpl(p).getSolver().getInverse();
        assertEquals(2, pInverse.getRowDimension());
        assertEquals(2, pInverse.getColumnDimension());

        // Solve example
        Fraction[][] coefficientsData = { { new Fraction(2), new Fraction(3), new Fraction(-2) }, { new Fraction(-1), new Fraction(7), new Fraction(6) },
                { new Fraction(4), new Fraction(-3), new Fraction(-5) } };
        FieldMatrix<Fraction> coefficients = createSparseMatrix(coefficientsData);
        Fraction[] constants = { new Fraction(1), new Fraction(-2), new Fraction(1) };
        Fraction[] solution = new FieldLUDecompositionImpl<Fraction>(coefficients).getSolver().solve(constants);
        assertEquals((new Fraction(2).multiply((solution[0])).add(new Fraction(3).multiply(solution[1])).subtract(new Fraction(2).multiply(solution[2]))).doubleValue(),
                constants[0].doubleValue(), 1E-12);
        assertEquals(((new Fraction(-1).multiply(solution[0])).add(new Fraction(7).multiply(solution[1])).add(new Fraction(6).multiply(solution[2]))).doubleValue(),
                constants[1].doubleValue(), 1E-12);
        assertEquals(((new Fraction(4).multiply(solution[0])).subtract(new Fraction(3).multiply( solution[1])).subtract(new Fraction(5).multiply(solution[2]))).doubleValue(),
                constants[2].doubleValue(), 1E-12);

    }

    // test submatrix accessors
    public void testSubMatrix() {
        FieldMatrix<Fraction> m = createSparseMatrix(subTestData);
        FieldMatrix<Fraction> mRows23Cols00 = createSparseMatrix(subRows23Cols00);
        FieldMatrix<Fraction> mRows00Cols33 = createSparseMatrix(subRows00Cols33);
        FieldMatrix<Fraction> mRows01Cols23 = createSparseMatrix(subRows01Cols23);
        FieldMatrix<Fraction> mRows02Cols13 = createSparseMatrix(subRows02Cols13);
        FieldMatrix<Fraction> mRows03Cols12 = createSparseMatrix(subRows03Cols12);
        FieldMatrix<Fraction> mRows03Cols123 = createSparseMatrix(subRows03Cols123);
        FieldMatrix<Fraction> mRows20Cols123 = createSparseMatrix(subRows20Cols123);
        FieldMatrix<Fraction> 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() {
        FieldMatrix<Fraction> m = createSparseMatrix(subTestData);
        FieldMatrix<Fraction> mRow0 = createSparseMatrix(subRow0);
        FieldMatrix<Fraction> 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() {
        FieldMatrix<Fraction> m = createSparseMatrix(subTestData);
        FieldMatrix<Fraction> mColumn1 = createSparseMatrix(subColumn1);
        FieldMatrix<Fraction> 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() {
        FieldMatrix<Fraction> m = createSparseMatrix(subTestData);
        FieldVector<Fraction> mRow0 = new ArrayFieldVector(subRow0[0]);
        FieldVector<Fraction> mRow3 = new ArrayFieldVector(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() {
        FieldMatrix<Fraction> m = createSparseMatrix(subTestData);
        FieldVector<Fraction> mColumn1 = columnToVector(subColumn1);
        FieldVector<Fraction> 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 FieldVector<Fraction> columnToVector(Fraction[][] column) {
        Fraction[] data = new Fraction[column.length];
        for (int i = 0; i < data.length; ++i) {
            data[i] = column[i][0];
        }
        return new ArrayFieldVector<Fraction>(data, false);
    }

    public void testEqualsAndHashCode() {
        SparseFieldMatrix<Fraction> m = createSparseMatrix(testData);
        SparseFieldMatrix<Fraction> m1 = (SparseFieldMatrix) m.copy();
        SparseFieldMatrix<Fraction> mt = (SparseFieldMatrix) 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)));
    }

    /* Disable for now
    public void testToString() {
        SparseFieldMatrix<Fraction> m = createSparseMatrix(testData);
        assertEquals("SparseFieldMatrix<Fraction>{{1.0,2.0,3.0},{2.0,5.0,3.0},{1.0,0.0,8.0}}",
            m.toString());
        m = new SparseFieldMatrix<Fraction>(field, 1, 1);
        assertEquals("SparseFieldMatrix<Fraction>{{0.0}}", m.toString());
    }
    */

    public void testSetSubMatrix() throws Exception {
        SparseFieldMatrix<Fraction> m = createSparseMatrix(testData);
        m.setSubMatrix(detData2, 1, 1);
        FieldMatrix<Fraction> expected = createSparseMatrix(new Fraction[][] {
                { new Fraction(1), new Fraction(2), new Fraction(3) }, { new Fraction(2), new Fraction(1), new Fraction(3) }, { new Fraction(1), new Fraction(2), new Fraction(4) } });
        assertEquals(expected, m);

        m.setSubMatrix(detData2, 0, 0);
        expected = createSparseMatrix(new Fraction[][] {
                { new Fraction(1), new Fraction(3), new Fraction(3) }, { new Fraction(2), new Fraction(4), new Fraction(3) }, { new Fraction(1), new Fraction(2), new Fraction(4) } });
        assertEquals(expected, m);

        m.setSubMatrix(testDataPlus2, 0, 0);
        expected = createSparseMatrix(new Fraction[][] {
                { new Fraction(3), new Fraction(4), new Fraction(5) }, { new Fraction(4), new Fraction(7), new Fraction(5) }, { new Fraction(3), new Fraction(2), new Fraction(10) } });
        assertEquals(expected, m);

        // javadoc example
        SparseFieldMatrix<Fraction> matrix =
            createSparseMatrix(new Fraction[][] {
        { new Fraction(1), new Fraction(2), new Fraction(3), new Fraction(4) }, { new Fraction(5), new Fraction(6), new Fraction(7), new Fraction(8) }, { new Fraction(9), new Fraction(0), new Fraction(1), new Fraction(2) } });
        matrix.setSubMatrix(new Fraction[][] { { new Fraction(3), new Fraction(4) }, { new Fraction(5), new Fraction(6) } }, 1, 1);
        expected = createSparseMatrix(new Fraction[][] {
                { new Fraction(1), new Fraction(2), new Fraction(3), new Fraction(4) }, { new Fraction(5), new Fraction(3), new Fraction(4), new Fraction(8) }, { new Fraction(9), new Fraction(5), new Fraction(6), new Fraction(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 SparseFieldMatrix<Fraction>(field, 0, 0);
            fail("expecting IllegalArgumentException");
        } catch (IllegalArgumentException e) {
            // expected
        }

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

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

    }

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

    /** verifies that two matrices are close (1-norm) */
    protected void assertClose(String msg, FieldMatrix<Fraction> m, FieldMatrix n,
            double tolerance) {
        for(int i=0; i < m.getRowDimension(); i++){
            for(int j=0; j < m.getColumnDimension(); j++){
                assertEquals(msg, m.getEntry(i,j).doubleValue(), n.getEntry(i,j).doubleValue(), tolerance);
            }

        }
    }

    /** verifies that two vectors are close (sup norm) */
    protected void assertClose(String msg, Fraction[] m, Fraction[] 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].doubleValue(), n[i].doubleValue(),
                    tolerance);
        }
    }

    private SparseFieldMatrix<Fraction> createSparseMatrix(Fraction[][] data) {
        SparseFieldMatrix<Fraction> matrix = new SparseFieldMatrix(field, 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;
    }

}