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Java example source code file (ArrayFieldVectorTest.java)

This example Java source code file (ArrayFieldVectorTest.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

arrayfieldvector, arrayfieldvectortest, arrayindexoutofboundsexception, fieldmatrix, fieldvector, fieldvectorchangingvisitor, fieldvectorpreservingvisitor, fieldvectortestimpl, fraction, mathillegalargumentexception, numberistoosmallexception, outofrangeexception, reflection, test, unsupportedoperationexception, util

The ArrayFieldVectorTest.java Java example source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math3.linear;

import java.io.Serializable;
import java.lang.reflect.Array;
import java.util.Arrays;

import org.apache.commons.math3.Field;
import org.apache.commons.math3.FieldElement;
import org.apache.commons.math3.TestUtils;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.fraction.Fraction;
import org.apache.commons.math3.fraction.FractionField;
import org.junit.Assert;
import org.junit.Test;

/**
 * Test cases for the {@link ArrayFieldVector} class.
 *
 */
public class ArrayFieldVectorTest {

    //
    protected Fraction[][] ma1 = {
            {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)}
    };
    protected Fraction[] vec1 = {new Fraction(1), new Fraction(2), new Fraction(3)};
    protected Fraction[] vec2 = {new Fraction(4), new Fraction(5), new Fraction(6)};
    protected Fraction[] vec3 = {new Fraction(7), new Fraction(8), new Fraction(9)};
    protected Fraction[] vec4 = { 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)};
    protected Fraction[] vec_null = {Fraction.ZERO, Fraction.ZERO, Fraction.ZERO};
    protected Fraction[] dvec1 = {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)};
    protected Fraction[][] mat1 = {
            {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)}
    };

    // Testclass to test the FieldVector<Fraction> interface
    // only with enough content to support the test
    public static class FieldVectorTestImpl<T extends FieldElement
        implements FieldVector<T>, Serializable {

        private static final long serialVersionUID = 3970959016014158539L;

        private final Field<T> field;

        /** Entries of the vector. */
        protected T[] data;

        /** Build an array of elements.
         * @param length size of the array to build
         * @return a new array
         */
        @SuppressWarnings("unchecked") // field is of type T
        private T[] buildArray(final int length) {
            return (T[]) Array.newInstance(field.getRuntimeClass(), length);
        }

        public FieldVectorTestImpl(T[] d) {
            field = d[0].getField();
            data = d.clone();
        }

        public Field<T> getField() {
            return field;
        }

        private UnsupportedOperationException unsupported() {
            return new UnsupportedOperationException("Not supported, unneeded for test purposes");
        }

        public FieldVector<T> copy() {
            throw unsupported();
        }

        public FieldVector<T> add(FieldVector v) {
            throw unsupported();
        }

        public FieldVector<T> add(T[] v) {
            throw unsupported();
        }

        public FieldVector<T> subtract(FieldVector v) {
            throw unsupported();
        }

        public FieldVector<T> subtract(T[] v) {
            throw unsupported();
        }

        public FieldVector<T> mapAdd(T d) {
            throw unsupported();
        }

        public FieldVector<T> mapAddToSelf(T d) {
            throw unsupported();
        }

        public FieldVector<T> mapSubtract(T d) {
            throw unsupported();
        }

        public FieldVector<T> mapSubtractToSelf(T d) {
            throw unsupported();
        }

        public FieldVector<T> mapMultiply(T d) {
            T[] out = buildArray(data.length);
            for (int i = 0; i < data.length; i++) {
                out[i] = data[i].multiply(d);
            }
            return new FieldVectorTestImpl<T>(out);
        }

        public FieldVector<T> mapMultiplyToSelf(T d) {
            throw unsupported();
        }

        public FieldVector<T> mapDivide(T d) {
            throw unsupported();
        }

        public FieldVector<T> mapDivideToSelf(T d) {
            throw unsupported();
        }

        public FieldVector<T> mapInv() {
            throw unsupported();
        }

        public FieldVector<T> mapInvToSelf() {
            throw unsupported();
        }

        public FieldVector<T> ebeMultiply(FieldVector v) {
            throw unsupported();
        }

        public FieldVector<T> ebeMultiply(T[] v) {
            throw unsupported();
        }

        public FieldVector<T> ebeDivide(FieldVector v) {
            throw unsupported();
        }

        public FieldVector<T> ebeDivide(T[] v) {
            throw unsupported();
        }

        public T[] getData() {
            return data.clone();
        }

        public T dotProduct(FieldVector<T> v) {
            T dot = field.getZero();
            for (int i = 0; i < data.length; i++) {
                dot = dot.add(data[i].multiply(v.getEntry(i)));
            }
            return dot;
        }

        public T dotProduct(T[] v) {
            T dot = field.getZero();
            for (int i = 0; i < data.length; i++) {
                dot = dot.add(data[i].multiply(v[i]));
            }
            return dot;
        }

        public FieldVector<T> projection(FieldVector v) {
            throw unsupported();
        }

        public FieldVector<T> projection(T[] v) {
            throw unsupported();
        }

        public FieldMatrix<T> outerProduct(FieldVector v) {
            throw unsupported();
        }

        public FieldMatrix<T> outerProduct(T[] v) {
            throw unsupported();
        }

        public T getEntry(int index) {
            return data[index];
        }

        public int getDimension() {
            return data.length;
        }

        public FieldVector<T> append(FieldVector v) {
            throw unsupported();
        }

        public FieldVector<T> append(T d) {
            throw unsupported();
        }

        public FieldVector<T> append(T[] a) {
            throw unsupported();
        }

        public FieldVector<T> getSubVector(int index, int n) {
            throw unsupported();
        }

        public void setEntry(int index, T value) {
            throw unsupported();
        }

        public void setSubVector(int index, FieldVector<T> v) {
            throw unsupported();
        }

        public void setSubVector(int index, T[] v) {
            throw unsupported();
        }

        public void set(T value) {
            throw unsupported();
        }

        public T[] toArray() {
            return data.clone();
        }

    }

    @Test
    public void testConstructors() {

        ArrayFieldVector<Fraction> v0 = new ArrayFieldVector(FractionField.getInstance());
        Assert.assertEquals(0, v0.getDimension());

        ArrayFieldVector<Fraction> v1 = new ArrayFieldVector(FractionField.getInstance(), 7);
        Assert.assertEquals(7, v1.getDimension());
        Assert.assertEquals(Fraction.ZERO, v1.getEntry(6));

        ArrayFieldVector<Fraction> v2 = new ArrayFieldVector(5, new Fraction(123, 100));
        Assert.assertEquals(5, v2.getDimension());
        Assert.assertEquals(new Fraction(123, 100), v2.getEntry(4));

        ArrayFieldVector<Fraction> v3 = new ArrayFieldVector(FractionField.getInstance(), vec1);
        Assert.assertEquals(3, v3.getDimension());
        Assert.assertEquals(new Fraction(2), v3.getEntry(1));

        ArrayFieldVector<Fraction> v4 = new ArrayFieldVector(FractionField.getInstance(), vec4, 3, 2);
        Assert.assertEquals(2, v4.getDimension());
        Assert.assertEquals(new Fraction(4), v4.getEntry(0));
        try {
            new ArrayFieldVector<Fraction>(vec4, 8, 3);
            Assert.fail("MathIllegalArgumentException expected");
        } catch (MathIllegalArgumentException ex) {
            // expected behavior
        }

        FieldVector<Fraction> v5_i = new ArrayFieldVector(dvec1);
        Assert.assertEquals(9, v5_i.getDimension());
        Assert.assertEquals(new Fraction(9), v5_i.getEntry(8));

        ArrayFieldVector<Fraction> v5 = new ArrayFieldVector(dvec1);
        Assert.assertEquals(9, v5.getDimension());
        Assert.assertEquals(new Fraction(9), v5.getEntry(8));

        ArrayFieldVector<Fraction> v6 = new ArrayFieldVector(dvec1, 3, 2);
        Assert.assertEquals(2, v6.getDimension());
        Assert.assertEquals(new Fraction(4), v6.getEntry(0));
        try {
            new ArrayFieldVector<Fraction>(dvec1, 8, 3);
            Assert.fail("MathIllegalArgumentException expected");
        } catch (MathIllegalArgumentException ex) {
            // expected behavior
        }

        ArrayFieldVector<Fraction> v7 = new ArrayFieldVector(v1);
        Assert.assertEquals(7, v7.getDimension());
        Assert.assertEquals(Fraction.ZERO, v7.getEntry(6));

        FieldVectorTestImpl<Fraction> v7_i = new FieldVectorTestImpl(vec1);

        ArrayFieldVector<Fraction> v7_2 = new ArrayFieldVector(v7_i);
        Assert.assertEquals(3, v7_2.getDimension());
        Assert.assertEquals(new Fraction(2), v7_2.getEntry(1));

        ArrayFieldVector<Fraction> v8 = new ArrayFieldVector(v1, true);
        Assert.assertEquals(7, v8.getDimension());
        Assert.assertEquals(Fraction.ZERO, v8.getEntry(6));
        Assert.assertNotSame("testData not same object ", v1.getDataRef(), v8.getDataRef());

        ArrayFieldVector<Fraction> v8_2 = new ArrayFieldVector(v1, false);
        Assert.assertEquals(7, v8_2.getDimension());
        Assert.assertEquals(Fraction.ZERO, v8_2.getEntry(6));
        Assert.assertArrayEquals(v1.getDataRef(), v8_2.getDataRef());

        ArrayFieldVector<Fraction> v9 = new ArrayFieldVector((FieldVector) v1, (FieldVector) v3);
        Assert.assertEquals(10, v9.getDimension());
        Assert.assertEquals(new Fraction(1), v9.getEntry(7));

    }

    @Test
    public void testDataInOut() {

        ArrayFieldVector<Fraction> v1 = new ArrayFieldVector(vec1);
        ArrayFieldVector<Fraction> v2 = new ArrayFieldVector(vec2);
        ArrayFieldVector<Fraction> v4 = new ArrayFieldVector(vec4);
        FieldVectorTestImpl<Fraction> v2_t = new FieldVectorTestImpl(vec2);

        FieldVector<Fraction> v_append_1 = v1.append(v2);
        Assert.assertEquals(6, v_append_1.getDimension());
        Assert.assertEquals(new Fraction(4), v_append_1.getEntry(3));

        FieldVector<Fraction> v_append_2 = v1.append(new Fraction(2));
        Assert.assertEquals(4, v_append_2.getDimension());
        Assert.assertEquals(new Fraction(2), v_append_2.getEntry(3));

        FieldVector<Fraction> v_append_4 = v1.append(v2_t);
        Assert.assertEquals(6, v_append_4.getDimension());
        Assert.assertEquals(new Fraction(4), v_append_4.getEntry(3));

        FieldVector<Fraction> v_copy = v1.copy();
        Assert.assertEquals(3, v_copy.getDimension());
        Assert.assertNotSame("testData not same object ", v1.getDataRef(), v_copy.toArray());

        Fraction[] a_frac = v1.toArray();
        Assert.assertEquals(3, a_frac.length);
        Assert.assertNotSame("testData not same object ", v1.getDataRef(), a_frac);


//      ArrayFieldVector<Fraction> vout4 = (ArrayFieldVector) v1.clone();
//      Assert.assertEquals(3, vout4.getDimension());
//      Assert.assertEquals(v1.getDataRef(), vout4.getDataRef());


        FieldVector<Fraction> vout5 = v4.getSubVector(3, 3);
        Assert.assertEquals(3, vout5.getDimension());
        Assert.assertEquals(new Fraction(5), vout5.getEntry(1));
        try {
            v4.getSubVector(3, 7);
            Assert.fail("OutOfRangeException expected");
        } catch (OutOfRangeException ex) {
            // expected behavior
        }

        ArrayFieldVector<Fraction> v_set1 = (ArrayFieldVector) v1.copy();
        v_set1.setEntry(1, new Fraction(11));
        Assert.assertEquals(new Fraction(11), v_set1.getEntry(1));
        try {
            v_set1.setEntry(3, new Fraction(11));
            Assert.fail("OutOfRangeException expected");
        } catch (OutOfRangeException ex) {
            // expected behavior
        }

        ArrayFieldVector<Fraction> v_set2 = (ArrayFieldVector) v4.copy();
        v_set2.set(3, v1);
        Assert.assertEquals(new Fraction(1), v_set2.getEntry(3));
        Assert.assertEquals(new Fraction(7), v_set2.getEntry(6));
        try {
            v_set2.set(7, v1);
            Assert.fail("OutOfRangeException expected");
        } catch (OutOfRangeException ex) {
            // expected behavior
        }

        ArrayFieldVector<Fraction> v_set3 = (ArrayFieldVector) v1.copy();
        v_set3.set(new Fraction(13));
        Assert.assertEquals(new Fraction(13), v_set3.getEntry(2));

        try {
            v_set3.getEntry(23);
            Assert.fail("ArrayIndexOutOfBoundsException expected");
        } catch (ArrayIndexOutOfBoundsException ex) {
            // expected behavior
        }

        ArrayFieldVector<Fraction> v_set4 = (ArrayFieldVector) v4.copy();
        v_set4.setSubVector(3, v2_t);
        Assert.assertEquals(new Fraction(4), v_set4.getEntry(3));
        Assert.assertEquals(new Fraction(7), v_set4.getEntry(6));
        try {
            v_set4.setSubVector(7, v2_t);
            Assert.fail("OutOfRangeException expected");
        } catch (OutOfRangeException ex) {
            // expected behavior
        }


        ArrayFieldVector<Fraction> vout10 = (ArrayFieldVector) v1.copy();
        ArrayFieldVector<Fraction> vout10_2 = (ArrayFieldVector) v1.copy();
        Assert.assertEquals(vout10, vout10_2);
        vout10_2.setEntry(0, new Fraction(11, 10));
        Assert.assertNotSame(vout10, vout10_2);

    }

    @Test
    public void testMapFunctions() {
        ArrayFieldVector<Fraction> v1 = new ArrayFieldVector(vec1);

        //octave =  v1 .+ 2.0
        FieldVector<Fraction> v_mapAdd = v1.mapAdd(new Fraction(2));
        Fraction[] result_mapAdd = {new Fraction(3), new Fraction(4), new Fraction(5)};
        checkArray("compare vectors" ,result_mapAdd,v_mapAdd.toArray());

        //octave =  v1 .+ 2.0
        FieldVector<Fraction> v_mapAddToSelf = v1.copy();
        v_mapAddToSelf.mapAddToSelf(new Fraction(2));
        Fraction[] result_mapAddToSelf = {new Fraction(3), new Fraction(4), new Fraction(5)};
        checkArray("compare vectors" ,result_mapAddToSelf,v_mapAddToSelf.toArray());

        //octave =  v1 .- 2.0
        FieldVector<Fraction> v_mapSubtract = v1.mapSubtract(new Fraction(2));
        Fraction[] result_mapSubtract = {new Fraction(-1), Fraction.ZERO, new Fraction(1)};
        checkArray("compare vectors" ,result_mapSubtract,v_mapSubtract.toArray());

        //octave =  v1 .- 2.0
        FieldVector<Fraction> v_mapSubtractToSelf = v1.copy();
        v_mapSubtractToSelf.mapSubtractToSelf(new Fraction(2));
        Fraction[] result_mapSubtractToSelf = {new Fraction(-1), Fraction.ZERO, new Fraction(1)};
        checkArray("compare vectors" ,result_mapSubtractToSelf,v_mapSubtractToSelf.toArray());

        //octave =  v1 .* 2.0
        FieldVector<Fraction> v_mapMultiply = v1.mapMultiply(new Fraction(2));
        Fraction[] result_mapMultiply = {new Fraction(2), new Fraction(4), new Fraction(6)};
        checkArray("compare vectors" ,result_mapMultiply,v_mapMultiply.toArray());

        //octave =  v1 .* 2.0
        FieldVector<Fraction> v_mapMultiplyToSelf = v1.copy();
        v_mapMultiplyToSelf.mapMultiplyToSelf(new Fraction(2));
        Fraction[] result_mapMultiplyToSelf = {new Fraction(2), new Fraction(4), new Fraction(6)};
        checkArray("compare vectors" ,result_mapMultiplyToSelf,v_mapMultiplyToSelf.toArray());

        //octave =  v1 ./ 2.0
        FieldVector<Fraction> v_mapDivide = v1.mapDivide(new Fraction(2));
        Fraction[] result_mapDivide = {new Fraction(1, 2), new Fraction(1), new Fraction(3, 2)};
        checkArray("compare vectors" ,result_mapDivide,v_mapDivide.toArray());

        //octave =  v1 ./ 2.0
        FieldVector<Fraction> v_mapDivideToSelf = v1.copy();
        v_mapDivideToSelf.mapDivideToSelf(new Fraction(2));
        Fraction[] result_mapDivideToSelf = {new Fraction(1, 2), new Fraction(1), new Fraction(3, 2)};
        checkArray("compare vectors" ,result_mapDivideToSelf,v_mapDivideToSelf.toArray());

        //octave =  v1 .^-1
        FieldVector<Fraction> v_mapInv = v1.mapInv();
        Fraction[] result_mapInv = {new Fraction(1),new Fraction(1, 2),new Fraction(1, 3)};
        checkArray("compare vectors" ,result_mapInv,v_mapInv.toArray());

        //octave =  v1 .^-1
        FieldVector<Fraction> v_mapInvToSelf = v1.copy();
        v_mapInvToSelf.mapInvToSelf();
        Fraction[] result_mapInvToSelf = {new Fraction(1),new Fraction(1, 2),new Fraction(1, 3)};
        checkArray("compare vectors" ,result_mapInvToSelf,v_mapInvToSelf.toArray());

    }

    @Test
    public void testBasicFunctions() {
        ArrayFieldVector<Fraction> v1 = new ArrayFieldVector(vec1);
        ArrayFieldVector<Fraction> v2 = new ArrayFieldVector(vec2);
        new ArrayFieldVector<Fraction>(vec_null);

        FieldVectorTestImpl<Fraction> v2_t = new FieldVectorTestImpl(vec2);

        //octave =  v1 + v2
        ArrayFieldVector<Fraction> v_add = v1.add(v2);
        Fraction[] result_add = {new Fraction(5), new Fraction(7), new Fraction(9)};
        checkArray("compare vect" ,v_add.getData(),result_add);

        FieldVectorTestImpl<Fraction> vt2 = new FieldVectorTestImpl(vec2);
        FieldVector<Fraction> v_add_i = v1.add(vt2);
        Fraction[] result_add_i = {new Fraction(5), new Fraction(7), new Fraction(9)};
        checkArray("compare vect" ,v_add_i.toArray(),result_add_i);

        //octave =  v1 - v2
        ArrayFieldVector<Fraction> v_subtract = v1.subtract(v2);
        Fraction[] result_subtract = {new Fraction(-3), new Fraction(-3), new Fraction(-3)};
        checkArray("compare vect" ,v_subtract.getData(),result_subtract);

        FieldVector<Fraction> v_subtract_i = v1.subtract(vt2);
        Fraction[] result_subtract_i = {new Fraction(-3), new Fraction(-3), new Fraction(-3)};
        checkArray("compare vect" ,v_subtract_i.toArray(),result_subtract_i);

        // octave v1 .* v2
        ArrayFieldVector<Fraction>  v_ebeMultiply = v1.ebeMultiply(v2);
        Fraction[] result_ebeMultiply = {new Fraction(4), new Fraction(10), new Fraction(18)};
        checkArray("compare vect" ,v_ebeMultiply.getData(),result_ebeMultiply);

        FieldVector<Fraction>  v_ebeMultiply_2 = v1.ebeMultiply(v2_t);
        Fraction[] result_ebeMultiply_2 = {new Fraction(4), new Fraction(10), new Fraction(18)};
        checkArray("compare vect" ,v_ebeMultiply_2.toArray(),result_ebeMultiply_2);

        // octave v1 ./ v2
        ArrayFieldVector<Fraction>  v_ebeDivide = v1.ebeDivide(v2);
        Fraction[] result_ebeDivide = {new Fraction(1, 4), new Fraction(2, 5), new Fraction(1, 2)};
        checkArray("compare vect" ,v_ebeDivide.getData(),result_ebeDivide);

        FieldVector<Fraction>  v_ebeDivide_2 = v1.ebeDivide(v2_t);
        Fraction[] result_ebeDivide_2 = {new Fraction(1, 4), new Fraction(2, 5), new Fraction(1, 2)};
        checkArray("compare vect" ,v_ebeDivide_2.toArray(),result_ebeDivide_2);

        // octave  dot(v1,v2)
        Fraction dot =  v1.dotProduct(v2);
        Assert.assertEquals("compare val ",new Fraction(32), dot);

        // octave  dot(v1,v2_t)
        Fraction dot_2 =  v1.dotProduct(v2_t);
        Assert.assertEquals("compare val ",new Fraction(32), dot_2);

        FieldMatrix<Fraction> m_outerProduct = v1.outerProduct(v2);
        Assert.assertEquals("compare val ",new Fraction(4), m_outerProduct.getEntry(0,0));

        FieldMatrix<Fraction> m_outerProduct_2 = v1.outerProduct(v2_t);
        Assert.assertEquals("compare val ",new Fraction(4), m_outerProduct_2.getEntry(0,0));

        ArrayFieldVector<Fraction> v_projection = v1.projection(v2);
        Fraction[] result_projection = {new Fraction(128, 77), new Fraction(160, 77), new Fraction(192, 77)};
        checkArray("compare vect", v_projection.getData(), result_projection);

        FieldVector<Fraction> v_projection_2 = v1.projection(v2_t);
        Fraction[] result_projection_2 = {new Fraction(128, 77), new Fraction(160, 77), new Fraction(192, 77)};
        checkArray("compare vect", v_projection_2.toArray(), result_projection_2);

    }

    @Test
    public void testMisc() {
        ArrayFieldVector<Fraction> v1 = new ArrayFieldVector(vec1);
        ArrayFieldVector<Fraction> v4 = new ArrayFieldVector(vec4);
        FieldVector<Fraction> v4_2 = new ArrayFieldVector(vec4);

        String out1 = v1.toString();
        Assert.assertTrue("some output ",  out1.length()!=0);
        /*
         Fraction[] dout1 = v1.copyOut();
        Assert.assertEquals(3, dout1.length);
        assertNotSame("testData not same object ", v1.getDataRef(), dout1);
         */
        try {
            v1.checkVectorDimensions(2);
            Assert.fail("MathIllegalArgumentException expected");
        } catch (MathIllegalArgumentException ex) {
            // expected behavior
        }

       try {
            v1.checkVectorDimensions(v4);
            Assert.fail("MathIllegalArgumentException expected");
        } catch (MathIllegalArgumentException ex) {
            // expected behavior
        }

        try {
            v1.checkVectorDimensions(v4_2);
            Assert.fail("MathIllegalArgumentException expected");
        } catch (MathIllegalArgumentException ex) {
            // expected behavior
        }

    }

    @Test
    public void testSerial()  {
        ArrayFieldVector<Fraction> v = new ArrayFieldVector(vec1);
        Assert.assertEquals(v,TestUtils.serializeAndRecover(v));
    }

    @Test
    public void testZeroVectors() {

        // when the field is not specified, array cannot be empty
        try {
            new ArrayFieldVector<Fraction>(new Fraction[0]);
            Assert.fail("MathIllegalArgumentException expected");
        } catch (MathIllegalArgumentException ex) {
            // expected behavior
        }
        try {
            new ArrayFieldVector<Fraction>(new Fraction[0], true);
            Assert.fail("MathIllegalArgumentException expected");
        } catch (MathIllegalArgumentException ex) {
            // expected behavior
        }
        try {
            new ArrayFieldVector<Fraction>(new Fraction[0], false);
            Assert.fail("MathIllegalArgumentException expected");
        } catch (MathIllegalArgumentException ex) {
            // expected behavior
        }

        // when the field is specified, array can be empty
        Assert.assertEquals(0, new ArrayFieldVector<Fraction>(FractionField.getInstance(), new Fraction[0]).getDimension());
        Assert.assertEquals(0, new ArrayFieldVector<Fraction>(FractionField.getInstance(), new Fraction[0], true).getDimension());
        Assert.assertEquals(0, new ArrayFieldVector<Fraction>(FractionField.getInstance(), new Fraction[0], false).getDimension());

    }

    @Test
    public void testOuterProduct() {
        final ArrayFieldVector<Fraction> u
            = new ArrayFieldVector<Fraction>(FractionField.getInstance(),
                                             new Fraction[] {new Fraction(1),
                                                             new Fraction(2),
                                                             new Fraction(-3)});
        final ArrayFieldVector<Fraction> v
            = new ArrayFieldVector<Fraction>(FractionField.getInstance(),
                                             new Fraction[] {new Fraction(4),
                                                             new Fraction(-2)});

        final FieldMatrix<Fraction> uv = u.outerProduct(v);

        final double tol = Math.ulp(1d);
        Assert.assertEquals(new Fraction(4).doubleValue(), uv.getEntry(0, 0).doubleValue(), tol);
        Assert.assertEquals(new Fraction(-2).doubleValue(), uv.getEntry(0, 1).doubleValue(), tol);
        Assert.assertEquals(new Fraction(8).doubleValue(), uv.getEntry(1, 0).doubleValue(), tol);
        Assert.assertEquals(new Fraction(-4).doubleValue(), uv.getEntry(1, 1).doubleValue(), tol);
        Assert.assertEquals(new Fraction(-12).doubleValue(), uv.getEntry(2, 0).doubleValue(), tol);
        Assert.assertEquals(new Fraction(6).doubleValue(), uv.getEntry(2, 1).doubleValue(), tol);
    }

    /** verifies that two vectors are equals */
    protected void checkArray(String msg, Fraction[] m, Fraction[] n) {
        if (m.length != n.length) {
            Assert.fail("vectors have different lengths");
        }
        for (int i = 0; i < m.length; i++) {
            Assert.assertEquals(msg + " " +  i + " elements differ", m[i],n[i]);
        }
    }

    /*
     * TESTS OF THE VISITOR PATTERN
     */

    /** The whole vector is visited. */
    @Test
    public void testWalkInDefaultOrderPreservingVisitor1() {
        final Fraction[] data = new Fraction[] {
            Fraction.ZERO, Fraction.ONE, Fraction.ZERO,
            Fraction.ZERO, Fraction.TWO, Fraction.ZERO,
            Fraction.ZERO, Fraction.ZERO, new Fraction(3)
        };
        final ArrayFieldVector<Fraction> v = new ArrayFieldVector(data);
        final FieldVectorPreservingVisitor<Fraction> visitor;
        visitor = new FieldVectorPreservingVisitor<Fraction>() {

            private int expectedIndex;

            public void visit(final int actualIndex, final Fraction actualValue) {
                Assert.assertEquals(expectedIndex, actualIndex);
                Assert.assertEquals(Integer.toString(actualIndex),
                                    data[actualIndex], actualValue);
                ++expectedIndex;
            }

            public void start(final int actualSize, final int actualStart,
                              final int actualEnd) {
                Assert.assertEquals(data.length, actualSize);
                Assert.assertEquals(0, actualStart);
                Assert.assertEquals(data.length - 1, actualEnd);
                expectedIndex = 0;
            }

            public Fraction end() {
                return Fraction.ZERO;
            }
        };
        v.walkInDefaultOrder(visitor);
    }

    /** Visiting an invalid subvector. */
    @Test
    public void testWalkInDefaultOrderPreservingVisitor2() {
        final ArrayFieldVector<Fraction> v = create(5);
        final FieldVectorPreservingVisitor<Fraction> visitor;
        visitor = new FieldVectorPreservingVisitor<Fraction>() {

            public void visit(int index, Fraction value) {
                // Do nothing
            }

            public void start(int dimension, int start, int end) {
                // Do nothing
            }

            public Fraction end() {
                return Fraction.ZERO;
            }
        };
        try {
            v.walkInDefaultOrder(visitor, -1, 4);
            Assert.fail();
        } catch (OutOfRangeException e) {
            // Expected behavior
        }
        try {
            v.walkInDefaultOrder(visitor, 5, 4);
            Assert.fail();
        } catch (OutOfRangeException e) {
            // Expected behavior
        }
        try {
            v.walkInDefaultOrder(visitor, 0, -1);
            Assert.fail();
        } catch (OutOfRangeException e) {
            // Expected behavior
        }
        try {
            v.walkInDefaultOrder(visitor, 0, 5);
            Assert.fail();
        } catch (OutOfRangeException e) {
            // Expected behavior
        }
        try {
            v.walkInDefaultOrder(visitor, 4, 0);
            Assert.fail();
        } catch (NumberIsTooSmallException e) {
            // Expected behavior
        }
    }

    /** Visiting a valid subvector. */
    @Test
    public void testWalkInDefaultOrderPreservingVisitor3() {
        final Fraction[] data = new Fraction[] {
            Fraction.ZERO, Fraction.ONE, Fraction.ZERO,
            Fraction.ZERO, Fraction.TWO, Fraction.ZERO,
            Fraction.ZERO, Fraction.ZERO, new Fraction(3)
        };
        final ArrayFieldVector<Fraction> v = new ArrayFieldVector(data);
        final int expectedStart = 2;
        final int expectedEnd = 7;
        final FieldVectorPreservingVisitor<Fraction> visitor;
        visitor = new FieldVectorPreservingVisitor<Fraction>() {

            private int expectedIndex;

            public void visit(final int actualIndex, final Fraction actualValue) {
                Assert.assertEquals(expectedIndex, actualIndex);
                Assert.assertEquals(Integer.toString(actualIndex),
                                    data[actualIndex], actualValue);
                ++expectedIndex;
            }

            public void start(final int actualSize, final int actualStart,
                              final int actualEnd) {
                Assert.assertEquals(data.length, actualSize);
                Assert.assertEquals(expectedStart, actualStart);
                Assert.assertEquals(expectedEnd, actualEnd);
                expectedIndex = expectedStart;
            }

            public Fraction end() {
                return Fraction.ZERO;
            }
        };
        v.walkInDefaultOrder(visitor, expectedStart, expectedEnd);
    }

    /** The whole vector is visited. */
    @Test
    public void testWalkInOptimizedOrderPreservingVisitor1() {
        final Fraction[] data = new Fraction[] {
            Fraction.ZERO, Fraction.ONE, Fraction.ZERO,
            Fraction.ZERO, Fraction.TWO, Fraction.ZERO,
            Fraction.ZERO, Fraction.ZERO, new Fraction(3)
        };
        final ArrayFieldVector<Fraction> v = new ArrayFieldVector(data);
        final FieldVectorPreservingVisitor<Fraction> visitor;
        visitor = new FieldVectorPreservingVisitor<Fraction>() {
            private final boolean[] visited = new boolean[data.length];

            public void visit(final int actualIndex, final Fraction actualValue) {
                visited[actualIndex] = true;
                Assert.assertEquals(Integer.toString(actualIndex),
                                    data[actualIndex], actualValue);
            }

            public void start(final int actualSize, final int actualStart,
                              final int actualEnd) {
                Assert.assertEquals(data.length, actualSize);
                Assert.assertEquals(0, actualStart);
                Assert.assertEquals(data.length - 1, actualEnd);
                Arrays.fill(visited, false);
            }

            public Fraction end() {
                for (int i = 0; i < data.length; i++) {
                    Assert.assertTrue("entry " + i + "has not been visited",
                                      visited[i]);
                }
                return Fraction.ZERO;
            }
        };
        v.walkInOptimizedOrder(visitor);
    }

    /** Visiting an invalid subvector. */
    @Test
    public void testWalkInOptimizedOrderPreservingVisitor2() {
        final ArrayFieldVector<Fraction> v = create(5);
        final FieldVectorPreservingVisitor<Fraction> visitor;
        visitor = new FieldVectorPreservingVisitor<Fraction>() {

            public void visit(int index, Fraction value) {
                // Do nothing
            }

            public void start(int dimension, int start, int end) {
                // Do nothing
            }

            public Fraction end() {
                return Fraction.ZERO;
            }
        };
        try {
            v.walkInOptimizedOrder(visitor, -1, 4);
            Assert.fail();
        } catch (OutOfRangeException e) {
            // Expected behavior
        }
        try {
            v.walkInOptimizedOrder(visitor, 5, 4);
            Assert.fail();
        } catch (OutOfRangeException e) {
            // Expected behavior
        }
        try {
            v.walkInOptimizedOrder(visitor, 0, -1);
            Assert.fail();
        } catch (OutOfRangeException e) {
            // Expected behavior
        }
        try {
            v.walkInOptimizedOrder(visitor, 0, 5);
            Assert.fail();
        } catch (OutOfRangeException e) {
            // Expected behavior
        }
        try {
            v.walkInOptimizedOrder(visitor, 4, 0);
            Assert.fail();
        } catch (NumberIsTooSmallException e) {
            // Expected behavior
        }
    }

    /** Visiting a valid subvector. */
    @Test
    public void testWalkInOptimizedOrderPreservingVisitor3() {
        final Fraction[] data = new Fraction[] {
            Fraction.ZERO, Fraction.ONE, Fraction.ZERO,
            Fraction.ZERO, Fraction.TWO, Fraction.ZERO,
            Fraction.ZERO, Fraction.ZERO, new Fraction(3)
        };
        final ArrayFieldVector<Fraction> v = new ArrayFieldVector(data);
        final int expectedStart = 2;
        final int expectedEnd = 7;
        final FieldVectorPreservingVisitor<Fraction> visitor;
        visitor = new FieldVectorPreservingVisitor<Fraction>() {
            private final boolean[] visited = new boolean[data.length];

            public void visit(final int actualIndex, final Fraction actualValue) {
                Assert.assertEquals(Integer.toString(actualIndex),
                                    data[actualIndex], actualValue);
                visited[actualIndex] = true;
            }

            public void start(final int actualSize, final int actualStart,
                              final int actualEnd) {
                Assert.assertEquals(data.length, actualSize);
                Assert.assertEquals(expectedStart, actualStart);
                Assert.assertEquals(expectedEnd, actualEnd);
                Arrays.fill(visited, true);
            }

            public Fraction end() {
                for (int i = expectedStart; i <= expectedEnd; i++) {
                    Assert.assertTrue("entry " + i + "has not been visited",
                                      visited[i]);
                }
                return Fraction.ZERO;
            }
        };
        v.walkInOptimizedOrder(visitor, expectedStart, expectedEnd);
    }

    /** The whole vector is visited. */
    @Test
    public void testWalkInDefaultOrderChangingVisitor1() {
        final Fraction[] data = new Fraction[] {
            Fraction.ZERO, Fraction.ONE, Fraction.ZERO,
            Fraction.ZERO, Fraction.TWO, Fraction.ZERO,
            Fraction.ZERO, Fraction.ZERO, new Fraction(3)
        };
        final ArrayFieldVector<Fraction> v = new ArrayFieldVector(data);
        final FieldVectorChangingVisitor<Fraction> visitor;
        visitor = new FieldVectorChangingVisitor<Fraction>() {

            private int expectedIndex;

            public Fraction visit(final int actualIndex, final Fraction actualValue) {
                Assert.assertEquals(expectedIndex, actualIndex);
                Assert.assertEquals(Integer.toString(actualIndex),
                                    data[actualIndex], actualValue);
                ++expectedIndex;
                return actualValue.add(actualIndex);
            }

            public void start(final int actualSize, final int actualStart,
                              final int actualEnd) {
                Assert.assertEquals(data.length, actualSize);
                Assert.assertEquals(0, actualStart);
                Assert.assertEquals(data.length - 1, actualEnd);
                expectedIndex = 0;
            }

            public Fraction end() {
                return Fraction.ZERO;
            }
        };
        v.walkInDefaultOrder(visitor);
        for (int i = 0; i < data.length; i++) {
            Assert.assertEquals("entry " + i, data[i].add(i), v.getEntry(i));
        }
    }

    /** Visiting an invalid subvector. */
    @Test
    public void testWalkInDefaultOrderChangingVisitor2() {
        final ArrayFieldVector<Fraction> v = create(5);
        final FieldVectorChangingVisitor<Fraction> visitor;
        visitor = new FieldVectorChangingVisitor<Fraction>() {

            public Fraction visit(int index, Fraction value) {
                return Fraction.ZERO;
            }

            public void start(int dimension, int start, int end) {
                // Do nothing
            }

            public Fraction end() {
                return Fraction.ZERO;
            }
        };
        try {
            v.walkInDefaultOrder(visitor, -1, 4);
            Assert.fail();
        } catch (OutOfRangeException e) {
            // Expected behavior
        }
        try {
            v.walkInDefaultOrder(visitor, 5, 4);
            Assert.fail();
        } catch (OutOfRangeException e) {
            // Expected behavior
        }
        try {
            v.walkInDefaultOrder(visitor, 0, -1);
            Assert.fail();
        } catch (OutOfRangeException e) {
            // Expected behavior
        }
        try {
            v.walkInDefaultOrder(visitor, 0, 5);
            Assert.fail();
        } catch (OutOfRangeException e) {
            // Expected behavior
        }
        try {
            v.walkInDefaultOrder(visitor, 4, 0);
            Assert.fail();
        } catch (NumberIsTooSmallException e) {
            // Expected behavior
        }
    }

    /** Visiting a valid subvector. */
    @Test
    public void testWalkInDefaultOrderChangingVisitor3() {
        final Fraction[] data = new Fraction[] {
            Fraction.ZERO, Fraction.ONE, Fraction.ZERO,
            Fraction.ZERO, Fraction.TWO, Fraction.ZERO,
            Fraction.ZERO, Fraction.ZERO, new Fraction(3)
        };
        final ArrayFieldVector<Fraction> v = new ArrayFieldVector(data);
        final int expectedStart = 2;
        final int expectedEnd = 7;
        final FieldVectorChangingVisitor<Fraction> visitor;
        visitor = new FieldVectorChangingVisitor<Fraction>() {

            private int expectedIndex;

            public Fraction visit(final int actualIndex, final Fraction actualValue) {
                Assert.assertEquals(expectedIndex, actualIndex);
                Assert.assertEquals(Integer.toString(actualIndex),
                                    data[actualIndex], actualValue);
                ++expectedIndex;
                return actualValue.add(actualIndex);
            }

            public void start(final int actualSize, final int actualStart,
                              final int actualEnd) {
                Assert.assertEquals(data.length, actualSize);
                Assert.assertEquals(expectedStart, actualStart);
                Assert.assertEquals(expectedEnd, actualEnd);
                expectedIndex = expectedStart;
            }

            public Fraction end() {
                return Fraction.ZERO;
            }
        };
        v.walkInDefaultOrder(visitor, expectedStart, expectedEnd);
        for (int i = expectedStart; i <= expectedEnd; i++) {
            Assert.assertEquals("entry " + i, data[i].add(i), v.getEntry(i));
        }
    }

    /** The whole vector is visited. */
    @Test
    public void testWalkInOptimizedOrderChangingVisitor1() {
        final Fraction[] data = new Fraction[] {
            Fraction.ZERO, Fraction.ONE, Fraction.ZERO,
            Fraction.ZERO, Fraction.TWO, Fraction.ZERO,
            Fraction.ZERO, Fraction.ZERO, new Fraction(3)
        };
        final ArrayFieldVector<Fraction> v = new ArrayFieldVector(data);
        final FieldVectorChangingVisitor<Fraction> visitor;
        visitor = new FieldVectorChangingVisitor<Fraction>() {
            private final boolean[] visited = new boolean[data.length];

            public Fraction visit(final int actualIndex, final Fraction actualValue) {
                visited[actualIndex] = true;
                Assert.assertEquals(Integer.toString(actualIndex),
                                    data[actualIndex], actualValue);
                return actualValue.add(actualIndex);
            }

            public void start(final int actualSize, final int actualStart,
                              final int actualEnd) {
                Assert.assertEquals(data.length, actualSize);
                Assert.assertEquals(0, actualStart);
                Assert.assertEquals(data.length - 1, actualEnd);
                Arrays.fill(visited, false);
            }

            public Fraction end() {
                for (int i = 0; i < data.length; i++) {
                    Assert.assertTrue("entry " + i + "has not been visited",
                                      visited[i]);
                }
                return Fraction.ZERO;
            }
        };
        v.walkInOptimizedOrder(visitor);
        for (int i = 0; i < data.length; i++) {
            Assert.assertEquals("entry " + i, data[i].add(i), v.getEntry(i));
        }
    }

    /** Visiting an invalid subvector. */
    @Test
    public void testWalkInOptimizedOrderChangingVisitor2() {
        final ArrayFieldVector<Fraction> v = create(5);
        final FieldVectorChangingVisitor<Fraction> visitor;
        visitor = new FieldVectorChangingVisitor<Fraction>() {

            public Fraction visit(int index, Fraction value) {
                return Fraction.ZERO;
            }

            public void start(int dimension, int start, int end) {
                // Do nothing
            }

            public Fraction end() {
                return Fraction.ZERO;
            }
        };
        try {
            v.walkInOptimizedOrder(visitor, -1, 4);
            Assert.fail();
        } catch (OutOfRangeException e) {
            // Expected behavior
        }
        try {
            v.walkInOptimizedOrder(visitor, 5, 4);
            Assert.fail();
        } catch (OutOfRangeException e) {
            // Expected behavior
        }
        try {
            v.walkInOptimizedOrder(visitor, 0, -1);
            Assert.fail();
        } catch (OutOfRangeException e) {
            // Expected behavior
        }
        try {
            v.walkInOptimizedOrder(visitor, 0, 5);
            Assert.fail();
        } catch (OutOfRangeException e) {
            // Expected behavior
        }
        try {
            v.walkInOptimizedOrder(visitor, 4, 0);
            Assert.fail();
        } catch (NumberIsTooSmallException e) {
            // Expected behavior
        }
    }

    /** Visiting a valid subvector. */
    @Test
    public void testWalkInOptimizedOrderChangingVisitor3() {
        final Fraction[] data = new Fraction[] {
            Fraction.ZERO, Fraction.ONE, Fraction.ZERO,
            Fraction.ZERO, Fraction.TWO, Fraction.ZERO,
            Fraction.ZERO, Fraction.ZERO, new Fraction(3)
        };
        final ArrayFieldVector<Fraction> v = new ArrayFieldVector(data);
        final int expectedStart = 2;
        final int expectedEnd = 7;
        final FieldVectorChangingVisitor<Fraction> visitor;
        visitor = new FieldVectorChangingVisitor<Fraction>() {
            private final boolean[] visited = new boolean[data.length];

            public Fraction visit(final int actualIndex, final Fraction actualValue) {
                Assert.assertEquals(Integer.toString(actualIndex),
                                    data[actualIndex], actualValue);
                visited[actualIndex] = true;
                return actualValue.add(actualIndex);
            }

            public void start(final int actualSize, final int actualStart,
                              final int actualEnd) {
                Assert.assertEquals(data.length, actualSize);
                Assert.assertEquals(expectedStart, actualStart);
                Assert.assertEquals(expectedEnd, actualEnd);
                Arrays.fill(visited, true);
            }

            public Fraction end() {
                for (int i = expectedStart; i <= expectedEnd; i++) {
                    Assert.assertTrue("entry " + i + "has not been visited",
                                      visited[i]);
                }
                return Fraction.ZERO;
            }
        };
        v.walkInOptimizedOrder(visitor, expectedStart, expectedEnd);
        for (int i = expectedStart; i <= expectedEnd; i++) {
            Assert.assertEquals("entry " + i, data[i].add(i), v.getEntry(i));
        }
    }

    private ArrayFieldVector<Fraction> create(int n) {
        Fraction[] t = new Fraction[n];
        for (int i = 0; i < n; ++i) {
            t[i] = Fraction.ZERO;
        }
        return new ArrayFieldVector<Fraction>(t);
    }
}

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