    1   /*
    2    *
    3    * Copyright (c) 2003-2004 The Apache Software Foundation. All rights reserved.
    4    *
    5    * Licensed under the Apache License, Version 2.0 (the "License"); you may not
    6    * use this file except in compliance with the License. You may obtain a copy
    7    * of the License at
    8    *
    9    * http://www.apache.org/licenses/LICENSE-2.0
    10   *
    11   * Unless required by applicable law or agreed to in writing, software
    12   * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
    13   * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
    14   * License for the specific language governing permissions and limitations
    15   * under the License.
    16   *
    17   */
    18  package org.apache.commons.math.analysis;
    19
    20  // commons-math
    21  import org.apache.commons.math.MathException;
    22
    23  // junit
    24  import junit.framework.TestCase;
    25
    26  /***
    27   * Tests the PolynomialFunction implementation of a UnivariateRealFunction.
    28   *
    29   * @version $Revision: 1.6 $
    30   * @author Matt Cliff <matt@mattcliff.com>
    31   */
    32  public final class PolynomialFunctionTest extends TestCase {
    33
    34      /*** Error tolerance for tests */
    35      protected double tolerance = 1.0e-12;
    36
    37      /***
    38       * tests the value of a constant polynomial.
    39       *
    40       * <p>value of this is 2.5 everywhere.</p>
    41       */
    42      public void testConstants() throws MathException {
    43          double[] c = { 2.5 };
    44          PolynomialFunction f = new PolynomialFunction( c );
    45
    46          // verify that we are equal to c[0] at several (nonsymmetric) places
    47          assertEquals( f.value( 0.0), c[0], tolerance );
    48          assertEquals( f.value( -1.0), c[0], tolerance );
    49          assertEquals( f.value( -123.5), c[0], tolerance );
    50          assertEquals( f.value( 3.0), c[0], tolerance );
    51          assertEquals( f.value( 456.89), c[0], tolerance );
    52
    53          assertEquals(f.degree(), 0);
    54          assertEquals(f.derivative().value(0), 0, tolerance);
    55
    56          assertEquals(f.polynomialDerivative().derivative().value(0), 0, tolerance);
    57      }
    58
    59      /***
    60       * tests the value of a linear polynomial.
    61       *
    62       * <p>This will test the function f(x) = 3*x - 1.5</p>
    63       * <p>This will have the values
    64       *  <tt>f(0.0) = -1.5, f(-1.0) = -4.5, f(-2.5) = -9.0,
    65       *      f(0.5) = 0.0, f(1.5) = 3.0</tt> and <tt>f(3.0) = 7.5</tt>
    66       * </p>
    67       */
    68      public void testLinear() throws MathException {
    69          double[] c = { -1.5, 3.0 };
    70          PolynomialFunction f = new PolynomialFunction( c );
    71
    72          // verify that we are equal to c[0] when x=0
    73          assertEquals( f.value( 0.0), c[0], tolerance );
    74
    75          // now check a few other places
    76          assertEquals( -4.5, f.value( -1.0), tolerance );
    77          assertEquals( -9.0, f.value( -2.5), tolerance );
    78          assertEquals( 0.0, f.value( 0.5), tolerance );
    79          assertEquals( 3.0, f.value( 1.5), tolerance );
    80          assertEquals( 7.5, f.value( 3.0), tolerance );
    81
    82          assertEquals(f.degree(), 1);
    83
    84          assertEquals(f.polynomialDerivative().derivative().value(0), 0, tolerance);
    85
    86      }
    87
    88
    89      /***
    90       * Tests a second order polynomial.
    91       * <p> This will test the function f(x) = 2x^2 - 3x -2 = (2x+1)(x-2)</p>
    92       *
    93       */
    94      public void testQuadratic() throws MathException {
    95          double[] c = { -2.0, -3.0, 2.0 };
    96          PolynomialFunction f = new PolynomialFunction( c );
    97
    98          // verify that we are equal to c[0] when x=0
    99          assertEquals( f.value( 0.0), c[0], tolerance );
    100
    101         // now check a few other places
    102         assertEquals( 0.0, f.value( -0.5), tolerance );
    103         assertEquals( 0.0, f.value( 2.0), tolerance );
    104         assertEquals( -2.0, f.value( 1.5), tolerance );
    105         assertEquals( 7.0, f.value( -1.5), tolerance );
    106         assertEquals( 265.5312, f.value( 12.34), tolerance );
    107
    108     }
    109
    110
    111     /***
    112      * This will test the quintic function
    113      *   f(x) = x^2(x-5)(x+3)(x-1) = x^5 - 3x^4 -13x^3 + 15x^2</p>
    114      *
    115      */
    116     public void testQuintic() throws MathException {
    117         double[] c = { 0.0, 0.0, 15.0, -13.0, -3.0, 1.0 };
    118         PolynomialFunction f = new PolynomialFunction( c );
    119
    120         // verify that we are equal to c[0] when x=0
    121         assertEquals( f.value( 0.0), c[0], tolerance );
    122
    123         // now check a few other places
    124         assertEquals( 0.0, f.value( 5.0), tolerance );
    125         assertEquals( 0.0, f.value( 1.0), tolerance );
    126         assertEquals( 0.0, f.value( -3.0), tolerance );
    127         assertEquals( 54.84375, f.value( -1.5), tolerance );
    128         assertEquals( -8.06637, f.value( 1.3), tolerance );
    129
    130         assertEquals(f.degree(), 5);
    131
    132     }
    133
    134
    135     /***
    136      * tests the firstDerivative function by comparision
    137      *
    138      * <p>This will test the functions
    139      * <tt>f(x) = x^3 - 2x^2 + 6x + 3, g(x) = 3x^2 - 4x + 6</tt>
    140      * and <tt>h(x) = 6x - 4</tt>
    141      */
    142     public void testfirstDerivativeComparision() throws MathException {
    143         double[] f_coeff = { 3.0, 6.0, -2.0, 1.0 };
    144         double[] g_coeff = { 6.0, -4.0, 3.0 };
    145         double[] h_coeff = { -4.0, 6.0 };
    146
    147         PolynomialFunction f = new PolynomialFunction( f_coeff );
    148         PolynomialFunction g = new PolynomialFunction( g_coeff );
    149         PolynomialFunction h = new PolynomialFunction( h_coeff );
    150
    151         // compare f' = g
    152         assertEquals( f.derivative().value(0.0), g.value(0.0), tolerance );
    153         assertEquals( f.derivative().value(1.0), g.value(1.0), tolerance );
    154         assertEquals( f.derivative().value(100.0), g.value(100.0), tolerance );
    155         assertEquals( f.derivative().value(4.1), g.value(4.1), tolerance );
    156         assertEquals( f.derivative().value(-3.25), g.value(-3.25), tolerance );
    157
    158         // compare g' = h
    159
    160
    161         // compare f'' = h
    162     }
    163
    164 }