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testRoots.cpp

///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
// 
// All rights reserved.
// 
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
// *       Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
// *       Redistributions in binary form must reproduce the above
// copyright notice, this list of conditions and the following disclaimer
// in the documentation and/or other materials provided with the
// distribution.
// *       Neither the name of Industrial Light & Magic nor the names of
// its contributors may be used to endorse or promote products derived
// from this software without specific prior written permission. 
// 
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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///////////////////////////////////////////////////////////////////////////



#include <testRoots.h>
#include <ImathRoots.h>
#include <ImathFun.h>
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <assert.h>


using namespace std;


void
sort (int nx, double &x0, double &x1, double &x2)
{
    if (nx == 2)
    {
      if (x0 > x1)
          swap (x0, x1);
    }

    if (nx == 3)
    {
      if (x0 > x1)
          swap (x0, x1);
      if (x1 > x2)
          swap (x1, x2);
      if (x0 > x1)
          swap (x0, x1);
    }
}


void
sort (int nx, double x[])
{
    if (nx == 2)
    {
      if (x[0] > x[1])
          swap (x[0], x[1]);
    }

    if (nx == 3)
    {
      if (x[0] > x[1])
          swap (x[0], x[1]);
      if (x[1] > x[2])
          swap (x[1], x[2]);
      if (x[0] > x[1])
          swap (x[0], x[1]);
    }
}


void
solve (double a, double b, double c, double d,  // coefficients
       int nx,                            // number of expected solutions
       double x0, double x1, double x2)         // expected solutions
{
    cout << "coefficients: " <<
          setw(3) << a << ' ' <<
          setw(3) << b << ' ' <<
          setw(3) << c << ' ' <<
          setw(3) << d << ' ';

    //
    // Solve the equation a*x^3 + b*x^2 + c*x +d
    //

    double x[3];
    int n = Imath::solveCubic (a, b, c, d, x);

    //
    // Sort the numerical solutions.
    // Sorte the expected solutions.
    //
    sort (nx, x0, x1, x2);
    sort (n, x);

    //
    // Compare the numerical and the expected solutions.
    //

    assert (n == nx);

    cout << " solutions: ";

    if (n == -1)
      cout << "[-inf, inf]";

    if (n == 0)
      cout << "none";

    const double e = 0.0000001;           // maximum expected error for
                              // the test cases listed below
    if (n >= 1)
    {
      cout << x[0];
      assert (Imath::equal (x[0], x0, e));
    }
    if (n >= 2)
    {
      cout << ' ' << x[1];
      assert (Imath::equal (x[1], x1, e));
    }
    if (n >= 3)
    {
      cout << ' ' << x[2];
      assert (Imath::equal (x[2], x2, e));
    }

    cout << endl;
}


void
testRoots ()
{
    cout << "Testing functions in ImathRoots.h" << endl;

    //    coefficients         number of expected solutions
    //            |            |
    //            |            |   expected solutions
    //            |            |         |
    //    +-------+--------+   |  +------+-----+
    //    |                |   |  |            |
    solve (1,   6,  11,   6,   3,  -1,  -2,  -3); // real solutions: -1, -2, -3
    solve (2,   2, -20,  16,   3,   1,  -4,   2); // real solutions: 1, -4, 2
    solve (3,  -3,   1,  -1,   1,   1,   0,   0); // real solutions: 1
    solve (2,   0, -24, -32,   2,   4,  -2,   0); // real solutions: 4, -2
    solve (1,   0,   0,   0,   1,   0,   0,   0); // real solutions: 0
    solve (8, -24,  24,  -8,   1,   1,   0,   0); // real solutions: 1
    solve (0,   2, -10,  12,   2,   2,   3,   0); // real solutions: 2, 3
    solve (0,   1,  -1, -20,   2,   5,  -4,   0); // real solutions: 5, -4
    solve (0,   3, -12,  12,   1,   2,   0,   0); // real solutions: 2
    solve (0,   1,   0,   0,   1,   0,   0,   0); // real solutions: 0
    solve (0,   1,   0,   1,   0,   0,   0,   0); // real solutions: none
    solve (0,   0,   3,  -6,   1,   2,   0,   0); // real solutions: 2
    solve (0,   0,   5,  15,   1,  -3,   0,   0); // real solutions: -3
    solve (0,   0,   1,   0,   1,   0,   0,   0); // real solutions: 0
    solve (0,   0,   0,   1,   0,   0,   0,   0); // real solutions: none
    solve (0,   0,   0,   0,  -1,   0,   0,   0); // real solutions: [-inf, inf]

    cout << "ok\n" << endl;
}

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