261 lines
7.3 KiB
C++
261 lines
7.3 KiB
C++
///////////////////////////////////////////////////////////////////////////
|
|
//
|
|
// 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.
|
|
//
|
|
///////////////////////////////////////////////////////////////////////////
|
|
|
|
|
|
|
|
#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_INTERNAL_NAMESPACE::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_INTERNAL_NAMESPACE::equal (x[0], x0, e));
|
|
}
|
|
if (n >= 2)
|
|
{
|
|
cout << ' ' << x[1];
|
|
assert (IMATH_INTERNAL_NAMESPACE::equal (x[1], x1, e));
|
|
}
|
|
if (n >= 3)
|
|
{
|
|
cout << ' ' << x[2];
|
|
assert (IMATH_INTERNAL_NAMESPACE::equal (x[2], x2, e));
|
|
}
|
|
|
|
cout << endl;
|
|
}
|
|
|
|
void
|
|
solve (double a, double b, double c, // coefficients
|
|
int nx, // number of expected solutions
|
|
double x0, double x1) // expected solutions
|
|
{
|
|
cout << "coefficients: " <<
|
|
setw(3) << a << ' ' <<
|
|
setw(3) << b << ' ' <<
|
|
setw(3) << c << ' ';
|
|
//
|
|
// Solve the equation a*x^2 + b*x^1 + c*x
|
|
//
|
|
|
|
double x[2];
|
|
int n = IMATH_INTERNAL_NAMESPACE::solveQuadratic (a, b, c, x);
|
|
|
|
//
|
|
// Sort the numerical solutions.
|
|
// Sort the expected solutions.
|
|
//
|
|
// Dummy variable for sort
|
|
double x2;
|
|
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_INTERNAL_NAMESPACE::equal (x[0], x0, e));
|
|
}
|
|
|
|
if (n >= 2)
|
|
{
|
|
cout << ' ' << x[1];
|
|
assert (IMATH_INTERNAL_NAMESPACE::equal (x[1], x1, e));
|
|
}
|
|
|
|
cout << endl;
|
|
}
|
|
|
|
void
|
|
testRoots ()
|
|
{
|
|
cout << "Testing functions in ImathRoots.h" << endl;
|
|
|
|
cout << endl << "solveCubic" << endl;
|
|
// Solve cubiec equations
|
|
//
|
|
// 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 << endl << "solveQuadratic" << endl;
|
|
// Solve quadratic equations
|
|
//
|
|
// coefficients number of expected solutions
|
|
// | |
|
|
// | | expected solutions
|
|
// | | |
|
|
// +-----+-----+ | +---+---+
|
|
// | | | | |
|
|
solve (1, 3, 2, 2, -1, -2); // real solutions: -1, -2
|
|
solve (1, 0, -9, 2, -3, 3); // real solutions: -3, 3
|
|
solve (1, -4, 0, 2, 4, 0); // real solutions: 0, 4
|
|
solve (2, -4, 2, 1, 1, 0); // real solutions: 1
|
|
solve (0, -4, 8, 1, 2, 0); // real solutions: 2
|
|
solve (0, 7, 0, 1, 0, 0); // real solutions: 0
|
|
solve (10, 0, 0, 1, 0, 0); // real solutions: 0
|
|
solve (0, 0, 0, -1, 0, 0); // real solutions: [-inf, inf]
|
|
solve (0, 0, 1, 0, 0, 0); // real solutions: none
|
|
solve (3, -6, 30, 0, 0, 0); // real solutions: none
|
|
cout << "ok\n" << endl;
|
|
}
|
|
|
|
|