261 lines
7.3 KiB
C++
261 lines
7.3 KiB
C++
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///////////////////////////////////////////////////////////////////////////
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//
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// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
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// Digital Ltd. LLC
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//
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// All rights reserved.
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above
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// copyright notice, this list of conditions and the following disclaimer
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// in the documentation and/or other materials provided with the
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// distribution.
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// * Neither the name of Industrial Light & Magic nor the names of
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// its contributors may be used to endorse or promote products derived
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// from this software without specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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///////////////////////////////////////////////////////////////////////////
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#include <testRoots.h>
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#include "ImathRoots.h"
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#include "ImathFun.h"
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#include <iostream>
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#include <iomanip>
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#include <algorithm>
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#include <assert.h>
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using namespace std;
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void
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sort (int nx, double &x0, double &x1, double &x2)
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{
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if (nx == 2)
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{
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if (x0 > x1)
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swap (x0, x1);
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}
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if (nx == 3)
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{
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if (x0 > x1)
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swap (x0, x1);
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if (x1 > x2)
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swap (x1, x2);
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if (x0 > x1)
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swap (x0, x1);
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}
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}
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void
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sort (int nx, double x[])
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{
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if (nx == 2)
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{
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if (x[0] > x[1])
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swap (x[0], x[1]);
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}
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if (nx == 3)
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{
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if (x[0] > x[1])
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swap (x[0], x[1]);
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if (x[1] > x[2])
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swap (x[1], x[2]);
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if (x[0] > x[1])
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swap (x[0], x[1]);
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}
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}
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void
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solve (double a, double b, double c, double d, // coefficients
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int nx, // number of expected solutions
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double x0, double x1, double x2) // expected solutions
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{
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cout << "coefficients: " <<
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setw(3) << a << ' ' <<
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setw(3) << b << ' ' <<
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setw(3) << c << ' ' <<
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setw(3) << d << ' ';
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//
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// Solve the equation a*x^3 + b*x^2 + c*x +d
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//
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double x[3];
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int n = IMATH_INTERNAL_NAMESPACE::solveCubic (a, b, c, d, x);
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//
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// Sort the numerical solutions.
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// Sorte the expected solutions.
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//
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sort (nx, x0, x1, x2);
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sort (n, x);
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//
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// Compare the numerical and the expected solutions.
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//
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assert (n == nx);
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cout << " solutions: ";
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if (n == -1)
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cout << "[-inf, inf]";
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if (n == 0)
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cout << "none";
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const double e = 0.0000001; // maximum expected error for
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// the test cases listed below
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if (n >= 1)
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{
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cout << x[0];
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assert (IMATH_INTERNAL_NAMESPACE::equal (x[0], x0, e));
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}
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if (n >= 2)
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{
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cout << ' ' << x[1];
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assert (IMATH_INTERNAL_NAMESPACE::equal (x[1], x1, e));
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}
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if (n >= 3)
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{
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cout << ' ' << x[2];
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assert (IMATH_INTERNAL_NAMESPACE::equal (x[2], x2, e));
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}
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cout << endl;
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}
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void
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solve (double a, double b, double c, // coefficients
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int nx, // number of expected solutions
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double x0, double x1) // expected solutions
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{
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cout << "coefficients: " <<
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setw(3) << a << ' ' <<
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setw(3) << b << ' ' <<
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setw(3) << c << ' ';
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//
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// Solve the equation a*x^2 + b*x^1 + c*x
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//
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double x[2];
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int n = IMATH_INTERNAL_NAMESPACE::solveQuadratic (a, b, c, x);
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//
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// Sort the numerical solutions.
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// Sort the expected solutions.
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//
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// Dummy variable for sort
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double x2;
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sort (nx, x0, x1, x2);
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sort (n, x);
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//
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// Compare the numerical and the expected solutions.
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//
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assert (n == nx);
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cout << " solutions: ";
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if (n == -1)
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cout << "[-inf, inf]";
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if (n == 0)
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cout << "none";
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const double e = 0.0000001; // maximum expected error for
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// the test cases listed below
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if (n >= 1)
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{
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cout << x[0];
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assert (IMATH_INTERNAL_NAMESPACE::equal (x[0], x0, e));
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}
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if (n >= 2)
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{
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cout << ' ' << x[1];
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assert (IMATH_INTERNAL_NAMESPACE::equal (x[1], x1, e));
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}
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cout << endl;
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}
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void
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testRoots ()
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{
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cout << "Testing functions in ImathRoots.h" << endl;
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cout << endl << "solveCubic" << endl;
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// Solve cubiec equations
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//
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// coefficients number of expected solutions
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// | |
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// | | expected solutions
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// | | |
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// +-------+--------+ | +------+-----+
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// | | | | |
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solve (1, 6, 11, 6, 3, -1, -2, -3); // real solutions: -1, -2, -3
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solve (2, 2, -20, 16, 3, 1, -4, 2); // real solutions: 1, -4, 2
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solve (3, -3, 1, -1, 1, 1, 0, 0); // real solutions: 1
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solve (2, 0, -24, -32, 2, 4, -2, 0); // real solutions: 4, -2
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solve (1, 0, 0, 0, 1, 0, 0, 0); // real solutions: 0
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solve (8, -24, 24, -8, 1, 1, 0, 0); // real solutions: 1
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solve (0, 2, -10, 12, 2, 2, 3, 0); // real solutions: 2, 3
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solve (0, 1, -1, -20, 2, 5, -4, 0); // real solutions: 5, -4
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solve (0, 3, -12, 12, 1, 2, 0, 0); // real solutions: 2
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solve (0, 1, 0, 0, 1, 0, 0, 0); // real solutions: 0
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solve (0, 1, 0, 1, 0, 0, 0, 0); // real solutions: none
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solve (0, 0, 3, -6, 1, 2, 0, 0); // real solutions: 2
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solve (0, 0, 5, 15, 1, -3, 0, 0); // real solutions: -3
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solve (0, 0, 1, 0, 1, 0, 0, 0); // real solutions: 0
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solve (0, 0, 0, 1, 0, 0, 0, 0); // real solutions: none
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solve (0, 0, 0, 0, -1, 0, 0, 0); // real solutions: [-inf, inf]
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cout << endl << "solveQuadratic" << endl;
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// Solve quadratic equations
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//
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// coefficients number of expected solutions
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// | |
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// | | expected solutions
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// | | |
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// +-----+-----+ | +---+---+
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// | | | | |
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solve (1, 3, 2, 2, -1, -2); // real solutions: -1, -2
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solve (1, 0, -9, 2, -3, 3); // real solutions: -3, 3
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solve (1, -4, 0, 2, 4, 0); // real solutions: 0, 4
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solve (2, -4, 2, 1, 1, 0); // real solutions: 1
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solve (0, -4, 8, 1, 2, 0); // real solutions: 2
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solve (0, 7, 0, 1, 0, 0); // real solutions: 0
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solve (10, 0, 0, 1, 0, 0); // real solutions: 0
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solve (0, 0, 0, -1, 0, 0); // real solutions: [-inf, inf]
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solve (0, 0, 1, 0, 0, 0); // real solutions: none
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solve (3, -6, 30, 0, 0, 0); // real solutions: none
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cout << "ok\n" << endl;
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}
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