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/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
/*
* Main authors:
* Vincent Barichard <Vincent.Barichard@univ-angers.fr>
*
* Copyright:
* Vincent Barichard, 2012
*
* This file is part of Gecode, the generic constraint
* development environment:
* http://www.gecode.org
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
* LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
* OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
* WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
*/
#include <gecode/driver.hh>
#include <gecode/minimodel.hh>
#include <gecode/float.hh>
using namespace Gecode;
/**
* \brief %Example: Folium of Descartes
*
* The folium of Descartes is a curve defined by the equation:
* \f[
* x^3 + y^3 - 3axy = 0
* \f]
*
* A technique to solve it, is to write \f$y=px\f$ and solve for
* \f$x\f$ and \f$y\f$ in terms of \f$p\f$. By setting
* \f$a=1\f$, it yields to the paramatric equation:
*
* \f[
* x^3 + y^3 - 3xy = 0
* \f]
* \f[
* x=\frac{3p}{1+p^3},\quad y=\frac{3p^2}{1+p^3}
* \f]
*
* The parameter \f$p\f$ is related to the position on the curve
* and is constrained to get different solutions for \f$x\f$ and
* \f$y\f$. To get reasonable interval starting sizes, \f$p\f$
* and \f$y\f$ are restricted to \f$[-20;20]\f$ and \f$x\f$ is
* restricted to \f$[-1;2]\f$.
*
* \ingroup Example
*/
class DescartesFolium : public FloatMaximizeScript {
protected:
/// The numbers
FloatVarArray f;
/// Minimum distance between two solutions
double step;
public:
/// Actual model
DescartesFolium(const Options& opt)
: FloatMaximizeScript(opt), f(*this,3,-20,20) {
if (opt.trace() != 0)
trace(*this, f, opt.trace());
// Post equation
FloatVar p = f[0];
FloatVar x = f[1];
FloatVar y = f[2];
rel(*this, 3*p/(1+pow(p,3)) == x);
rel(*this, 3*sqr(p)/(1+pow(p,3)) == y);
rel(*this, pow(x,3) + pow(y,3) == 3 * x * y);
rel(*this, x == FloatVal(-1,2));
branch(*this,p,FLOAT_VAL_SPLIT_MIN());
}
/// Constructor for cloning \a p
DescartesFolium(DescartesFolium& p)
: FloatMaximizeScript(p) {
f.update(*this, p.f);
}
/// Copy during cloning
virtual Space* copy(void) {
return new DescartesFolium(*this);
}
/// Cost function
virtual FloatVar cost(void) const {
return f[0];
}
/// Print solution coordinates
virtual void print(std::ostream& os) const {
os << "XY " << f[1].med() << " " << f[2].med()
<< std::endl;
}
};
/** \brief Main-function
* \relates DescartesFolium
*/
int main(int argc, char* argv[]) {
Options opt("DescartesFolium");
opt.solutions(0);
opt.step(0.1);
opt.parse(argc,argv);
FloatMaximizeScript::run<DescartesFolium,BAB,Options>(opt);
return 0;
}
// STATISTICS: example-any
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