Jip J. Dekker
3e72b0e857
git-subtree-dir: software/gecode_on_record git-subtree-split: 37ed9bda495ea87e63217c19a374b5a93bb0078e
127 lines
3.6 KiB
C++
127 lines
3.6 KiB
C++
/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
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/*
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* Main authors:
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* Vincent Barichard <Vincent.Barichard@univ-angers.fr>
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*
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* Copyright:
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* Vincent Barichard, 2012
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*
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* This file is part of Gecode, the generic constraint
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* development environment:
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* http://www.gecode.org
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*
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* Permission is hereby granted, free of charge, to any person obtaining
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* a copy of this software and associated documentation files (the
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* "Software"), to deal in the Software without restriction, including
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* without limitation the rights to use, copy, modify, merge, publish,
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* distribute, sublicense, and/or sell copies of the Software, and to
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* permit persons to whom the Software is furnished to do so, subject to
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* the following conditions:
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*
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* The above copyright notice and this permission notice shall be
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* included in all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
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* LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
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* OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
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* WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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*
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*/
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#include <gecode/driver.hh>
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#include <gecode/minimodel.hh>
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#include <gecode/float.hh>
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using namespace Gecode;
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/**
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* \brief %Example: Folium of Descartes
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*
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* The folium of Descartes is a curve defined by the equation:
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* \f[
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* x^3 + y^3 - 3axy = 0
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* \f]
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*
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* A technique to solve it, is to write \f$y=px\f$ and solve for
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* \f$x\f$ and \f$y\f$ in terms of \f$p\f$. By setting
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* \f$a=1\f$, it yields to the paramatric equation:
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*
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* \f[
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* x^3 + y^3 - 3xy = 0
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* \f]
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* \f[
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* x=\frac{3p}{1+p^3},\quad y=\frac{3p^2}{1+p^3}
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* \f]
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*
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* The parameter \f$p\f$ is related to the position on the curve
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* and is constrained to get different solutions for \f$x\f$ and
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* \f$y\f$. To get reasonable interval starting sizes, \f$p\f$
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* and \f$y\f$ are restricted to \f$[-20;20]\f$ and \f$x\f$ is
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* restricted to \f$[-1;2]\f$.
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*
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* \ingroup Example
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*/
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class DescartesFolium : public FloatMaximizeScript {
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protected:
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/// The numbers
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FloatVarArray f;
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/// Minimum distance between two solutions
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double step;
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public:
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/// Actual model
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DescartesFolium(const Options& opt)
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: FloatMaximizeScript(opt), f(*this,3,-20,20) {
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if (opt.trace() != 0)
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trace(*this, f, opt.trace());
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// Post equation
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FloatVar p = f[0];
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FloatVar x = f[1];
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FloatVar y = f[2];
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rel(*this, 3*p/(1+pow(p,3)) == x);
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rel(*this, 3*sqr(p)/(1+pow(p,3)) == y);
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rel(*this, pow(x,3) + pow(y,3) == 3 * x * y);
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rel(*this, x == FloatVal(-1,2));
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branch(*this,p,FLOAT_VAL_SPLIT_MIN());
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}
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/// Constructor for cloning \a p
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DescartesFolium(DescartesFolium& p)
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: FloatMaximizeScript(p) {
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f.update(*this, p.f);
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}
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/// Copy during cloning
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virtual Space* copy(void) {
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return new DescartesFolium(*this);
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}
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/// Cost function
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virtual FloatVar cost(void) const {
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return f[0];
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}
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/// Print solution coordinates
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virtual void print(std::ostream& os) const {
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os << "XY " << f[1].med() << " " << f[2].med()
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<< std::endl;
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}
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};
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/** \brief Main-function
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* \relates DescartesFolium
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*/
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int main(int argc, char* argv[]) {
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Options opt("DescartesFolium");
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opt.solutions(0);
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opt.step(0.1);
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opt.parse(argc,argv);
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FloatMaximizeScript::run<DescartesFolium,BAB,Options>(opt);
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return 0;
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}
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// STATISTICS: example-any
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