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/*
* plot_algorithms.h -- plot function templates, for build use only
*
* Andrew D. Hwang <rot 13 nujnat at zngupf dot ubylpebff dot rqh>
*
* Version 1.0.16
* Last Change: October 14, 2006
*
*/
/*
* Copyright (C) 2001, 2002, 2003, 2004, 2005, 2006
* Andrew D. Hwang <rot 13 nujnat at zngupf dot ubylpebff dot rqh>
* Department of Mathematics and Computer Science
* College of the Holy Cross
* Worcester, MA, 01610-2395, USA
*/
/*
* ePiX is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* ePiX is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
* License for more details.
*
* You should have received a copy of the GNU General Public License
* along with ePiX; if not, write to the Free Software Foundation, Inc.,
* 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
/*
* This file provides plotting templates, with T a class
*
* void plot_map_dom(const T&, const domain&)
* void plot_map_domlist(const T&, const std::vector<domain>&)
* void plot_function(const T&, double, double, int)
* void euler_plot(const T&, const P&, double, double, int)
* P euler_flow(const T&, P start, double, int)
*/
#ifndef EPIX_PLOT_ALGO
#define EPIX_PLOT_ALGO
#include "triples.h"
#include "functions.h"
#include "domain.h"
namespace ePiX {
template<class T> void plot_map_dom(const T& map, const domain& R)
{
int i_max((R.dx1() > 0) ? R.coarse.n1() : 0); // max summation index
int j_max((R.dx2() > 0) ? R.coarse.n2() : 0);
int k_max((R.dx3() > 0) ? R.coarse.n3() : 0);
if (R.dx1() > 0) // there's something to draw
{
int count1(R.fine.n1()); // number of intervals in subdivision
std::vector<vertex> data1(1+count1);
double st1(R.dx1());
double st2(R.step2());
double st3(R.step3());
for (int j=0; j <= j_max; ++j)
for (int k=0; k <= k_max; ++k)
{
P curr(R.corner1 + (j*st2)*E_2 + (k*st3)*E_3);
for (int i=0; i <= count1; ++i, curr += st1*E_1)
data1.at(i) = vertex(map(curr));
// close path if initial and terminal points coincide
path path1(data1, false);
path1.draw();
}
}
if (R.dx2() > 0)
{
int count2(R.fine.n2());
std::vector<vertex> data2(1+count2);
double st1(R.step1());
double st2(R.dx2());
double st3(R.step3());
for (int i=0; i <= i_max; ++i)
for (int k=0; k <= k_max; ++k)
{
P curr(R.corner1 + (i*st1)*E_1 + (k*st3)*E_3);
for (int j=0; j <= count2; ++j, curr += st2*E_2)
data2.at(j) = vertex(map(curr));
// close path if initial and terminal points coincide
path path2(data2, false);
path2.draw();
}
}
if (R.dx3() > 0)
{
int count3(R.fine.n3());
std::vector<vertex> data3(1+count3);
double st1(R.step1());
double st2(R.step2());
double st3(R.dx3());
for (int i=0; i <= i_max; ++i)
for (int j=0; j <= j_max; ++j)
{
P curr(R.corner1 + (i*st1)*E_1 + (j*st2)*E_2);
for (int k=0; k <= count3; ++k, curr += st3*E_3)
data3.at(k) = vertex(map(curr));
// close path if initial and terminal points coincide
path path3(data3, false);
path3.draw();
}
}
}; // end of plot_map_dom
// plot over a list of domains
template<class T> void plot_map_domlist(const T& map,
const std::vector<domain>& R_list)
{
for (unsigned int i=0; i < R_list.size(); ++i)
plot_map_dom(map, R_list.at(i));
}
// paths
template<class T>void plot_function(const T& f, double t1, double t2, int n)
{
plot_map_dom(f, domain(t1, t2, n));
}
// Solutions of ODE systems
template<class VF> void euler_plot(const VF& field, const P& start,
double t_min, double t_max, int num_pts)
{
std::vector<vertex> data(num_pts+1);
P curr(start);
const double dt(t_max/(num_pts*EPIX_ITERATIONS));
const double dseek(t_min/(num_pts*EPIX_ITERATIONS));
if (fabs(t_min/num_pts) > EPIX_EPSILON) // seek beginning of path
for (int i=0; i <= num_pts*EPIX_ITERATIONS; ++i)
curr += dseek*field(curr);
// Euler's method ---v
for (int i=0; i <= num_pts*EPIX_ITERATIONS; ++i, curr += dt*field(curr))
if (i%EPIX_ITERATIONS == 0)
data.at(i/EPIX_ITERATIONS) = vertex(curr); // N.B. integer division
path temp(data, false);
temp.draw();
end_stanza();
} // end of euler_plot
// flow x0 under field for specified time; pass x0 by value
template<class VF> P euler_flow(const VF& field, P x0,
double t_max, int num_pts=0)
{
if (num_pts == 0) // use "sensible" default; hardwired constant 4
num_pts = 4*(1 + (int)ceil(fabs(t_max)));
const double dt(t_max/(num_pts*EPIX_ITERATIONS));
for (int i=0; i <= num_pts*EPIX_ITERATIONS; ++i)
x0 += dt*field(x0);
return x0;
}
} // end of namespace
#endif /* EPIX_PLOT_ALGO */
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