246 lines
7.2 KiB
Python
246 lines
7.2 KiB
Python
# This file is part of Bertini 2.
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#
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# python/test/system_test.py is free software: you can redistribute it and/or modify
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# it under the terms of the GNU General Public License as published by
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# the Free Software Foundation, either version 3 of the License, or
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# (at your option) any later version.
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#
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# python/test/system_test.py is distributed in the hope that it will be useful,
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# but WITHOUT ANY WARRANTY; without even the implied warranty of
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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# GNU General Public License for more details.
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#
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# You should have received a copy of the GNU General Public License
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# along with python/test/system_test.py. If not, see <http://www.gnu.org/licenses/>.
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#
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# Copyright(C) 2016-2018 by Bertini2 Development Team
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#
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# See <http://www.gnu.org/licenses/> for a copy of the license,
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# as well as COPYING. Bertini2 is provided with permitted
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# additional terms in the b2/licenses/ directory.
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# individual authors of this file include:
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#
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# James Collins
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# West Texas A&M University
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# Spring 2016
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#
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# silviana amethyst
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# UWEC
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# Spring, Summer 2018
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#
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__author__ = 'James Collins'
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from pybertini import *
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from pybertini.function_tree.symbol import *
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from pybertini.function_tree.root import *
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from pybertini.function_tree import *
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from pybertini.tracking import *
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from pybertini.tracking.config import *
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import unittest
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import numpy as np
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import pdb
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import pybertini.multiprec as mp
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from pybertini.multiprec import Float as mpfr_float
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from pybertini.multiprec import Complex as mpfr_complex
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class AMPTrackingTest(unittest.TestCase):
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def setUp(self):
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self.toldbl = 1e-15;
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self.x = Variable("x");
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self.y = Variable("y");
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self.z = Variable("z");
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self.t = Variable("t");
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self.a = Float("4.897", "1.23")
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#
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self.f = Function(self.x*self.y);
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self.g = Function(pow(self.x,2)*self.y - self.a*self.z*self.x);
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def test_tracker_linear(self):
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default_precision(30);
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x = self.x; y = self.y; t = self.t;
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s = System();
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vars = VariableGroup();
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vars.append(y);
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s.add_function(y-t);
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s.add_path_variable(t);
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s.add_variable_group(vars);
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ampconfig = amp_config_from(s);
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tracker = AMPTracker(s);
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stepping_pref = SteppingConfig();
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newton_pref = NewtonConfig();
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tracker.setup(Predictor.Euler, 1e-5, 1e5, stepping_pref, newton_pref);
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tracker.precision_setup(ampconfig);
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t_start = mpfr_complex(1)
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t_end = mpfr_complex(0)
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y_start = np.array([mpfr_complex(1)]);
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y_end = np.array(np.zeros(shape=(s.num_variables()), dtype=np.int64),dtype=mpfr_complex);
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tracker.track_path(y_end, t_start, t_end, y_start);
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self.assertEqual(y_end.shape, (s.num_variables(),))
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self.assertLessEqual(mp.abs(y_end[0]-mpfr_complex(0)), 1e-5)
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def test_tracker_quad(self):
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default_precision(30);
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y = self.y; t = self.t;
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s = System();
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vars = VariableGroup();
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vars.append(y);
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s.add_function(y-t**2);
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s.add_path_variable(t);
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s.add_variable_group(vars);
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s.precision(30);
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ampconfig = amp_config_from(s);
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tracker = AMPTracker(s);
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stepping_pref = SteppingConfig();
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newton_pref = NewtonConfig();
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tracker.setup(Predictor.Euler, 1e-5, 1e5, stepping_pref, newton_pref);
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tracker.precision_setup(ampconfig);
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t_start = mpfr_complex(1)
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t_end = mpfr_complex(-1)
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y_start = np.array([mpfr_complex(1)]);
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y_end = np.array(np.zeros(shape=(s.num_variables()), dtype=np.int64),dtype=mpfr_complex);
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tracker.track_path(y_end, t_start, t_end, y_start);
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self.assertEqual(y_end.shape, (s.num_variables(),))
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self.assertLessEqual(mp.abs(y_end[0]-mpfr_complex(0)), 1e-5)
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def test_tracker_sqrt(self):
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default_precision(30);
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x = self.x; y = self.y; t = self.t;
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s = System();
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vars = VariableGroup();
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vars.append(y); vars.append(x);
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s.add_function(x-t);
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s.add_function(y**2 - x)
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s.add_path_variable(t);
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s.add_variable_group(vars);
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s.precision(30);
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ampconfig = amp_config_from(s);
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tracker = AMPTracker(s);
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stepping_pref = SteppingConfig();
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newton_pref = NewtonConfig();
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tracker.setup(Predictor.Euler, 1e-5, 1e5, stepping_pref, newton_pref);
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tracker.precision_setup(ampconfig);
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t_start = mpfr_complex(1)
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t_end = mpfr_complex(0)
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y_start = np.array([mpfr_complex(1), mpfr_complex(1)]);
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y_end = np.array(np.zeros(shape=(s.num_variables()), dtype=np.int64),dtype=mpfr_complex);
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track_success = tracker.track_path(y_end, t_start, t_end, y_start);
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self.assertTrue(track_success == SuccessCode.Success)
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self.assertEqual(y_end.shape, (s.num_variables(),))
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self.assertLessEqual(mp.abs(y_end[0]-mpfr_complex(0)), 1e-5)
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self.assertLessEqual(mp.abs(y_end[1]-mpfr_complex(0)), 1e-5)
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y_start = np.array([mpfr_complex(1), mpfr_complex(-1)]);
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tracker.track_path(y_end, t_start, t_end, y_start);
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self.assertEqual(y_end.shape, (s.num_variables(),))
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self.assertLessEqual(mp.abs(y_end[0]-mpfr_complex(0)), 1e-5)
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self.assertLessEqual(mp.abs(y_end[1]-mpfr_complex(0)), 1e-5)
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y_start = np.array([mpfr_complex(-1), mpfr_complex(-1)]);
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tracker.track_path(y_end, t_start, t_end, y_start);
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self.assertEqual(y_end.shape, (s.num_variables(),))
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self.assertLessEqual(mp.abs(y_end[0]-mpfr_complex(0)), 1e-5)
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self.assertLessEqual(mp.abs(y_end[1]-mpfr_complex(0)), 1e-5)
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y_start = np.array([mpfr_complex(-1), mpfr_complex(0,1)]);
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track_success = tracker.track_path(y_end, t_start, t_end, y_start);
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self.assertTrue(track_success == SuccessCode.Success)
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self.assertEqual(y_end.shape, (s.num_variables(),))
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self.assertLessEqual(mp.abs(y_end[0]-mpfr_complex(0)), 1e-5)
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self.assertLessEqual(mp.abs(y_end[1]-mpfr_complex(0)), 1e-5)
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def test_tracker_singular_start(self):
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default_precision(30);
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x = self.x; y = self.y; t = self.t;
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s = System();
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vars = VariableGroup();
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vars.append(y); vars.append(x);
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s.add_function(x**2 + (1-t)*x);
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s.add_function(y**2 + (1-t)*y)
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s.add_path_variable(t);
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s.add_variable_group(vars);
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s.precision(30);
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ampconfig = amp_config_from(s);
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tracker = AMPTracker(s);
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stepping_pref = SteppingConfig();
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newton_pref = NewtonConfig();
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tracker.setup(Predictor.Euler, 1e-5, 1e5, stepping_pref, newton_pref);
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tracker.precision_setup(ampconfig);
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t_start = mpfr_complex(1)
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t_end = mpfr_complex(0)
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y_start = np.array([mpfr_complex(0), mpfr_complex(0)]);
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y_end = np.empty(shape=(s.num_variables(),),dtype=mpfr_complex);
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track_success = tracker.track_path(y_end, t_start, t_end, y_start);
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self.assertTrue(track_success == SuccessCode.SingularStartPoint)
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self.assertEqual(y_end.shape, (s.num_variables(),))
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if __name__ == '__main__':
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unittest.main();
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