def test_tracker_linear(self):
default_precision(30)
x = self.x
y = self.y
t = self.t
s = System()
vars = VariableGroup()
vars.append(y)
s.add_function(y - t)
s.add_path_variable(t)
s.add_variable_group(vars)
ampconfig = amp_config_from(s)
tracker = AMPTracker(s)
stepping_pref = SteppingConfig()
newton_pref = NewtonConfig()
tracker.setup(Predictor.Euler, 1e-5, 1e5, stepping_pref, newton_pref)
tracker.precision_setup(ampconfig)
t_start = mpfr_complex(1)
t_end = mpfr_complex(0)
y_start = mi.VectorXmp([mpfr_complex(1)])
y_end = mi.VectorXmp()
tracker.track_path(y_end, t_start, t_end, y_start)
self.assertEqual(y_end.rows(), 1)
self.assertLessEqual(mp.norm(y_end[0] - mpfr_complex(0)), 1e-5)
def setUp(self):
default_precision(30)
self.x_d = complex(-2.43, .21)
self.y_d = complex(4.84, -1.94)
self.z_d = complex(-6.48, -.731)
self.p_d = complex(-.321, -.72)
self.tol_d = float(1e-15)
#
self.x_mp = mpfr_complex("-2.43", ".21")
self.y_mp = mpfr_complex("4.84", "-1.94")
self.z_mp = mpfr_complex("-6.48", "-.731")
self.p_mp = mpfr_complex("-.321", "-.72")
self.tol_mp = mpfr_float("1e-27")
def test_sub(self):
x = self.x
y = self.y
z = self.z
p = self.p
a = self.a
b = self.b
tol_d = self.tol_d
tol_mp = self.tol_mp
#
f = Function(x - y - a)
self.assertLessEqual(np.abs(f.eval_d().real / (-10.39) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (1.538) - 1), tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float("-10.39") - 1), tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float("1.538") - 1), tol_mp)
#
f = Function(y - Float("3.87"))
self.assertLessEqual(np.abs(f.eval_d().real / (0.97) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (-1.94) - 1), tol_d)
#
f = Function(y - Float("3.87", "0"))
self.assertLessEqual(np.abs(f.eval_d().real / (0.97) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (-1.94) - 1), tol_d)
#
#
f = Function(y - mpfr_complex("3.87", "-2.1"))
self.assertLessEqual(np.abs(f.eval_d().real / (0.97) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (0.16) - 1), tol_d)
#
self.assertLessEqual(mp.abs(f.eval_mp().real / mpfr_float("0.97") - 1),
tol_mp)
self.assertLessEqual(mp.abs(f.eval_mp().imag / mpfr_float("0.16") - 1),
tol_mp)
#
f = Function(y - (-5))
self.assertLessEqual(np.abs(f.eval_d().real / (9.84) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (-1.94) - 1), tol_d)
#
f = Function(x)
f -= y
f -= a
self.assertLessEqual(np.abs(f.eval_d().real / (-10.39) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (1.538) - 1), tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float("-10.39") - 1), tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float("1.538") - 1), tol_mp)
#
f = Function(y)
f -= Float("3.87")
self.assertLessEqual(np.abs(f.eval_d().real / (0.97) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (-1.94) - 1), tol_d)
def test_plus(self):
x = self.x
y = self.y
z = self.z
p = self.p
a = self.a
b = self.b
tol_d = self.tol_d
tol_mp = self.tol_mp
#
f = Function(x + y + a)
self.assertLessEqual(np.abs(f.eval_d().real / (5.53) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (-1.118) - 1), tol_d)
#
self.assertLessEqual(mp.abs(f.eval_mp().real / mpfr_float("5.53") - 1),
tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float("-1.118") - 1), tol_mp)
#
f = Function(x + Float("3.87"))
self.assertLessEqual(np.abs(f.eval_d().real / (1.44) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (0.21) - 1), tol_d)
#
f = Function(x + mpfr_complex("3.87", "-2.1"))
self.assertLessEqual(np.abs(f.eval_d().real / (1.44) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (-1.89) - 1), tol_d)
#
self.assertLessEqual(mp.abs(f.eval_mp().real / mpfr_float("1.44") - 1),
tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float("-1.89") - 1), tol_mp)
#
f = Function(x + (-5))
self.assertLessEqual(np.abs(f.eval_d().real / (-7.43) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (0.21) - 1), tol_d)
#
self.assertLessEqual(
mp.abs(f.eval_mp().real / mpfr_float("-7.43") - 1), tol_mp)
self.assertLessEqual(mp.abs(f.eval_mp().imag / mpfr_float("0.21") - 1),
tol_mp)
#
f = Function(x)
f += y
f += a
self.assertLessEqual(np.abs(f.eval_d().real / (5.53) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (-1.118) - 1), tol_d)
#
self.assertLessEqual(mp.abs(f.eval_mp().real / mpfr_float("5.53") - 1),
tol_mp)
self.assertLessEqual(
mp.abs(f.eval_mp().imag / mpfr_float("-1.118") - 1), tol_mp)
#
f = Function(x)
f += Float("3.87")
self.assertLessEqual(np.abs(f.eval_d().real / (1.44) - 1), tol_d)
self.assertLessEqual(np.abs(f.eval_d().imag / (0.21) - 1), tol_d)
def test_tracker_singular_start(self):
default_precision(30)
x = self.x
y = self.y
t = self.t
s = System()
vars = VariableGroup()
vars.append(y)
vars.append(x)
s.add_function(x**2 + (1 - t) * x)
s.add_function(y**2 + (1 - t) * y)
s.add_path_variable(t)
s.add_variable_group(vars)
s.precision(30)
ampconfig = amp_config_from(s)
tracker = AMPTracker(s)
stepping_pref = SteppingConfig()
newton_pref = NewtonConfig()
tracker.setup(Predictor.Euler, 1e-5, 1e5, stepping_pref, newton_pref)
tracker.precision_setup(ampconfig)
t_start = mpfr_complex(1)
t_end = mpfr_complex(0)
y_start = mi.VectorXmp([mpfr_complex(0),
mpfr_complex(0)])
y_end = mi.VectorXmp()
track_success = tracker.track_path(y_end, t_start, t_end, y_start)
self.assertTrue(track_success == SuccessCode.SingularStartPoint)
self.assertEqual(y_end.rows(), 0)
def setUp(self):
default_precision(30)
self.x = Variable("x")
self.x.set_current_value(complex(-2.43, .21))
self.y = Variable("y")
self.y.set_current_value(complex(4.84, -1.94))
self.z = Variable("z")
self.z.set_current_value(complex(-6.48, -.731))
self.p = Variable("p")
self.p.set_current_value(complex(-.321, -.72))
self.a = Float(mpfr_complex("3.12", ".612"))
self.b = Float(mpfr_complex("-.823", "2.62"))
self.tol_d = float(9e-14)
#
self.x.set_current_value(mpfr_complex("-2.43", ".21"))
self.y.set_current_value(mpfr_complex("4.84", "-1.94"))
self.z.set_current_value(mpfr_complex("-6.48", "-.731"))
self.p.set_current_value(mpfr_complex("-.321", "-.72"))
self.a = Float(mpfr_complex("3.12", ".612"))
self.b = Float(mpfr_complex("-.823", "2.62"))
self.tol_mp = mpfr_float("1e-27")
def test_using_total_degree_ss(self):
default_precision(self.ambient_precision);
x = Variable("x");
y = Variable("y");
t = Variable("t");
#
sys = System();
#
var_grp = VariableGroup();
var_grp.append(x);
var_grp.append(y);
sys.add_variable_group(var_grp);
sys.add_function((x-1)**3)
sys.add_function((y-1)**2)
sys.homogenize();
sys.auto_patch();
self.assertEqual(sys.is_patched(), 1)
self.assertEqual(sys.is_homogeneous(), 1)
td = ss.TotalDegree(sys);
self.assertEqual(td.is_patched(), 1)
self.assertEqual(td.is_homogeneous(), 1)
gamma = Rational.rand();
final_system = (1-t)*sys + gamma*t*td;
final_system.add_path_variable(t);
print(final_system)
prec_config = AMPConfig(final_system);
stepping_pref = SteppingConfig();
newton_pref = NewtonConfig();
tracker = AMPTracker(final_system);
tracker.setup(Predictor.RK4, 1e-5, 1e5, stepping_pref, newton_pref);
tracker.precision_setup(prec_config);
num_paths_to_track = td.num_start_points();
n = int(str(num_paths_to_track));
t_start = mpfr_complex(1);
t_endgame_boundary = mpfr_complex("0.1");
t_final = mpfr_complex(0);
bdry_points = [mi.VectorXmp() for i in range(n)]
for i in range(n):
default_precision(self.ambient_precision);
final_system.precision(self.ambient_precision);
start_point = td.start_point_mp(i);
bdry_pt = mi.VectorXmp();
track_success_code = tracker.track_path(bdry_pt,t_start, t_endgame_boundary, start_point);
bdry_points[i] = bdry_pt;
self.assertEqual(track_success_code, SuccessCode.Success)
tracker.setup(Predictor.HeunEuler, 1e-6, 1e5, stepping_pref, newton_pref);
my_endgame = AMPCauchyEG(tracker);
final_homogenized_solutions = [mi.VectorXmp() for i in range(n)]
for i in range(n):
default_precision(bdry_points[i][0].precision());
final_system.precision(bdry_points[i][0].precision());
track_success_code = my_endgame.run(mpfr_complex(t_endgame_boundary),bdry_points[i]);
final_homogenized_solutions[i] = my_endgame.final_approximation();
print(final_system.dehomogenize_point(final_homogenized_solutions[i]));
self.assertEqual(track_success_code, SuccessCode.Success)