def test_cash_karp(self):
a = RKcashKarp.phi()
b = inverse(a)
c = composition_ssa(a, b)
result = equal_up_to_order(c, unit, self.max_order)
self.assertEqual(result, self.max_order)
c = composition_ssa(b, a)
result = equal_up_to_order(c, unit, self.max_order)
self.assertEqual(result, self.max_order)
def test_explicit_euler(self):
a = RKeuler.phi()
b = inverse(a)
c = composition_ssa(a, b)
result = equal_up_to_order(c, unit, self.max_order)
self.assertEqual(result, self.max_order)
c = composition_ssa(b, a)
result = equal_up_to_order(c, unit, self.max_order)
self.assertEqual(result, self.max_order)
def test_exact(self):
a = exponential
b = inverse(a)
c = composition_ssa(a, b)
result = equal_up_to_order(c, unit, self.max_order)
self.assertEqual(result, self.max_order)
c = composition_ssa(b, a)
result = equal_up_to_order(c, unit, self.max_order)
self.assertEqual(result, self.max_order)
def test_no_2(self):
max_order = 5
trapezoidal = RKimplicitTrapezoidal.phi()
imp_midpoint = RKimplicitMidpoint.phi()
half_imp_euler = stepsize_adjustment(RKimplicitEuler.phi(),
Fraction(1, 2))
# half_exp_euler = stepsize_adjustment(RKeuler.phi(),\
# Fraction(1, 2))
the_conjugate = conjugate_by_commutator(imp_midpoint, half_imp_euler)
equal_up_to_order(trapezoidal, the_conjugate, max_order)
def test_exp_explicit_euler(self):
a = RKeuler.phi()
alpha_1 = log(a)
a_1 = exp(alpha_1)
result = equal_up_to_order(a, a_1, self.max_order)
self.assertEqual(self.max_order, result)
alpha_2 = modified_equation(a)
result = equal_up_to_order(alpha_1, alpha_2, self.max_order)
self.assertEqual(self.max_order, result)
a_2 = exp(alpha_2)
result = equal_up_to_order(a, a_2, self.max_order)
self.assertEqual(self.max_order, result)
def test_composition(self):
"It is known that the explicit and implicit Euler methods are adjoint.\
Furthermore, the composition implicit o explicit = trapezoidal,\
and explicit o implicit = implicit midpoint.\
This verifies the coproduct."
max_order = 5
explicit_euler = RKeuler.phi()
implicit_euler = RKimplicitEuler.phi()
implicit_midpoint = RKimplicitMidpoint.phi()
implicit_trapezoidal = RKimplicitTrapezoidal.phi()
result1 = composition_ssa(explicit_euler, implicit_euler)
tmp = equal_up_to_order(result1, implicit_trapezoidal, max_order)
self.assertEqual(tmp, max_order)
result2 = composition_ssa(implicit_euler, explicit_euler)
tmp = equal_up_to_order(result2, implicit_midpoint, max_order)
self.assertEqual(tmp, max_order)
def order(self):
# a = exponential
b = self.phi()
return equal_up_to_order(exponential, b)
def test(self):
modified = modified_equation(exponential)
result = equal_up_to_order(modified, unit_field, 8)
self.assertEqual(8, result)
def test_implicit_euler(self):
a = RKimplicitEuler.phi()
b = adjoint(a)
result = equal_up_to_order(b, RKeuler.phi(), self.max_order)
self.assertEqual(result, self.max_order)
def test_lobattoB(self):
# symmetric
a = RKlobattoIIIB4.phi()
b = adjoint(a)
result = equal_up_to_order(a, b, self.max_order)
self.assertEqual(result, self.max_order)
def test_implicit_midpoint(self):
# symmetric
a = RKimplicitMidpoint.phi()
b = adjoint(a)
result = equal_up_to_order(a, b, self.max_order)
self.assertEqual(result, self.max_order)
def test_exact(self):
# symmetric
a = exponential
b = adjoint(a)
result = equal_up_to_order(a, b, self.max_order)
self.assertEqual(result, self.max_order)
