def test_adaptive(self):
"""test for adaptive_step_size"""
# compute numerical solution of the ODE
operator = mdl.signaling_cascade(2).tt2qtt([[2] * 6] * 2,
[[2] * 6] * 2)
initial_value = tt.unit(operator.row_dims, [0] * operator.order)
initial_guess = tt.ones(operator.row_dims, [1] * operator.order,
ranks=self.rank).ortho_right()
solution_ie, _ = ode.adaptive_step_size(operator,
initial_value,
initial_guess,
300,
step_size_first=1,
second_method='two_step_Euler',
progress=False)
solution_tr, _ = ode.adaptive_step_size(
operator,
initial_value,
initial_guess,
300,
step_size_first=1,
second_method='trapezoidal_rule',
progress=False)
# compute norm of the derivatives at the final time step
derivative_ie = (operator.dot(solution_ie[-1])).norm()
derivative_tr = (operator.dot(solution_tr[-1])).norm()
# check if converged to stationary distribution
self.assertLess(derivative_ie, self.tol)
self.assertLess(derivative_tr, self.tol)
def test_errors(self):
"""test for error computations"""
# compute numerical solution of the ODE
operator = mdl.signaling_cascade(3).tt2qtt([[2] * 6] * 3,
[[2] * 6] * 3)
initial_value = tt.unit(operator.row_dims, [0] * operator.order)
initial_guess = tt.ones(operator.row_dims, [1] * operator.order,
ranks=self.rank).ortho_right()
step_sizes = [0.1] * 10
solution_ee = ode.explicit_euler(operator,
initial_value,
step_sizes,
progress=False,
max_rank=self.max_rank)
solution_ie = ode.implicit_euler(operator,
initial_value,
initial_guess,
step_sizes,
progress=False)
solution_tr = ode.trapezoidal_rule(operator,
initial_value,
initial_guess,
step_sizes,
progress=False)
# compute errors
errors_ee = ode.errors_expl_euler(operator, solution_ee, step_sizes)
errors_ie = ode.errors_impl_euler(operator, solution_ie, step_sizes)
errors_tr = ode.errors_trapezoidal(operator, solution_tr, step_sizes)
# check if errors are smaller than tolerance
self.assertLess(np.max(errors_ee), self.tol)
self.assertLess(np.max(errors_ie), self.tol)
self.assertLess(np.max(errors_tr), self.tol)
def test_unit(self):
"""test unit tensor train"""
# construct unit tensor train, convert to full format, and flatten
t_unit = tt.unit(self.row_dims, [0] * self.order).full().flatten()
# construct unit vector
t_full = np.eye(np.int(np.prod(self.row_dims)), 1).T
# compute relative error
rel_err = np.linalg.norm(t_unit - t_full) / np.linalg.norm(t_full)
# check if relative error is smaller than tolerance
self.assertLess(rel_err, self.tol)
def test_explicit_euler(self):
"""test for explicit Euler method"""
# compute numerical solution of the ODE
operator = mdl.signaling_cascade(2).tt2qtt([[2] * 6] * 2, [[2] * 6] * 2)
initial_value = tt.unit(operator.row_dims, [0] * operator.order)
step_sizes = [0.1] * 3000
solution = ode.explicit_euler(operator, initial_value, step_sizes, progress=False, max_rank=self.max_rank)
# compute norm of the derivatives at the final 10 time steps
derivatives = []
for i in range(10):
derivatives.append((operator.dot(solution[-i - 1])).norm())
# check if explicit Euler method converged to stationary distribution
for i in range(10):
self.assertLess(derivatives[i], self.tol)
def test_implicit_euler(self):
"""test for implicit Euler method"""
# compute numerical solution of the ODE
operator = mdl.signaling_cascade(2).tt2qtt([[2] * 6] * 2,
[[2] * 6] * 2)
initial_value = tt.unit(operator.row_dims, [0] * operator.order)
initial_guess = tt.ones(operator.row_dims, [1] * operator.order,
ranks=self.rank).ortho_right()
step_sizes = [1] * 300
solution_als = ode.implicit_euler(operator,
initial_value,
initial_guess,
step_sizes,
tt_solver='als',
progress=False)
solution_mals = ode.implicit_euler(operator,
initial_value,
initial_guess,
step_sizes,
tt_solver='mals',
max_rank=self.rank,
progress=False)
# compute norm of the derivatives at the final 10 time steps
derivatives_als = []
derivatives_mals = []
for i in range(10):
derivatives_als.append((operator.dot(solution_als[-i - 1])).norm())
derivatives_mals.append(
(operator.dot(solution_mals[-i - 1])).norm())
# check if implicit Euler method converged to stationary distribution
for i in range(10):
self.assertLess(derivatives_als[i], self.tol)
self.assertLess(derivatives_mals[i], self.tol)
string_p_CO = '10^' + (p_CO_exp[i] >= 0) * '+' + str("%.1f" % p_CO_exp[i])
string_method = ' ' * 9 + 'EVP' + ' ' * 9
string_rank = (R[i] < 10) * ' ' + str(R[i]) + ' ' * 8
string_closeness = str("%.2e" % (operator @ solution).norm()) + ' ' * 6
string_time = (time.elapsed < 10) * ' ' + str("%.2f" % time.elapsed) + 's'
print(string_p_CO + string_method + string_rank + string_closeness +
string_time)
# apply adaptive step size scheme to the ODE to find the stationary distribution
# ------------------------------------------------------------------------------
for i in range(8, len(R)):
# integrate ODE to approximate stationary distribution
operator = mdl.co_oxidation(20, 10**(8 + p_CO_exp[i]))
initial_value = tt.unit(operator.row_dims, [1] * operator.order)
initial_guess = tt.ones(operator.row_dims, [1] * operator.order,
ranks=R[i]).ortho_left().ortho_right()
with utl.timer() as time:
solution = ode.adaptive_step_size(operator, initial_value,
initial_guess, 100)
# compute turn-over frequency of CO2 desorption
tof.append(utl.two_cell_tof(solution[-1], [2, 1], 1.7e5))
# print results
string_p_CO = '10^' + (p_CO_exp[i] >= 0) * '+' + str("%.1f" % p_CO_exp[i])
string_method = ' ' * 9 + 'IEM' + ' ' * 9
string_rank = (R[i] < 10) * ' ' + str(R[i]) + ' ' * 8
string_closeness = str("%.2e" % (operator @ solution[-1]).norm()) + ' ' * 6
string_time = (time.elapsed < 10) * ' ' + str("%.2f" % time.elapsed) + 's'