Manually checking convergence order

Here is a script for manually checking convergence order for a given method and a given problem. The output table is shown below.

import numpy as np

from ozone.tests.ode_function_library.simple_nonlinear_func import SimpleNonlinearODEFunction
from ozone.utils.run_utils import compute_convergence_order


num_times_vector = np.array([16, 32, 64, 128, 256])
method_name = 'ImplicitMidpoint'
formulation = 'solver-based'

ode_function = SimpleNonlinearODEFunction()
state_name = 'y'
initial_conditions = {'y': 1.}
t0 = 0.
t1 = 1.

errors_vector, step_sizes_vector, orders_vector, ideal_order = compute_convergence_order(
    num_times_vector, t0, t1, state_name,
    ode_function, formulation, method_name, initial_conditions)

print('-'*47)
print('| {:4s} | {:10s} | {:10s} | {:10s} |'.format('Num.', 'h', 'Error', 'Rate'))
print('-'*47)
for i in range(len(num_times_vector)):
    print('| {:4d} | {:.4e} | {:.4e} | {:.4e} |'.format(
        num_times_vector[i],
        step_sizes_vector[i],
        errors_vector[i],
        orders_vector[i - 1] if i != 0 else 0.,
    ))

-----------------------------------------------
| Num. | h          | Error      | Rate       |
-----------------------------------------------
|   16 | 6.6667e-02 | 2.7362e-03 | 0.0000e+00 |
|   32 | 3.2258e-02 | 6.3909e-04 | 2.0033e+00 |
|   64 | 1.5873e-02 | 1.5465e-04 | 2.0008e+00 |
|  128 | 7.8740e-03 | 3.8052e-05 | 2.0002e+00 |
|  256 | 3.9216e-03 | 9.4381e-06 | 2.0000e+00 |