def test_add_dict_fcn():
# test exponent conversion
dict_builder = DictionaryBuilder(dict_fcns=[])
d_f = "x1^2"
dict_builder.add_dict_fcn(d_f=d_f)
dict_fcn = dict_builder.dict_fcns.pop()
d_f_replaced = d_f.replace("^", "**")
assert str(dict_fcn.symbolic_expression) == d_f_replaced
# test an undefined function
d_f = ["f(x1)"]
dict_builder = DictionaryBuilder(dict_fcns=d_f)
data = {"x1": [5, 2]}
with pytest.raises(NameError):
dict_builder.evaluate_dict(input_data=data)
def test_dictionary_builder_addition():
db = DictionaryBuilder.from_mak_generator(number_of_states=2, max_order=2)
assert len(db) == 3
db2 = DictionaryBuilder.from_mak_generator(number_of_states=1, max_order=2)
assert len(db2) == 1
new_dictionary = db + db2
assert len(new_dictionary) == 4
with pytest.raises(ValueError, match=r"Dictionary cannot be empty!"):
db3 = db + DictionaryBuilder(dict_fcns=[])
len(db3)
def test_evaluate_dict():
d_f = ["x1*x2", "x1**2"]
dict_builder = DictionaryBuilder(dict_fcns=d_f)
data_x1 = [1, 5, 10]
data_x2 = [3, 7, 15]
data = {"x1": data_x1, "x2": data_x2}
A = dict_builder.evaluate_dict(input_data=data)
sym_expr_df1 = parse_expr(s=d_f[0], evaluate=False)
df1_eval = [
sym_expr_df1.evalf(subs=dict(x1=x1, x2=x2))
for x1, x2 in zip(data_x1, data_x2)
]
sym_expr_df2 = parse_expr(s=d_f[1], evaluate=False)
df2_eval = [
sym_expr_df2.evalf(subs=dict(x1=x1, x2=x2))
for x1, x2 in zip(data_x1, data_x2)
]
B = np.array([df1_eval, df2_eval]).T
assert np.array_equal(A, B)
def test_dictionary_builder():
d_f = ["x1", "x1*x2", "x2"]
dict_builder = DictionaryBuilder(dict_fcns=d_f)
assert len(d_f) == len(dict_builder.dict_fcns)
plt.title("Observable state y")
plt.legend(loc="best")
plt.subplot(212)
plt.plot(t, dx2, label="RHS diff")
plt.plot(t, dy_spline, c='r', alpha=0.4, label="Spline diff")
plt.plot(t_gp, dydt, c='orange', label="GP diff")
plt.fill_between(t_gp, dydt - 2*dydt_std, dydt + 2*dydt_std, alpha=0.2, color='k')
plt.ylabel("Value (AU)")
plt.xlabel("time (s)")
plt.title("Derivative of y")
plt.legend(loc="best")
plt.show()
# step 1 define a dictionary
d_f = ["1", "x", "y", "z", "x*z", "y*x"]
dict_builder = DictionaryBuilder(dict_fcns=d_f)
dict_functions = dict_builder.dict_fcns
# associate variables with data
data = {"x": y[0, :].T, "y": y[1, :].T, "z": y[2, :].T}
#data = {"x": x_samples.T, "y": y_samples.T, "z": z_samples.T}
A = dict_builder.evaluate_dict(input_data=data)
# step 2 define an SBL problem
# with the Lin reg model and solve it
config_dict = {
"solver": {"name": "ECOS", "show_time": False, "settings": {}},
"verbose": False,
}
norm_vect = np.linalg.norm(A, axis=0)
A_norm = A / norm_vect
def test_sbl_on_lotka_volterra():
# define Lotka-Volerra model
states = {"x1": "alpha*x1-beta*x1*x2", "x2": "delta*x1*x2-gamma*x2"}
parameters = {"alpha": 2 / 3, "beta": 4 / 3, "delta": 1, "gamma": 1}
ss = StateSpaceModel.from_string(states=states, parameters=parameters)
states = ["x1", "x2"]
t_span = [0, 30]
x0 = {"x1": 1.2, "x2": 1.0}
# simulate model
gm = MeasurementsGenerator(ss=ss, time_span=t_span, initial_values=x0)
t, y = gm.get_measurements()
# compute the time derivative of the state variables
rhs_preprop = RHSEvalSignalPreprocessor(t=t,
y=y,
rhs_function=ss.get_rhs,
states=states)
rhs_preprop.calculate_time_derivative()
dydt_rhs = rhs_preprop.dydt
dx1 = dydt_rhs[0, :]
dx2 = dydt_rhs[1, :]
# step 1 define a dictionary
d_f = ["x1", "x2", "x1*x1", "x1*x2", "x2*x2"]
dict_builder = DictionaryBuilder(dict_fcns=d_f)
dict_functions = dict_builder.dict_fcns
data = {"x1": y[0, :], "x2": y[1, :]}
A = dict_builder.evaluate_dict(input_data=data)
# step 2 define an SBL problem and solve it
lambda_param_x1 = 0.1
lambda_param_x2 = 0.05
sbl_x1 = SBL(
dict_mtx=A,
data_vec=dx1,
lambda_param=lambda_param_x1,
state_name="x1",
dict_fcns=dict_functions,
)
sbl_x1.compute_model_structure()
sbl_x2 = SBL(
dict_mtx=A,
data_vec=dx2,
lambda_param=lambda_param_x2,
state_name="x2",
dict_fcns=dict_functions,
)
sbl_x2.compute_model_structure()
# test SBL results
zero_th = 1e-8
x1_results = [
str(item.symbolic_expression)
for item in sbl_x1.get_results(zero_th=zero_th)
]
assert len(x1_results) == 2
assert "x1" in x1_results
assert "x1*x2" in x1_results
x2_results = [
str(item.symbolic_expression)
for item in sbl_x2.get_results(zero_th=zero_th)
]
assert len(x2_results) == 2
assert "x2" in x2_results
assert "x1*x2" in x2_results