def test_type_errors():
np.random.seed(0) # Set a seed for repeatability
### Making data
hour = np.linspace(1, 10, 100)
noise = 0.1 * np.random.randn(len(hour))
temperature_c = np.log(hour) + noise
### Fit
def model(x, p):
return p["m"] * x + p["b"]
x_data = hour
y_data = temperature_c
fitted_model = FittedModel(
model=model,
x_data=x_data,
y_data=y_data,
parameter_guesses={
"m": 0,
"b": 0,
},
residual_norm_type="Linf",
)
fitted_model(5)
with pytest.raises(TypeError):
fitted_model({"temperature": 5})
def model(x, p):
return p["m"] * x["hour"] + p["b"]
fitted_model = FittedModel(
model=model,
x_data={"hour": hour},
y_data=y_data,
parameter_guesses={
"m": 0,
"b": 0,
},
residual_norm_type="Linf",
)
fitted_model({"hour": 5})
with pytest.raises(TypeError):
fitted_model(5)
def test_Linf_without_x_in_dict():
np.random.seed(0) # Set a seed for repeatability
### Making data
hour = np.linspace(1, 10, 100)
noise = 0.1 * np.random.randn(len(hour))
temperature_c = np.log(hour) + noise
### Fit
def model(x, p):
return p["m"] * x + p["b"]
x_data = hour
y_data = temperature_c
fitted_model = FittedModel(
model=model,
x_data=x_data,
y_data=y_data,
parameter_guesses={
"m": 0,
"b": 0,
},
residual_norm_type="Linf",
)
# Check that the fit is right
assert fitted_model.parameters["m"] == pytest.approx(0.247116, abs=1e-5)
assert fitted_model.parameters["b"] == pytest.approx(0.227797, abs=1e-5)
def fit_model_with_norm(residual_norm_type):
return FittedModel(model=model,
x_data=time,
y_data=measured_temperature,
parameter_guesses={
"1": 0,
"0": 0,
},
residual_norm_type=residual_norm_type)
def test_fit_model_weighting():
x = np.linspace(0, 10)
y = np.sin(x)
fm = FittedModel(
model=lambda x, p: p["m"] * x + p["b"],
x_data=x,
y_data=y,
parameter_guesses={
"m": 0,
"b": 0,
},
weights=None
) # Fit a model with no weighting
assert fm(10) != pytest.approx(5, abs=1) # Doesn't give a high value at x = 10
fm = FittedModel(
model=lambda x, p: p["m"] * x + p["b"],
x_data=x,
y_data=y,
parameter_guesses={
"m": 0,
"b": 0,
},
weights=(x > 0) & (x < 2)
) # Fit a model with weighting
assert fm(10) == pytest.approx(5, abs=1) # Gives a high value at x = 10
fm.plot()
def get_fitted_model():
### Fit a model
def model(x, p):
return p["m"] * x + p["b"] # Linear regression
fitted_model = FittedModel(
model=model,
x_data=time,
y_data=measured_temperature,
parameter_guesses={
"m": 0,
"b": 0,
},
)
return fitted_model
def test_single_dimensional_polynomial_fitting():
np.random.seed(0) # Set a seed for repeatability.
### Make some data
x = np.linspace(0, 10, 50)
noise = 5 * np.random.randn(len(x))
y = x**2 - 8 * x + 5 + noise
### Fit data
def model(x, p):
return (p["a"] * x["x1"]**2 + p["b"] * x["x1"] + p["c"])
x_data = {"x1": x}
fitted_model = FittedModel(
model=model,
x_data=x_data,
y_data=y,
parameter_guesses={
"a": 1,
"b": 1,
"c": 1,
},
parameter_bounds={
"a": (None, None),
"b": (None, None),
"c": (None, None),
},
)
### Plot data and fit
if plot:
fig, ax = plt.subplots(1, 1, figsize=(6.4, 4.8), dpi=200)
plt.plot(x, y, ".", label="Data")
plt.plot(x, model(x_data, fitted_parameters), "-", label="Fit")
plt.xlabel(r"$x$")
plt.ylabel(r"$y$")
plt.title(r"Automatic-Differentiable Fitting")
plt.tight_layout()
plt.legend()
# plt.savefig("C:/Users/User/Downloads/temp.svg")
plt.show()
### Check that the fit is right
assert fitted_model.parameters["a"] == pytest.approx(1.046091, abs=1e-3)
assert fitted_model.parameters["b"] == pytest.approx(-9.166716, abs=1e-3)
assert fitted_model.parameters["c"] == pytest.approx(9.984351, abs=1e-3)
def test_multidimensional_power_law_fitting():
np.random.seed(0) # Set a seed for repeatability.
### Make some data z(x,y)
x = np.logspace(0, 3)
y = np.logspace(0, 3)
X, Y = np.meshgrid(x, y, indexing="ij")
noise = np.random.lognormal(mean=0, sigma=0.05)
Z = 0.5 * X**0.75 * Y**1.25 * noise
### Fit data
def model(x, p):
return (p["multiplier"] * x["X"]**p["X_power"] * x["Y"]**p["Y_power"])
x_data = {
"X": X.flatten(),
"Y": Y.flatten(),
}
fitted_model = FittedModel(
model=model,
x_data=x_data,
y_data=Z.flatten(),
parameter_guesses={
"multiplier": 1,
"X_power": 1,
"Y_power": 1,
},
parameter_bounds={
"multiplier": (None, None),
"X_power": (None, None),
"Y_power": (None, None),
},
put_residuals_in_logspace=True
# Putting residuals in logspace minimizes the norm of log-error instead of absolute error
)
### Check that the fit is right
assert fitted_model.parameters["multiplier"] == pytest.approx(0.546105,
abs=1e-3)
assert fitted_model.parameters["X_power"] == pytest.approx(0.750000,
abs=1e-3)
assert fitted_model.parameters["Y_power"] == pytest.approx(1.250000,
abs=1e-3)