def fit_data(data, guess=10.0, use_err=False):
x_data = data[:, 0]
y_data = 1 - data[:, 1]
if use_err:
data_err = data[:, 2]
x, y = sf.variables('x, y')
pKa, n = sf.parameters('pKa, n')
model = sf.Model({y: (10**(n * (pKa - x)) + 1)**-1.0})
pKa.value = guess
n.value = 1
if use_err:
fit = sf.Fit(model,
x=x_data,
y=y_data,
sigma_y=data_err,
minimizer=Powell,
absolute_sigma=True)
else:
fit = sf.Fit(model, x=x_data, y=y_data, minimizer=Powell)
result = fit.execute()
print("pKa.....................................", result.value(pKa), '+/-',
result.stdev(pKa))
print("n.......................................", result.value(n), '+/-',
result.stdev(n))
print("Regression coefficent:................", result.r_squared, '\n')
x_out = np.arange(min(x_data), max(x_data), 10**-3.0)
y_out = fit.model(x=x_out, **result.params)[0]
return x_out, y_out, result.value(pKa), result.stdev(
pKa), result.r_squared, result.value(n), result.stdev(n)
def test_harmonic_oscillator_errors():
"""
Make sure the errors produced by fitting ODE's are the same as when
fitting an exact solution.
"""
x, v, t = sf.variables('x, v, t')
k = sf.Parameter(name='k', value=100)
m = 1
a = -k/m * x
ode_model = sf.ODEModel({sf.D(v, t): a,
sf.D(x, t): v},
initial={t: 0, v: 0, x: 1})
t_data = np.linspace(0, 10, 250)
np.random.seed(2)
noise = np.random.normal(1, 0.05, size=t_data.shape)
x_data = ode_model(t=t_data, k=100).x * noise
ode_fit = sf.Fit(ode_model, t=t_data, x=x_data, v=None)
ode_result = ode_fit.execute()
phi = 0
A = 1
model = sf.Model({x: A * sf.cos(sf.sqrt(k/m) * t + phi)})
fit = sf.Fit(model, t=t_data, x=x_data)
result = fit.execute()
assert result.value(k) == pytest.approx(ode_result.value(k), 1e-4)
assert result.stdev(k) == pytest.approx(ode_result.stdev(k), 1e-2)
assert result.stdev(k) >= ode_result.stdev(k)
def fit_plane(xyz):
"""
Fit a plane to the point coordinates in xyz.
Dev note: An alternative implementation is possible that omits the `f`
variable, and thus has one fewer degree of freedom. This means the fit is
easier and maybe more precise. This could be tested. The notebook
req4.1_fit_plane.ipynb in the explore repository
(https://github.com/sundial-pointcloud-geometry/explore) has some notes on
this. The problem with those models where f is just zero and the named
symfit model is created for one of x, y or z instead is that you have to
divide by one of the a, b or c parameters respectively. If one of these
turns out to be zero, symfit will not find a fit. A solution would be
to actually create three models and try another if one of them fails to
converge.
"""
a, b, c, d = sf.parameters('a, b, c, d')
x, y, z, f = sf.variables('x, y, z, f')
plane_model = {f: x * a + y * b + z * c + d}
plane_fit = sf.Fit(plane_model, x=xyz[0], y=xyz[1], z=xyz[2],
f=np.zeros_like(xyz[0]),
constraints=[sf.Equality(a**2 + b**2 + c**2, 1)]) # keep plane normal a unit vector
plane_fit_result = plane_fit.execute()
return plane_fit_result
def test_ODE_stdev():
"""
Make sure that parameters from ODEModels get standard deviations.
"""
x, v, t = sf.variables('x, v, t')
k = sf.Parameter(name='k')
k.min = 0
k.value = 10
a = -k * x
model = sf.ODEModel({
sf.D(v, t): a,
sf.D(x, t): v,
},
initial={
v: 0,
x: 1,
t: 0
})
t_data = np.linspace(0, 10, 150)
noise = np.random.normal(1, 0.05, t_data.shape)
x_data = model(t=t_data, k=11).x * noise
v_data = model(t=t_data, k=11).v * noise
fit = sf.Fit(model, t=t_data, x=x_data, v=v_data)
result = fit.execute()
assert result.stdev(k) is not None
assert np.isfinite(result.stdev(k))
def run(
self,
angle=0.02472,
pixel_to_micron_x=9.81e-8,
beam_waist_xy=0.5e-6,
beam_waist_z=2e-6,
rbc_radius=4e-6,
s=1,
tau=0.001,
):
# create parameters for symfit
distances = self.data.keys()
v = sf.parameters('v_', value=500, min=0, max=1000)[0]
d = sf.parameters('D_', value=50, min=0, max=100)[0]
y0_p = sf.parameters(
self.create_distance_strings('y0'),
min=0,
max=1,
)
b_p = sf.parameters(
self.create_distance_strings('b'),
value=50,
min=0,
max=100,
)
# create variables for symfit
x = sf.variables('x')[0]
y_var = sf.variables(self.create_distance_strings('y'))
# create model
# pixel_to_micron_x
model = sf.Model({
y:
y0 + b * sf.exp(-(dst * pixel_to_micron_x - v * (sf.cos(angle)) * x)**2 / (beam_waist_xy + 0.5 * rbc_radius**2 + 4 * d * x)) * sf.exp(-(x**2) * (v * sf.sin(angle) - pixel_to_micron_x / tau)**2 / (beam_waist_xy + 0.5 * rbc_radius**2 + angle * d * x)) / (4 * d * x + beam_waist_xy + 0.5 * rbc_radius**2)
for y, y0, b, dst in zip(y_var, y0_p, b_p, distances)
})
# dependent variables dict
data = {y.name: self.data[dst] for y, dst in zip(y_var, distances)}
# independent variable x
n_data_points = len(list(self.data.values())[0])
max_time = n_data_points * tau
x_data = np.linspace(0, max_time, n_data_points)
# fit
fit = sf.Fit(model, x=x_data, **data)
res = fit.execute()
return res
def do_glob_fit(self):
"""this method performs global fit on the CCPS"""
# create parameters for symfit
dist = self.data.keys()
v = sf.parameters('v_', value=500, min=0, max=1000)[0]
d = sf.parameters('D_', value=50, min=0, max=100)[0]
y0_p = sf.parameters(', '.join('y0_{}'.format(key)
for key in self.data.keys()),
min=0,
max=1)
b_p = sf.parameters(', '.join('b_{}'.format(key)
for key in self.data.keys()),
value=50,
min=0,
max=100)
# create variables for symfit
x = sf.variables('x')[0]
y_var = sf.variables(', '.join('y_{}'.format(key)
for key in self.data.keys()))
# get fixed & shared params
dx, a, w2, a2, tau, s, wz2 = self.get_params()
# create model
model = sf.Model({
y: y0 + b * sf.exp(-(dst * dx - v * (sf.cos(a)) * x)**2 /
(w2 + 0.5 * a2 + 4 * d * x)) *
sf.exp(-(x**2) * (v * sf.sin(a) - dx / tau)**2 /
(w2 + 0.5 * a2 + a * d * x)) / (4 * d * x + w2 + 0.5 * a2)
for y, y0, b, dst in zip(y_var, y0_p, b_p, dist)
})
# dependent variables dict
data = {y.name: self.data[dst] for y, dst in zip(y_var, dist)}
# independent variable x
max_time = len(self.data[20]) * tau
x_data = np.linspace(0, max_time, len(self.data[20]))
# fit
fit = sf.Fit(model, x=x_data, **data)
res = fit.execute()
return res
def generator_execute(self, *, k_start=0, **minimizer_kwargs):
"""
Hand over the rains to :mod:`symfit`, and regularize that inversion. Use
this in case of a very expensive calculation, so the results can e.g.
be written to disk.
:param k_start:
:param minimizer_kwargs:
:return: generator over the subfits per data set, starting from dataset
``k_start``.
"""
# Select the symbols which depend on all the data sets
global_symbols = []
local_symbols = {}
for s in self.model.ordered_symbols:
if isinstance(s, sf.MatrixSymbol) and N_sets in s.shape:
global_symbols.append(s)
# Turn into a vector
local_symbols[s] = s.func(*s.args[:-1], 1)
local_model = self.localize_model(local_symbols)
for set_index in range(k_start, self.shapes[N_sets]):
# Select the right component
data = self.data.copy()
for s in global_symbols:
if s in data:
# Select the component, but maintain shape
data[s] = data[s][:, set_index][..., None]
fit = sf.Fit(local_model, **key2str(data), **self.fit_options)
fit_result = fit.execute(**minimizer_kwargs)
model_ans = fit.model(**key2str(fit.independent_data),
**fit_result.params)
fit_result.model_ans = model_ans
yield fit_result
['$B_0$']).setaxis('$B_0$', x_finer).set_units(
'$B_0$', d.get_units('$B_0$'))
plot(d, label='data')
plot(guess_nddata, ':', label='guess')
model = s.Model({y_var: dVoigt})
if interactive:
guess = InteractiveGuess(model,
y=d.data.real,
B=d.getaxis('$B_0$'),
n_points=500)
guess.execute()
logger.info(strm(guess))
y_var = s.Variable('y')
logger.info(strm("about to run fit"))
fit = s.Fit(
model, d.getaxis('$B_0$'), d.data.real
) # really want to use minpack here, but gives "not proper array of floats
fit_result = fit.execute()
logger.info(strm("fit is done"))
plt.figure()
plt.title('data with fit')
plot(d, '.', label='data')
fit_nddata = nddata(
fit.model(B=x_finer, **fit_result.params).y, [-1],
['$B_0$']).setaxis('$B_0$', x_finer)
plot(fit_nddata, label='fit')
logger.info(strm(fit_result))
conc_list.append(concentration)
R_list.append(fit_result.params['R'])
sigma_list.append(fit_result.params['sigma'])
A_list.append(fit_result.params['A'])
t: 0.0,
S: S_0,
I: I_0,
R: R_0,
D: D_0
})
idx = sorted_data["country"] == country
x = sorted_data[idx]["days_since_100_cases"].values
y = sorted_data[idx]["cumulative_deaths"].values
fit = sf.Fit(
ode_model[country],
t=x,
S=None,
I=None,
R=None,
D=y,
minimizer=[DifferentialEvolution, BFGS],
)
fit_result[country] = fit.execute(DifferentialEvolution={
"seed": 0,
"tol": 1e-2,
"maxiter": 5
},
BFGS={"tol": 1e-6})
print(fit_result[country])
logger.info("Inferencing...")
n_days = 365 # Daily predictions
def fit_lanes(self, points_left, points_right, fit_globally=False) -> dict:
"""
Applies and returns a polynomial fit for given points along the left and right lane line.
Both lanes are described by a second order polynomial x(y) = ay^2 + by + x0. In the `fit_globally` case,
a and b are modeled as equal, making the lines perfectly parallel. Otherwise, each line is fit independent of
the other. The parameters of the model are returned in a dictionary with keys 'al', 'bl', 'x0l' for the left
lane parameters and 'ar', 'br', 'x0r' for the right lane.
:param points_left: Two lists of the x and y positions along the left lane line.
:param points_right: Two lists of the x and y positions along the right lane line.
:param fit_globally: Set True to use the global, parallel line fit model. In practice this does not allays work.
:return: fit_vals, a dictionary containing the fitting parameters for the left and right lane as above.
"""
xl, yl = points_left
xr, yr = points_right
fit_vals = {}
if fit_globally:
# Define global model to fit
x_left, y_left, x_right, y_right = symfit.variables(
'x_left, y_left, x_right, y_right')
a, b, x0_left, x0_right = symfit.parameters(
'a, b, x0_left, x0_right')
model = symfit.Model({
x_left:
a * y_left**2 + b * y_left + x0_left,
x_right:
a * y_right**2 + b * y_right + x0_right
})
# Apply fit
xl, yl = points_left
xr, yr = points_right
fit = symfit.Fit(model,
x_left=xl,
y_left=yl,
x_right=xr,
y_right=yr)
fit = fit.execute()
fit_vals.update({
'ar': fit.value(a),
'al': fit.value(a),
'bl': fit.value(b),
'br': fit.value(b),
'x0l': fit.value(x0_left),
'x0r': fit.value(x0_right)
})
else:
# Fit lines independently
x, y = symfit.variables('x, y')
a, b, x0 = symfit.parameters('a, b, x0')
model = symfit.Model({
x: a * y**2 + b * y + x0,
})
# Apply fit on left
fit = symfit.Fit(model, x=xl, y=yl)
fit = fit.execute()
fit_vals.update({
'al': fit.value(a),
'bl': fit.value(b),
'x0l': fit.value(x0)
})
# Apply fit on right
fit = symfit.Fit(model, x=xr, y=yr)
fit = fit.execute()
fit_vals.update({
'ar': fit.value(a),
'br': fit.value(b),
'x0r': fit.value(x0)
})
return fit_vals