def fourier_series(x, f, n=0):
# Make the parameter objects for all the terms
a0, *A = parameters(','.join([f'a{i}' for i in range(0, n + 1)]))
B = parameters(','.join([f'b{i}' for i in range(1, n + 1)]))
# Construct the series
series = a0 + sum(ai*cos(i*f*x) + bi*sin(i*f*x)
for i, (ai, bi) in enumerate(zip(A, B), start=1))
return series
def Fourier_series(x, f, n = 0):
"""Construit la série de Fourier comme modèle de référence pour le fitting."""
a0, *cos_a = parameters(','.join(['a{}'.format(i) for i in range(0, n + 1)]))
sin_b = parameters(','.join(['b{}'.format(i) for i in range(1, n + 1)]))
series = a0 + sum(ai * cos(i * f * x) + bi * sin(i * f * x) for i, (ai, bi) in enumerate(zip(cos_a, sin_b), start=1))
return series
def fourier_series(self, x, f, n=2):
a0, *cos_a = parameters(','.join(
['a{}'.format(i) for i in range(0, n + 1)]))
sin_b = parameters(','.join(['b{}'.format(i)
for i in range(1, n + 1)]))
series = a0 + sum(
ai * cos(i * f * x) + bi * sin(i * f * x)
for i, (ai, bi) in enumerate(zip(cos_a, sin_b), start=1))
return series
def fourier_series(x, f, n=0):
"""
Returns a symbolic fourier series of order `n`.
:param n: Order of the fourier series.
:param x: Independent variable
:param f: Frequency of the fourier series
"""
# Make the parameter objects for all the terms
a0, *cos_a = parameters(','.join(['a{}'.format(i) for i in range(0, n + 1)]))
sin_b = parameters(','.join(['b{}'.format(i) for i in range(1, n + 1)]))
# Construct the series
series = a0 + sum(ai * cos(i * f * x) + bi * sin(i * f * x)
for i, (ai, bi) in enumerate(zip(cos_a, sin_b), start=1))
return series
def fit_model(df_avg, frequency):
Model = {
y: a * exp(-b * x) + c * sin(2 * pi * frequency * x + phi) + delta
}
avg_osc = df_avg.groupby("time").mean()["psc"]
argmax_ind = avg_osc.values.argmax()
ydata = avg_osc.values[argmax_ind:]
xdata = real_time[argmax_ind:]
sigma_y = df_avg.groupby("time").std()["psc"].values[argmax_ind:]
fit = Fit(model, x=xdata, y=ydata, sigma_y=sigma_y)
fit_result = fit.execute()
yfit = model[y](x=xdata, **fit_result.params)
return avg_osc, xdata, ydata, fit_result, yfit
def fourier_series(x, period_list):
"""
Returns a symbolic fourier series of order `n`.
:param n: Order of the fourier series.
:param x: Independent variable
:param f: Frequency of the fourier series
"""
# Make the parameter objects for all the terms
(a0, ) = parameters("a0")
cos_a = parameters(",".join(
["a{}".format(i) for i in range2(len(period_list))]))
sin_b = parameters(",".join(
["b{}".format(i) for i in range2(len(period_list))]))
# Construct the series
print(period_list)
series = a0 + sum(
ai * cos(2 * math.pi / tau * x) + bi * sin(2 * math.pi / tau * x)
for (tau, ai, bi) in zip(period_list, cos_a, sin_b))
return series
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 fourier_series(x, f, n=0):
a0, *cos_a = parameters(",".join([f"a{i}" for i in range(n + 1)]))
sin_b = parameters(",".join([f"b{i}" for i in range(1, n + 1)]))
series = a0 + sum(ai * cos(i * f * x) + bi * sin(i * f * x)
for i, (ai, bi) in enumerate(zip(cos_a, sin_b), start=1))
return series
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
