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unbinned_angular_fit.py
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import tensorflow as tf
import zfit
import numpy as np
from root_pandas import read_root, to_root
import json
import matplotlib.pyplot as plt
from zfit.minimize import DefaultToyStrategy
from matplotlib import rc
rc('font',**{'family':'serif','serif':['Roman']})
rc('text', usetex=True)
#3D decay rate PDF with acceptance corrections
class CustomPDF(zfit.pdf.ZPDF):
_PARAMS = ['H0_amp',
'Hm_amp',
'Hp_amp',
'H0_phi',
'Hm_phi',
'Hp_phi',
'costheta_D_p0',
'costheta_D_p1',
'costheta_D_p2',
'costheta_D_p3',
'costheta_D_p4',
'costheta_D_p5',
'costheta_D_p6',
'costheta_X_p0',
'costheta_X_p1',
'costheta_X_p2',
'costheta_X_p3',
'costheta_X_p4',
'costheta_X_p5',
'costheta_X_p6',
'chi_p0',
'chi_p1',
'chi_p2',
'chi_p3',
'chi_p4'
]
_N_OBS = 3
def _unnormalized_pdf(self, x):
costheta_D, costheta_X, chi = x.unstack_x()
H0_amp = self.params['H0_amp']
H0_phi = self.params['H0_phi']
Hm_amp = self.params['Hm_amp']
Hp_amp = self.params['Hp_amp']
Hm_phi = self.params['Hm_phi']
Hp_phi = self.params['Hp_phi']
costheta_D_p0 = self.params['costheta_D_p0']
costheta_D_p1 = self.params['costheta_D_p1']
costheta_D_p2 = self.params['costheta_D_p2']
costheta_D_p3 = self.params['costheta_D_p3']
costheta_D_p4 = self.params['costheta_D_p4']
costheta_D_p5 = self.params['costheta_D_p5']
costheta_D_p6 = self.params['costheta_D_p6']
costheta_X_p0 = self.params['costheta_X_p0']
costheta_X_p1 = self.params['costheta_X_p1']
costheta_X_p2 = self.params['costheta_X_p2']
costheta_X_p3 = self.params['costheta_X_p3']
costheta_X_p4 = self.params['costheta_X_p4']
costheta_X_p5 = self.params['costheta_X_p5']
costheta_X_p6 = self.params['costheta_X_p6']
chi_p0 = self.params['chi_p0']
chi_p1 = self.params['chi_p1']
chi_p2 = self.params['chi_p2']
chi_p3 = self.params['chi_p3']
chi_p4 = self.params['chi_p4']
sintheta_D = tf.math.sqrt( 1.0 - costheta_D * costheta_D )
sintheta_X = tf.math.sqrt( 1.0 - costheta_X * costheta_X )
sintheta_D2 = (2.0 * sintheta_D * costheta_D)
sintheta_X2 = (2.0 * sintheta_X * costheta_X)
coschi = tf.math.cos(chi)
sinchi = tf.math.sin(chi)
cos2chi = 2*coschi*coschi-1
sin2chi = 2*sinchi*coschi
h_0 = tf.complex(H0_amp*tf.cos(H0_phi),H0_amp*tf.sin(H0_phi))
h_p = tf.complex(Hp_amp*tf.cos(Hp_phi),Hp_amp*tf.sin(Hp_phi))
h_m = tf.complex(Hm_amp*tf.cos(Hm_phi),Hm_amp*tf.sin(Hm_phi))
h_0st = tf.math.conj(h_0)
h_pst = tf.math.conj(h_p)
h_mst = tf.math.conj(h_m)
HpHmst = h_p*h_mst
HpH0st = h_p*h_0st
HmH0st = h_m*h_0st
#True decay rate
pdf = H0_amp**2 * costheta_D**2 * sintheta_X**2
pdf += 0.25 * (Hp_amp**2 + Hm_amp**2) * sintheta_D**2 * (1.0 + costheta_X**2)
pdf += -0.5 * tf.math.real(HpHmst) * sintheta_D**2 * sintheta_X**2 * cos2chi
pdf += 0.5 * tf.math.imag(HpHmst) * sintheta_D**2 * sintheta_X**2 * sin2chi
pdf += -0.25 * tf.math.real(HpH0st + HmH0st) * sintheta_D2 * sintheta_X2 * coschi
pdf += 0.25 * tf.math.imag(HpH0st - HmH0st) * sintheta_D2 * sintheta_X2 * sinchi
pdf = pdf * 9./8.
#Normalise to 1
#pdf = pdf * (1./tf.reduce_sum(pdf))
#Acceptance corrections
acc_pdf_costheta_D = costheta_D_p0 + costheta_D_p1 * costheta_D + costheta_D_p2 * costheta_D**2 + costheta_D_p3 * costheta_D**3 + costheta_D_p4 * costheta_D**4 + costheta_D_p5 * costheta_D**5 + costheta_D_p6 * costheta_D**6
acc_pdf_costheta_X = costheta_X_p0 + costheta_X_p1 * costheta_X + costheta_X_p2 * costheta_X**2 + costheta_X_p3 * costheta_X**3 + costheta_X_p4 * costheta_X**4 + costheta_X_p5 * costheta_X**5 + costheta_X_p6 * costheta_X**6
acc_pdf_chi = chi_p0 + chi_p1 * chi + chi_p2 * chi**2 + chi_p3 * chi**3 + chi_p4 * chi**4
acc_pdf_chi = tf.abs(acc_pdf_chi)
acc_pdf = tf.multiply(acc_pdf_costheta_D,acc_pdf_costheta_X)
acc_pdf = tf.multiply(acc_pdf,acc_pdf_chi)
pdf = tf.multiply(pdf,acc_pdf)
return pdf
def main():
#Angular phase space
xobs = zfit.Space('costheta_D_reco', (-1, 1))
yobs = zfit.Space('costheta_X_VV_reco', (-1, 1))
zobs = zfit.Space('chi_VV_reco', (-np.pi, np.pi))
obs = xobs * yobs * zobs
obs_dict = {"costheta_D_reco": [0,"$\\cos(\\theta_D)$",-1,1,xobs],
"costheta_X_VV_reco": [1,"$\\cos(\\theta_X)$",-1,1,yobs],
"chi_VV_reco": [2,"$\\chi$ [rad]",-np.pi,np.pi,zobs]
}
#Helicity amplitude parameters
fL_val = 0.579
H0_amp = zfit.Parameter("H0_amp", np.sqrt(fL_val), floating=False)
Hm_amp = zfit.Parameter("Hm_amp", 0.2, 0., 1.)
def Hp_amp_func(H0_amp, Hm_amp):
return tf.sqrt(1. - H0_amp**2 - Hm_amp**2)
Hp_amp = zfit.ComposedParameter("Hp_amp", Hp_amp_func, dependents=[H0_amp, Hm_amp])
H0_phi = zfit.Parameter("H0_phi", 0., floating=False)
Hp_phi = zfit.Parameter("Hp_phi", 0., -np.pi, np.pi)
Hm_phi = zfit.Parameter("Hm_phi", 0.,-np.pi, np.pi)
#Acceptance corrections
#Default costheta_D and costheta_X corrections
with open("acc_pars_costheta_X_D.json",'r') as f:
acc_dict = json.load(f)
costheta_D_p0 = zfit.Parameter("costheta_D_p0" , acc_dict[f"costheta_D_a0"][0], floating=False)
costheta_D_p1 = zfit.Parameter("costheta_D_p1" , acc_dict[f"costheta_D_a1"][0], floating=False)
costheta_D_p2 = zfit.Parameter("costheta_D_p2" , acc_dict[f"costheta_D_a2"][0], floating=False)
costheta_D_p3 = zfit.Parameter("costheta_D_p3" , acc_dict[f"costheta_D_a3"][0], floating=False)
costheta_D_p4 = zfit.Parameter("costheta_D_p4" , acc_dict[f"costheta_D_a4"][0], floating=False)
costheta_D_p5 = zfit.Parameter("costheta_D_p5" , acc_dict[f"costheta_D_a5"][0], floating=False)
costheta_D_p6 = zfit.Parameter("costheta_D_p6" , acc_dict[f"costheta_D_a6"][0], floating=False)
costheta_X_p0 = zfit.Parameter("costheta_X_p0" , acc_dict[f"costheta_X_VV_a0"][0], floating=False)
costheta_X_p1 = zfit.Parameter("costheta_X_p1" , acc_dict[f"costheta_X_VV_a1"][0], floating=False)
costheta_X_p2 = zfit.Parameter("costheta_X_p2" , acc_dict[f"costheta_X_VV_a2"][0], floating=False)
costheta_X_p3 = zfit.Parameter("costheta_X_p3" , acc_dict[f"costheta_X_VV_a3"][0], floating=False)
costheta_X_p4 = zfit.Parameter("costheta_X_p4" , acc_dict[f"costheta_X_VV_a4"][0], floating=False)
costheta_X_p5 = zfit.Parameter("costheta_X_p5" , acc_dict[f"costheta_X_VV_a5"][0], floating=False)
costheta_X_p6 = zfit.Parameter("costheta_X_p6" , acc_dict[f"costheta_X_VV_a6"][0], floating=False)
with open("acc_pars_chi.json",'r') as f:
acc_dict_chi = json.load(f)
chi_p0 = zfit.Parameter("chi_p0" , acc_dict_chi["chi_VV_a0"][0], floating=False)
chi_p1 = zfit.Parameter("chi_p1" , acc_dict_chi["chi_VV_a1"][0], floating=False)
chi_p2 = zfit.Parameter("chi_p2" , acc_dict_chi["chi_VV_a2"][0], floating=False)
chi_p3 = zfit.Parameter("chi_p3" , acc_dict_chi["chi_VV_a3"][0], floating=False)
chi_p4 = zfit.Parameter("chi_p4" , acc_dict_chi["chi_VV_a4"][0], floating=False)
custom_pdf = CustomPDF(obs=obs,
H0_amp=H0_amp,
Hm_amp=Hm_amp,
Hp_amp=Hp_amp,
H0_phi=H0_phi,
Hm_phi=Hm_phi,
Hp_phi=Hp_phi,
costheta_D_p0 = costheta_D_p0,
costheta_D_p1 = costheta_D_p1,
costheta_D_p2 = costheta_D_p2,
costheta_D_p3 = costheta_D_p3,
costheta_D_p4 = costheta_D_p4,
costheta_D_p5 = costheta_D_p5,
costheta_D_p6 = costheta_D_p6,
costheta_X_p0 = costheta_X_p0,
costheta_X_p1 = costheta_X_p1,
costheta_X_p2 = costheta_X_p2,
costheta_X_p3 = costheta_X_p3,
costheta_X_p4 = costheta_X_p4,
costheta_X_p5 = costheta_X_p5,
costheta_X_p6 = costheta_X_p6,
chi_p0 = chi_p0,
chi_p1 = chi_p1,
chi_p2 = chi_p2,
chi_p3 = chi_p3,
chi_p4 = chi_p4)
integral = custom_pdf.integrate(limits=obs) # = 1 since normalized
#Load data
path = "test.root"
df = read_root(path, "RooTreeDataStore_data_data", columns = ["costheta_D_reco","costheta_X_VV_reco","chi_VV_reco","n_sig_sw"])
df_data = df[["costheta_D_reco","costheta_X_VV_reco","chi_VV_reco"]]
df_w = df["n_sig_sw"]
data = zfit.Data.from_pandas(df_data, obs=obs, weights=df_w)
# Stage 1: create an unbinned likelihood with the given PDF and dataset
nll = zfit.loss.UnbinnedNLL(model=custom_pdf, data=data)
# Stage 2: instantiate a minimiser (in this case a basic minuit
minimizer = zfit.minimize.Minuit(tolerance=1e-5)
#Stage 3: minimise the given negative likelihood
result = minimizer.minimize(nll)
param_errors, _ = result.errors(method="minuit_minos")
print("Function minimum:", result.fmin)
print("Converged:", result.converged)
print("Full minimizer information:", result.info)
params = result.params
print(params)
#Plot results as 1D projections in the angles
bins = 30
data_np = zfit.run(data)
print(data_np)
for v in obs_dict:
fig, ax = plt.subplots(figsize=(7,7))
lower = obs_dict[v][2]
upper = obs_dict[v][3]
counts, bin_edges = np.histogram(df_data[v], bins=bins, range=(lower, upper), weights=df["n_sig_sw"])
bin_centres = (bin_edges[:-1] + bin_edges[1:])/2.
err = np.sqrt(counts)
#Normalise
err = err / np.sum(counts)
counts = counts / np.sum(counts)
#Plot the data
plt.errorbar(bin_centres, counts, yerr=err, fmt='o', color='xkcd:black')
#Plot the PDF
n_p = 1000
x_plot = np.linspace(lower, upper, num=n_p)
x_plot_data = zfit.Data.from_numpy(array=x_plot, obs=obs_dict[v][4])
#Other dims
other_obs = []
for k in obs_dict:
if(k!=v):
other_obs.append(obs_dict[k][4])
#Observables to integrate over
obs_int = other_obs[0] * other_obs[1]
#Integrating over the other dimensions
pdf_x = custom_pdf.partial_integrate(x=x_plot_data, limits=obs_int)
y_plot = zfit.run(pdf_x)
#Normalise
y_plot = y_plot / np.sum(y_plot) * (n_p/bins)
plt.plot(x_plot, y_plot, color='crimson')
#Labels and axis ranges
plt.xlabel(obs_dict[v][1],fontsize=25)
bin_width = float(upper - lower)/bins
y_min, y_max = ax.get_ylim()
plt.ylim(0.0,y_max*1.4)
plt.xlim(lower, upper)
ax.tick_params(axis='both', which='major', labelsize=25)
plt.tight_layout()
fig.savefig(f"{v}_unbinned_fit.pdf")
if __name__ == '__main__':
main()