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model.py
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from scipy import interpolate
from scipy.optimize import curve_fit
from numpy import cos, pi, sqrt, floor
from files import Files
from bin import Bin
import pandas as pd
import numpy as np
class Model:
def __init__(self, options, W: list, Q2: list, cos_th: list, phi: list):
# Check the channel
assert options[
'channel'] == "K+L" or options['channel'] == "K+S0", f"Channel name: {options['channel']} is invalid"
# Check the phase space parameters
for i in Q2:
assert i >= 0, f"Q2: {i} is lower than zero"
for i in cos_th:
assert i >= -1 and i <= 1, f"cos_th: {i} is out of [-1, 1] interval"
assert options['E_beam'] >= 0, f"E_beam: {options['E_beam']} is lower than zero"
# if options['channel'] == "K+L":
# for i in W:
# assert i >= 1.61, f"W: {i} is less than threshold for KLambda channel"
# elif options['channel'] == "K+S0":
# for i in W:
# assert i >= 1.68632, f"W: {i} is less than threshold for KSigma0 channel"
# Assignment
self.__name = options['channel']
self.__W = W
self.__Q2 = Q2
self.__cos_th = cos_th
self.__phi = phi
self.__E_beam = options['E_beam']
self.__Data = Files(options['channel'])
self.__ratio_str = options['ratio_str']
self.__add_factor = options['add_factor']
self.__W_sys = options['W_sys']
self.__err_option = options['err_option']
vol = []
vol_sf = []
for i in W:
for j in Q2:
for k in cos_th:
vol_sf.append([i, j, k])
for z in phi:
vol.append([i, j, k, z])
self.__req_volume = pd.DataFrame(vol, columns=['W', 'Q2', 'cos_th', 'phi'])
self.__req_volume['E'] = self.__E_beam
self.__req_volume['eps'] = self.eps(self.__req_volume['W'], self.__req_volume['Q2'])
self.__req_volume_sf = pd.DataFrame(vol_sf, columns=['W', 'Q2', 'cos_th'])
del vol, vol_sf
@property
def name(self):
return self.__name
@property
def W(self):
return self.__W
@property
def Q2(self):
return self.__Q2
@property
def cos_th(self):
return self.__cos_th
@property
def phi(self):
return self.__phi
@property
def E_beam(self):
return self.__E_beam
@property
def Data(self):
return self.__Data
@property
def ratio_str(self):
return self.__ratio_str
@property
def add_factor(self):
return self.__add_factor
@property
def W_sys(self):
return self.__W_sys
@property
def err_option(self):
return self.__err_option
@property
def req_volume(self):
return self.__req_volume
@property
def req_volume_sf(self):
return self.__req_volume_sf
@W.setter
def W(self, value):
self.__W = value
@Q2.setter
def Q2(self, value):
self.__Q2 = value
@cos_th.setter
def cos_th(self, value):
self.__cos_th = value
@phi.setter
def phi(self, value):
self.__phi = value
@E_beam.setter
def E_beam(self, value):
self.__E_beam = value
@ratio_str.setter
def ratio_str(self, value):
self.__ratio_str = value
@add_factor.setter
def add_factor(self, value):
self.__add_factor = value
@W_sys.setter
def W_sys(self, value):
self.__W_sys = value
@err_option.setter
def err_option(self, value):
self.__err_option = value
def __repr__(self):
return f'Model("{self.name}", {[x for x in self.W]}, {[x for x in self.Q2]}, {[x for x in self.cos_th]}, {[x for x in self.phi]}, {self.E_beam}, {self.ratio_str}, {self.add_factor}, {self.W_sys}, {self.err_option})'
def __str__(self):
print(f" Channel: {self.name}")
print(f"\n Phase space parameters:")
print(f"\t W\t= {self.W} GeV")
print(f"\t Q2\t= {self.Q2} GeV2")
print(f"\t cos_th\t= {self.cos_th}")
print(f"\t phi\t= {self.phi} degree")
print(f"\t E_beam\t= {self.E_beam} GeV\n\n")
print(f" {self.ratio_str} - Special ratio method")
print(f" {self.add_factor} - Factorized S_LT and S_TT")
print(f" {self.W_sys} - Additional sys. error for W extrapolation for S_T str. func")
if self.err_option == 3:
print(f"\n Quad. extrapolation of errors for cos_th axis\n")
elif self.err_option == 2:
print(f"\n Linear exrapolation of errors(up to 100%) for cos_th axis\n")
elif self.err_option == 1:
print(f"\n Constant extrapolation of errors for cos_th axis\n")
# print(self.Data)
return ' '
def __interp_cub_PP(self, data_table):
result = pd.DataFrame()
data_table = data_table.copy()
data_table['dcs_plus'] = data_table['cs'] + data_table['dcs']
W = data_table.iloc[0]['W']
x = np.array(data_table['cos_th'])
cs = np.array(data_table['cs'])
dcs_plus = np.array(data_table['dcs_plus'])
f1 = interpolate.interp1d(x, cs, kind='cubic', copy=False)
f1_plus = interpolate.interp1d(x, dcs_plus, kind='cubic', copy=False)
e1 = interpolate.InterpolatedUnivariateSpline(x, cs, k=2)
e1_plus = interpolate.InterpolatedUnivariateSpline(x, dcs_plus, k=2)
for cos_th in self.cos_th:
if cos_th >= x.min() and cos_th <= x.max():
result = pd.concat([result, pd.DataFrame({'W': [W], 'cos_th': [cos_th], 'dSt': [f1_plus(
cos_th).astype(np.float) - f1(cos_th).astype(np.float)]})], ignore_index=True)
else:
result = pd.concat([result, pd.DataFrame({'W': [W], 'cos_th': [cos_th], 'dSt': [e1_plus(
cos_th).astype(np.float) - e1(cos_th).astype(np.float)]})], ignore_index=True)
return result
def __interp_cub_PPSigma(self, data_table):
result = pd.DataFrame()
data_table = data_table.copy()
data_table['dSigma_plus'] = data_table['Sigma'] + data_table['dSigma']
W = data_table.iloc[0]['W']
x = np.array(data_table['cos_th'])
cs = np.array(data_table['Sigma'])
dcs_plus = np.array(data_table['dSigma_plus'])
f1 = interpolate.interp1d(x, cs, kind='cubic', copy=False)
f1_plus = interpolate.interp1d(x, dcs_plus, kind='cubic', copy=False)
e1 = interpolate.InterpolatedUnivariateSpline(x, cs, k=2)
e1_plus = interpolate.InterpolatedUnivariateSpline(x, dcs_plus, k=2)
for cos_th in self.cos_th:
if cos_th >= x.min() and cos_th <= x.max():
result = pd.concat([result, pd.DataFrame({'W': [W], 'cos_th': [cos_th], 'dSigma': [f1_plus(
cos_th).astype(np.float) - f1(cos_th).astype(np.float)]})], ignore_index=True)
else:
result = pd.concat([result, pd.DataFrame({'W': [W], 'cos_th': [cos_th], 'dSigma': [e1_plus(
cos_th).astype(np.float) - e1(cos_th).astype(np.float)]})], ignore_index=True)
return result
def __interp_cub(self, data_table):
result = pd.DataFrame()
data_table = data_table.copy()
data_table['dSt_plus'] = data_table['St'] + data_table['dSt']
data_table['dSl_plus'] = data_table['Sl'] + data_table['dSl']
data_table['dSlt_plus'] = data_table['Slt'] + data_table['dSlt']
data_table['dStt_plus'] = data_table['Stt'] + data_table['dStt']
W = data_table.iloc[0]['W']
Q2 = data_table.iloc[0]['Q2']
x = np.array(data_table['cos_th'])
St = np.array(data_table['St'])
Sl = np.array(data_table['Sl'])
Slt = np.array(data_table['Slt'])
Stt = np.array(data_table['Stt'])
dSt_plus = np.array(data_table['dSt_plus'])
dSl_plus = np.array(data_table['dSl_plus'])
dSlt_plus = np.array(data_table['dSlt_plus'])
dStt_plus = np.array(data_table['dStt_plus'])
type = ''
if len(x) < 4:
type = 'quadratic'
else:
type = 'cubic'
f1 = interpolate.interp1d(x, St, kind=type, copy=False)
f2 = interpolate.interp1d(x, Sl, kind=type, copy=False)
f3 = interpolate.interp1d(x, Slt, kind=type, copy=False)
f4 = interpolate.interp1d(x, Stt, kind=type, copy=False)
f1_plus = interpolate.interp1d(x, dSt_plus, kind=type, copy=False)
f2_plus = interpolate.interp1d(x, dSl_plus, kind=type, copy=False)
f3_plus = interpolate.interp1d(x, dSlt_plus, kind=type, copy=False)
f4_plus = interpolate.interp1d(x, dStt_plus, kind=type, copy=False)
e1 = interpolate.InterpolatedUnivariateSpline(x, St, k=2)
e2 = interpolate.InterpolatedUnivariateSpline(x, Sl, k=2)
e3 = interpolate.InterpolatedUnivariateSpline(x, Slt, k=2)
e4 = interpolate.InterpolatedUnivariateSpline(x, Stt, k=2)
e1_plus = interpolate.InterpolatedUnivariateSpline(x, dSt_plus, k=2)
e2_plus = interpolate.InterpolatedUnivariateSpline(x, dSl_plus, k=2)
e3_plus = interpolate.InterpolatedUnivariateSpline(x, dSlt_plus, k=2)
e4_plus = interpolate.InterpolatedUnivariateSpline(x, dStt_plus, k=2)
for cos_th in self.cos_th:
if cos_th >= x.min() and cos_th <= x.max():
result = pd.concat([result, pd.DataFrame({'W': [W], 'Q2': [Q2], 'cos_th': [cos_th], 'dSt': [f1_plus(cos_th).astype(np.float) - f1(cos_th).astype(np.float)], 'dSl': [f2_plus(
cos_th).astype(np.float) - f2(cos_th).astype(np.float)], 'dSlt': [f3_plus(cos_th).astype(np.float) - f3(cos_th).astype(np.float)], 'dStt': [f4_plus(cos_th).astype(np.float) - f4(cos_th).astype(np.float)]})], ignore_index=True)
else:
result = pd.concat([result, pd.DataFrame({'W': [W], 'Q2': [Q2], 'cos_th': [cos_th], 'dSt': [e1_plus(cos_th).astype(np.float) - e1(cos_th).astype(np.float)], 'dSl': [e2_plus(
cos_th).astype(np.float) - e2(cos_th).astype(np.float)], 'dSlt': [e3_plus(cos_th).astype(np.float) - e3(cos_th).astype(np.float)], 'dStt': [e4_plus(cos_th).astype(np.float) - e4(cos_th).astype(np.float)]})], ignore_index=True)
return result
def __interp_cub_extraQ2(self, data_table, Q2_list):
result = pd.DataFrame()
data_table = data_table.copy()
data_table['dSt_plus'] = data_table['St'] + data_table['dSt']
data_table['dSl_plus'] = data_table['Sl'] + data_table['dSl']
data_table['dSlt_plus'] = data_table['Slt'] + data_table['dSlt']
data_table['dStt_plus'] = data_table['Stt'] + data_table['dStt']
W = data_table.iloc[0]['W']
cos_th = data_table.iloc[0]['cos_th']
x = np.array(data_table['Q2'])
St = np.array(data_table['St'])
Sl = np.array(data_table['Sl'])
Slt = np.array(data_table['Slt'])
Stt = np.array(data_table['Stt'])
dSt_plus = np.array(data_table['dSt_plus'])
dSl_plus = np.array(data_table['dSl_plus'])
dSlt_plus = np.array(data_table['dSlt_plus'])
dStt_plus = np.array(data_table['dStt_plus'])
e1 = interpolate.InterpolatedUnivariateSpline(x, St, k=2)
e2 = interpolate.InterpolatedUnivariateSpline(x, Sl, k=2)
e3 = interpolate.InterpolatedUnivariateSpline(x, Slt, k=2)
e4 = interpolate.InterpolatedUnivariateSpline(x, Stt, k=2)
e1_plus = interpolate.InterpolatedUnivariateSpline(x, dSt_plus, k=2)
e2_plus = interpolate.InterpolatedUnivariateSpline(x, dSl_plus, k=2)
e3_plus = interpolate.InterpolatedUnivariateSpline(x, dSlt_plus, k=2)
e4_plus = interpolate.InterpolatedUnivariateSpline(x, dStt_plus, k=2)
for Q2 in Q2_list:
result = pd.concat([result, pd.DataFrame({'W': [W], 'Q2': [Q2], 'cos_th': [cos_th], 'dSt': [e1_plus(Q2).astype(np.float) - e1(Q2).astype(np.float)], 'dSl': [e2_plus(
Q2).astype(np.float) - e2(Q2).astype(np.float)], 'dSlt': [e3_plus(Q2).astype(np.float) - e3(Q2).astype(np.float)], 'dStt': [e4_plus(Q2).astype(np.float) - e4(Q2).astype(np.float)]})], ignore_index=True)
return result
@staticmethod
def __interp_cub_TT_LT(data_table, arg_th: float):
x = np.array(data_table['cos_th'])
if 'Slt' in data_table.columns:
y = np.array(data_table['Slt'])
elif 'Stt' in data_table.columns:
y = np.array(data_table['Stt'])
else:
return 0
x = np.append(x, -1)
y = np.append(y, 0)
f = interpolate.interp1d(x, y, kind='cubic', copy=False)
del x, y
return f(arg_th).astype(np.float)
def __approx_cos_leg(self, data_table):
W = data_table.iloc[0]['W']
Q2 = data_table.iloc[0]['Q2']
x = data_table['cos_th']
St = data_table['St']
dSt = data_table['dSt']
Sl = data_table['Sl']
dSl = data_table['dSl']
Slt = data_table['Slt']
dSlt = data_table['dSlt']
Stt = data_table['Stt']
dStt = data_table['dStt']
def Su(x, a, b, c, d, e):
y = a + b*x + c*0.5*(3*x**2 - 1) + d*0.5*(5*x**3 - 3*x) + e*(35*x**4 - 30*x**2 + 3)/8
return y
def SLT_f(x, a, b, c, d, e):
y = np.sin(np.arccos(x))*(a + b*x + c*0.5*(3*x**2 - 1) + d *
0.5*(5*x**3 - 3*x) + e*(35*x**4 - 30*x**2 + 3)/8)
return y
def STT_f(x, a, b, c, d, e):
y = (1-x**2)*(a + b*x + c*0.5*(3*x**2 - 1) + d*0.5 *
(5*x**3 - 3*x) + e*(35*x**4 - 30*x**2 + 3)/8)
return y
def Su4(x, a, b, c, d):
y = a + b*x + c*0.5*(3*x**2 - 1) + d*0.5*(5*x**3 - 3*x)
return y
def SLT_f4(x, a, b, c, d):
y = np.sin(np.arccos(x))*(a + b*x + c*0.5*(3*x**2 - 1) + d*0.5*(5*x**3 - 3*x))
return y
def STT_f4(x, a, b, c, d):
y = (1-x**2)*(a + b*x + c*0.5*(3*x**2 - 1) + d*0.5*(5*x**3 - 3*x))
return y
def Su3(x, a, b, c):
y = a + b*x + c*0.5*(3*x**2 - 1)
return y
def SLT_f3(x, a, b, c):
y = np.sin(np.arccos(x))*(a + b*x + c*0.5*(3*x**2 - 1))
return y
def STT_f3(x, a, b, c):
y = (1-x**2)*(a + b*x + c*0.5*(3*x**2 - 1))
return y
result = pd.DataFrame()
if len(x) > 4:
popt_St, pcov_St = curve_fit(Su, x, St, sigma=dSt, absolute_sigma=True)
popt_Sl, pcov_Sl = curve_fit(Su, x, Sl, sigma=dSl, absolute_sigma=True)
if self.add_factor:
popt_Slt, pcov_Slt = curve_fit(SLT_f, x, Slt, sigma=dSlt, absolute_sigma=True)
popt_Stt, pcov_Stt = curve_fit(STT_f, x, Stt, sigma=dStt, absolute_sigma=True)
else:
popt_Slt, pcov_Slt = curve_fit(Su, x, Slt, sigma=dSlt, absolute_sigma=True)
popt_Stt, pcov_Stt = curve_fit(Su, x, Stt, sigma=dStt, absolute_sigma=True)
for cos_th in self.cos_th:
buff = {'W': [W], 'Q2': [Q2], 'cos_th': [cos_th]}
arg = cos_th
buff['St'] = [Su(cos_th, popt_St[0], popt_St[1],
popt_St[2], popt_St[3], popt_St[4])]
buff['Sl'] = [Su(cos_th, popt_Sl[0], popt_Sl[1],
popt_Sl[2], popt_Sl[3], popt_Sl[4])]
if self.add_factor:
buff['Slt'] = [SLT_f(cos_th, popt_Slt[0], popt_Slt[1],
popt_Slt[2], popt_Slt[3], popt_Slt[4])]
buff['Stt'] = [STT_f(cos_th, popt_Stt[0], popt_Stt[1],
popt_Stt[2], popt_Stt[3], popt_Stt[4])]
if arg < x.min():
buff['Slt'] = [self.__interp_cub_TT_LT(
data_table[['cos_th', 'Slt', 'dSlt']], arg)]
buff['Stt'] = [self.__interp_cub_TT_LT(
data_table[['cos_th', 'Stt', 'dStt']], arg)]
else:
buff['Slt'] = [Su(cos_th, popt_Slt[0], popt_Slt[1],
popt_Slt[2], popt_Slt[3], popt_Slt[4])]
buff['Stt'] = [Su(cos_th, popt_Stt[0], popt_Stt[1],
popt_Stt[2], popt_Stt[3], popt_Stt[4])]
result = pd.concat([result, pd.DataFrame(buff)], ignore_index=True)
result_for_merge = self.__interp_cub(data_table)
result_for_merge.set_index(['W', 'Q2', 'cos_th'], inplace=True, drop=True)
result.set_index(['W', 'Q2', 'cos_th'], inplace=True, drop=True)
result = result_for_merge.merge(result, on=['W', 'Q2', 'cos_th'])
result.reset_index(inplace=True)
if self.err_option == 1:
result.loc[result['cos_th'] < x.min(), 'dSt'] = data_table.iloc[0]['dSt']
result.loc[result['cos_th'] < x.min(), 'dSl'] = data_table.iloc[0]['dSl']
result.loc[result['cos_th'] < x.min(), 'dSlt'] = data_table.iloc[0]['dSlt']
result.loc[result['cos_th'] < x.min(), 'dStt'] = data_table.iloc[0]['dStt']
result.loc[result['cos_th'] >
x.max(), 'dSt'] = data_table.iloc[len(data_table)-1]['dSt']
result.loc[result['cos_th'] >
x.max(), 'dSl'] = data_table.iloc[len(data_table)-1]['dSl']
result.loc[result['cos_th'] >
x.max(), 'dSlt'] = data_table.iloc[len(data_table)-1]['dSlt']
result.loc[result['cos_th'] >
x.max(), 'dStt'] = data_table.iloc[len(data_table)-1]['dStt']
if self.err_option == 2:
result.loc[result['cos_th'] < x.min(), 'dSt'] = data_table.iloc[0]['dSt'] * \
((-result.loc[(result['cos_th'] < x.min()),
'cos_th'] + x.min())/(1 + x.min()) + 1)
result.loc[result['cos_th'] < x.min(), 'dSl'] = data_table.iloc[0]['dSl'] * \
((-result.loc[(result['cos_th'] < x.min()),
'cos_th'] + x.min())/(1 + x.min()) + 1)
result.loc[result['cos_th'] < x.min(), 'dSlt'] = data_table.iloc[0]['dSlt'] * \
((-result.loc[(result['cos_th'] < x.min()),
'cos_th'] + x.min())/(1 + x.min()) + 1)
result.loc[result['cos_th'] < x.min(), 'dStt'] = data_table.iloc[0]['dStt'] * \
((-result.loc[(result['cos_th'] < x.min()),
'cos_th'] + x.min())/(1 + x.min()) + 1)
result.loc[result['cos_th'] > x.max(), 'dSt'] = data_table.iloc[len(
data_table)-1]['dSt']*((result.loc[(result['cos_th'] > x.max()), 'cos_th'] - x.max())/(1 - x.max()) + 1)
result.loc[result['cos_th'] > x.max(), 'dSl'] = data_table.iloc[len(
data_table)-1]['dSl']*((result.loc[(result['cos_th'] > x.max()), 'cos_th'] - x.max())/(1 - x.max()) + 1)
result.loc[result['cos_th'] > x.max(), 'dSlt'] = data_table.iloc[len(
data_table)-1]['dSlt']*((result.loc[(result['cos_th'] > x.max()), 'cos_th'] - x.max())/(1 - x.max()) + 1)
result.loc[result['cos_th'] > x.max(), 'dStt'] = data_table.iloc[len(
data_table)-1]['dStt']*((result.loc[(result['cos_th'] > x.max()), 'cos_th'] - x.max())/(1 - x.max()) + 1)
result.loc[result['cos_th'] < x.min(), 'St'] = Su(
x.min(), popt_St[0], popt_St[1], popt_St[2], popt_St[3], popt_St[4])
result.loc[result['cos_th'] < x.min(), 'Sl'] = Su(
x.min(), popt_Sl[0], popt_Sl[1], popt_Sl[2], popt_Sl[3], popt_Sl[4])
result.loc[result['cos_th'] > x.max(), 'St'] = Su(
x.max(), popt_St[0], popt_St[1], popt_St[2], popt_St[3], popt_St[4])
result.loc[result['cos_th'] > x.max(), 'Sl'] = Su(
x.max(), popt_Sl[0], popt_Sl[1], popt_Sl[2], popt_Sl[3], popt_Sl[4])
if not(self.add_factor):
result.loc[result['cos_th'] < x.min(), 'Slt'] = Su(
x.min(), popt_Slt[0], popt_Slt[1], popt_Slt[2], popt_Slt[3], popt_Slt[4])
result.loc[result['cos_th'] < x.min(), 'Stt'] = Su(
x.min(), popt_Stt[0], popt_Stt[1], popt_Stt[2], popt_Stt[3], popt_Stt[4])
result.loc[result['cos_th'] > x.max(), 'Slt'] = Su(
x.max(), popt_Slt[0], popt_Slt[1], popt_Slt[2], popt_Slt[3], popt_Slt[4])
result.loc[result['cos_th'] > x.max(), 'Stt'] = Su(
x.max(), popt_Stt[0], popt_Stt[1], popt_Stt[2], popt_Stt[3], popt_Stt[4])
if self.add_factor:
result.loc[(result['cos_th'] < x.min()), 'dSlt'] = data_table.iloc[0]['dSlt'] * \
(result.loc[(result['cos_th'] < x.min()), 'cos_th'] + 1)/(1 + x.min())
result.loc[(result['cos_th'] < x.min()), 'dStt'] = data_table.iloc[0]['dStt'] * \
(result.loc[(result['cos_th'] < x.min()), 'cos_th'] + 1)/(1 + x.min())
result.loc[(result['cos_th'] > x.max()), 'dSlt'] = data_table.iloc[len(
data_table)-1]['dSlt']*(result.loc[(result['cos_th'] > x.max()), 'cos_th'] - 1)/(-1 + x.max())
result.loc[(result['cos_th'] > x.max()), 'dStt'] = data_table.iloc[len(
data_table)-1]['dStt']*(result.loc[(result['cos_th'] > x.max()), 'cos_th'] - 1)/(-1 + x.max())
result.loc[result['St'] < 0, 'St'] = 0
result.loc[result['Sl'] < 0, 'Sl'] = 0
elif len(x) == 4:
popt_St, pcov_St = curve_fit(Su4, x, St, sigma=dSt, absolute_sigma=True)
popt_Sl, pcov_Sl = curve_fit(Su4, x, Sl, sigma=dSl, absolute_sigma=True)
if self.add_factor:
popt_Slt, pcov_Slt = curve_fit(SLT_f4, x, Slt, sigma=dSlt, absolute_sigma=True)
popt_Stt, pcov_Stt = curve_fit(STT_f4, x, Stt, sigma=dStt, absolute_sigma=True)
else:
popt_Slt, pcov_Slt = curve_fit(Su4, x, Slt, sigma=dSlt, absolute_sigma=True)
popt_Stt, pcov_Stt = curve_fit(Su4, x, Stt, sigma=dStt, absolute_sigma=True)
for cos_th in self.cos_th:
buff = {'W': [W], 'Q2': [Q2], 'cos_th': [cos_th]}
arg = cos_th
buff['St'] = [Su4(cos_th, popt_St[0], popt_St[1], popt_St[2], popt_St[3])]
buff['Sl'] = [Su4(cos_th, popt_Sl[0], popt_Sl[1], popt_Sl[2], popt_Sl[3])]
if self.add_factor:
buff['Slt'] = [SLT_f4(cos_th, popt_Slt[0], popt_Slt[1],
popt_Slt[2], popt_Slt[3])]
buff['Stt'] = [STT_f4(cos_th, popt_Stt[0], popt_Stt[1],
popt_Stt[2], popt_Stt[3])]
if arg < x.min():
buff['Slt'] = [self.__interp_cub_TT_LT(
data_table[['cos_th', 'Slt', 'dSlt']], arg)]
buff['Stt'] = [self.__interp_cub_TT_LT(
data_table[['cos_th', 'Stt', 'dStt']], arg)]
else:
buff['Slt'] = [Su4(cos_th, popt_Slt[0], popt_Slt[1], popt_Slt[2], popt_Slt[3])]
buff['Stt'] = [Su4(cos_th, popt_Stt[0], popt_Stt[1], popt_Stt[2], popt_Stt[3])]
result = pd.concat([result, pd.DataFrame(buff)], ignore_index=True)
result_for_merge = self.__interp_cub(data_table)
result_for_merge.set_index(['W', 'Q2', 'cos_th'], inplace=True, drop=True)
result.set_index(['W', 'Q2', 'cos_th'], inplace=True, drop=True)
result = result_for_merge.merge(result, on=['W', 'Q2', 'cos_th'])
result.reset_index(inplace=True)
if self.err_option == 1:
result.loc[result['cos_th'] < x.min(), 'dSt'] = data_table.iloc[0]['dSt']
result.loc[result['cos_th'] < x.min(), 'dSl'] = data_table.iloc[0]['dSl']
result.loc[result['cos_th'] < x.min(), 'dSlt'] = data_table.iloc[0]['dSlt']
result.loc[result['cos_th'] < x.min(), 'dStt'] = data_table.iloc[0]['dStt']
result.loc[result['cos_th'] >
x.max(), 'dSt'] = data_table.iloc[len(data_table)-1]['dSt']
result.loc[result['cos_th'] >
x.max(), 'dSl'] = data_table.iloc[len(data_table)-1]['dSl']
result.loc[result['cos_th'] >
x.max(), 'dSlt'] = data_table.iloc[len(data_table)-1]['dSlt']
result.loc[result['cos_th'] >
x.max(), 'dStt'] = data_table.iloc[len(data_table)-1]['dStt']
if self.err_option == 2:
result.loc[result['cos_th'] < x.min(), 'dSt'] = data_table.iloc[0]['dSt'] * \
((-result.loc[(result['cos_th'] < x.min()),
'cos_th'] + x.min())/(1 + x.min()) + 1)
result.loc[result['cos_th'] < x.min(), 'dSl'] = data_table.iloc[0]['dSl'] * \
((-result.loc[(result['cos_th'] < x.min()),
'cos_th'] + x.min())/(1 + x.min()) + 1)
result.loc[result['cos_th'] < x.min(), 'dSlt'] = data_table.iloc[0]['dSlt'] * \
((-result.loc[(result['cos_th'] < x.min()),
'cos_th'] + x.min())/(1 + x.min()) + 1)
result.loc[result['cos_th'] < x.min(), 'dStt'] = data_table.iloc[0]['dStt'] * \
((-result.loc[(result['cos_th'] < x.min()),
'cos_th'] + x.min())/(1 + x.min()) + 1)
result.loc[result['cos_th'] > x.max(), 'dSt'] = data_table.iloc[len(
data_table)-1]['dSt']*((result.loc[(result['cos_th'] > x.max()), 'cos_th'] - x.max())/(1 - x.max()) + 1)
result.loc[result['cos_th'] > x.max(), 'dSl'] = data_table.iloc[len(
data_table)-1]['dSl']*((result.loc[(result['cos_th'] > x.max()), 'cos_th'] - x.max())/(1 - x.max()) + 1)
result.loc[result['cos_th'] > x.max(), 'dSlt'] = data_table.iloc[len(
data_table)-1]['dSlt']*((result.loc[(result['cos_th'] > x.max()), 'cos_th'] - x.max())/(1 - x.max()) + 1)
result.loc[result['cos_th'] > x.max(), 'dStt'] = data_table.iloc[len(
data_table)-1]['dStt']*((result.loc[(result['cos_th'] > x.max()), 'cos_th'] - x.max())/(1 - x.max()) + 1)
result.loc[result['cos_th'] < x.min(), 'St'] = Su4(
x.min(), popt_St[0], popt_St[1], popt_St[2], popt_St[3])
result.loc[result['cos_th'] < x.min(), 'Sl'] = Su4(
x.min(), popt_Sl[0], popt_Sl[1], popt_Sl[2], popt_Sl[3])
result.loc[result['cos_th'] > x.max(), 'St'] = Su4(
x.max(), popt_St[0], popt_St[1], popt_St[2], popt_St[3])
result.loc[result['cos_th'] > x.max(), 'Sl'] = Su4(
x.max(), popt_Sl[0], popt_Sl[1], popt_Sl[2], popt_Sl[3])
if not(self.add_factor):
result.loc[result['cos_th'] < x.min(), 'Slt'] = Su4(
x.min(), popt_Slt[0], popt_Slt[1], popt_Slt[2], popt_Slt[3])
result.loc[result['cos_th'] < x.min(), 'Stt'] = Su4(
x.min(), popt_Stt[0], popt_Stt[1], popt_Stt[2], popt_Stt[3])
result.loc[result['cos_th'] > x.max(), 'Slt'] = Su4(
x.max(), popt_Slt[0], popt_Slt[1], popt_Slt[2], popt_Slt[3])
result.loc[result['cos_th'] > x.max(), 'Stt'] = Su4(
x.max(), popt_Stt[0], popt_Stt[1], popt_Stt[2], popt_Stt[3])
if self.add_factor:
result.loc[(result['cos_th'] < x.min()), 'dSlt'] = data_table.iloc[0]['dSlt'] * \
(result.loc[(result['cos_th'] < x.min()), 'cos_th'] + 1)/(1 + x.min())
result.loc[(result['cos_th'] < x.min()), 'dStt'] = data_table.iloc[0]['dStt'] * \
(result.loc[(result['cos_th'] < x.min()), 'cos_th'] + 1)/(1 + x.min())
result.loc[(result['cos_th'] > x.max()), 'dSlt'] = data_table.iloc[len(
data_table)-1]['dSlt']*(result.loc[(result['cos_th'] > x.max()), 'cos_th'] - 1)/(-1 + x.max())
result.loc[(result['cos_th'] > x.max()), 'dStt'] = data_table.iloc[len(
data_table)-1]['dStt']*(result.loc[(result['cos_th'] > x.max()), 'cos_th'] - 1)/(-1 + x.max())
result.loc[result['St'] < 0, 'St'] = 0
result.loc[result['Sl'] < 0, 'Sl'] = 0
elif len(x) < 4:
popt_St, pcov_St = curve_fit(Su3, x, St, sigma=dSt, absolute_sigma=True)
popt_Sl, pcov_Sl = curve_fit(Su3, x, Sl, sigma=dSl, absolute_sigma=True)
if self.add_factor:
popt_Slt, pcov_Slt = curve_fit(SLT_f3, x, Slt, sigma=dSlt, absolute_sigma=True)
popt_Stt, pcov_Stt = curve_fit(STT_f3, x, Stt, sigma=dStt, absolute_sigma=True)
else:
popt_Slt, pcov_Slt = curve_fit(Su3, x, Slt, sigma=dSlt, absolute_sigma=True)
popt_Stt, pcov_Stt = curve_fit(Su3, x, Stt, sigma=dStt, absolute_sigma=True)
for cos_th in self.cos_th:
buff = {'W': [W], 'Q2': [Q2], 'cos_th': [cos_th]}
arg = cos_th
buff['St'] = [Su3(cos_th, popt_St[0], popt_St[1], popt_St[2])]
buff['Sl'] = [Su3(cos_th, popt_Sl[0], popt_Sl[1], popt_Sl[2])]
if self.add_factor:
buff['Slt'] = [SLT_f3(cos_th, popt_Slt[0], popt_Slt[1], popt_Slt[2])]
buff['Stt'] = [STT_f3(cos_th, popt_Stt[0], popt_Stt[1], popt_Stt[2])]
if arg < x.min():
buff['Slt'] = [self.__interp_cub_TT_LT(
data_table[['cos_th', 'Slt', 'dSlt']], arg)]
buff['Stt'] = [self.__interp_cub_TT_LT(
data_table[['cos_th', 'Stt', 'dStt']], arg)]
else:
buff['Slt'] = [Su3(cos_th, popt_Slt[0], popt_Slt[1], popt_Slt[2])]
buff['Stt'] = [Su3(cos_th, popt_Stt[0], popt_Stt[1], popt_Stt[2])]
result = pd.concat([result, pd.DataFrame(buff)], ignore_index=True)
result_for_merge = self.__interp_cub(data_table)
result_for_merge.set_index(['W', 'Q2', 'cos_th'], inplace=True, drop=True)
result.set_index(['W', 'Q2', 'cos_th'], inplace=True, drop=True)
result = result_for_merge.merge(result, on=['W', 'Q2', 'cos_th'])
result.reset_index(inplace=True)
if self.err_option == 1:
result.loc[result['cos_th'] < x.min(), 'dSt'] = data_table.iloc[0]['dSt']
result.loc[result['cos_th'] < x.min(), 'dSl'] = data_table.iloc[0]['dSl']
result.loc[result['cos_th'] < x.min(), 'dSlt'] = data_table.iloc[0]['dSlt']
result.loc[result['cos_th'] < x.min(), 'dStt'] = data_table.iloc[0]['dStt']
result.loc[result['cos_th'] >
x.max(), 'dSt'] = data_table.iloc[len(data_table)-1]['dSt']
result.loc[result['cos_th'] >
x.max(), 'dSl'] = data_table.iloc[len(data_table)-1]['dSl']
result.loc[result['cos_th'] >
x.max(), 'dSlt'] = data_table.iloc[len(data_table)-1]['dSlt']
result.loc[result['cos_th'] >
x.max(), 'dStt'] = data_table.iloc[len(data_table)-1]['dStt']
if self.err_option == 2:
result.loc[result['cos_th'] < x.min(), 'dSt'] = data_table.iloc[0]['dSt'] * \
((-result.loc[(result['cos_th'] < x.min()),
'cos_th'] + x.min())/(1 + x.min()) + 1)
result.loc[result['cos_th'] < x.min(), 'dSl'] = data_table.iloc[0]['dSl'] * \
((-result.loc[(result['cos_th'] < x.min()),
'cos_th'] + x.min())/(1 + x.min()) + 1)
result.loc[result['cos_th'] < x.min(), 'dSlt'] = data_table.iloc[0]['dSlt'] * \
((-result.loc[(result['cos_th'] < x.min()),
'cos_th'] + x.min())/(1 + x.min()) + 1)
result.loc[result['cos_th'] < x.min(), 'dStt'] = data_table.iloc[0]['dStt'] * \
((-result.loc[(result['cos_th'] < x.min()),
'cos_th'] + x.min())/(1 + x.min()) + 1)
result.loc[result['cos_th'] > x.max(), 'dSt'] = data_table.iloc[len(
data_table)-1]['dSt']*((result.loc[(result['cos_th'] > x.max()), 'cos_th'] - x.max())/(1 - x.max()) + 1)
result.loc[result['cos_th'] > x.max(), 'dSl'] = data_table.iloc[len(
data_table)-1]['dSl']*((result.loc[(result['cos_th'] > x.max()), 'cos_th'] - x.max())/(1 - x.max()) + 1)
result.loc[result['cos_th'] > x.max(), 'dSlt'] = data_table.iloc[len(
data_table)-1]['dSlt']*((result.loc[(result['cos_th'] > x.max()), 'cos_th'] - x.max())/(1 - x.max()) + 1)
result.loc[result['cos_th'] > x.max(), 'dStt'] = data_table.iloc[len(
data_table)-1]['dStt']*((result.loc[(result['cos_th'] > x.max()), 'cos_th'] - x.max())/(1 - x.max()) + 1)
result.loc[result['cos_th'] < x.min(), 'St'] = Su3(
x.min(), popt_St[0], popt_St[1], popt_St[2])
result.loc[result['cos_th'] < x.min(), 'Sl'] = Su3(
x.min(), popt_Sl[0], popt_Sl[1], popt_Sl[2])
result.loc[result['cos_th'] > x.max(), 'St'] = Su3(
x.max(), popt_St[0], popt_St[1], popt_St[2])
result.loc[result['cos_th'] > x.max(), 'Sl'] = Su3(
x.max(), popt_Sl[0], popt_Sl[1], popt_Sl[2])
if not(self.add_factor):
result.loc[result['cos_th'] < x.min(), 'Slt'] = Su3(
x.min(), popt_Slt[0], popt_Slt[1], popt_Slt[2])
result.loc[result['cos_th'] < x.min(), 'Stt'] = Su3(
x.min(), popt_Stt[0], popt_Stt[1], popt_Stt[2])
result.loc[result['cos_th'] > x.max(), 'Slt'] = Su3(
x.max(), popt_Slt[0], popt_Slt[1], popt_Slt[2])
result.loc[result['cos_th'] > x.max(), 'Stt'] = Su3(
x.max(), popt_Stt[0], popt_Stt[1], popt_Stt[2])
if self.add_factor:
result.loc[(result['cos_th'] < x.min()), 'dSlt'] = data_table.iloc[0]['dSlt'] * \
(result.loc[(result['cos_th'] < x.min()), 'cos_th'] + 1)/(1 + x.min())
result.loc[(result['cos_th'] < x.min()), 'dStt'] = data_table.iloc[0]['dStt'] * \
(result.loc[(result['cos_th'] < x.min()), 'cos_th'] + 1)/(1 + x.min())
result.loc[(result['cos_th'] > x.max()), 'dSlt'] = data_table.iloc[len(
data_table)-1]['dSlt']*(result.loc[(result['cos_th'] > x.max()), 'cos_th'] - 1)/(-1 + x.max())
result.loc[(result['cos_th'] > x.max()), 'dStt'] = data_table.iloc[len(
data_table)-1]['dStt']*(result.loc[(result['cos_th'] > x.max()), 'cos_th'] - 1)/(-1 + x.max())
result.loc[result['St'] < 0, 'St'] = 0
result.loc[result['Sl'] < 0, 'Sl'] = 0
del x, St, dSt, Sl, dSl, Slt, dSlt, Stt, dStt
del buff, popt_St, pcov_St, popt_Sl, pcov_Sl
del popt_Slt, pcov_Slt, popt_Stt, pcov_Stt
del result_for_merge
return result
def eps(self, W: float, Q2: float):
m_p = 0.93827
nu = (W*W + Q2 - m_p*m_p)/(2*m_p)
return 1/(1 + 2*(nu*nu + Q2)/(4*(self.E_beam - nu)*self.E_beam - Q2))
@staticmethod
def eps_beam(W: float, Q2: float, E0: float):
m_p = 0.93827
nu = (W*W + Q2 - m_p*m_p)/(2*m_p)
return 1/(1 + 2*(nu*nu + Q2)/(4*(E0 - nu)*E0 - Q2))
def __isData1(self, W: float, Q2: float):
if self.name == "K+L":
return Q2 <= 1.0 and Q2 >= 0.65 and W <= 1.975 and W >= 1.65
elif self.name == "K+S0":
return Q2 <= 1.0 and Q2 >= 0.65 and W <= 2.05 and W >= 1.725
return False
def __isData2(self, W: float, Q2: float):
if self.name == "K+L":
return (Q2 <= 2.55 and Q2 >= 1.0 and W <= 2.15 and W >= 1.65) or (Q2 <= 2.05 and Q2 >= 1.0 and W <= 2.35 and W >= 2.15)
elif self.name == "K+S0":
return (Q2 <= 2.55 and Q2 >= 1.0 and W <= 2.15 and W >= 1.75) or (Q2 <= 2.05 and Q2 >= 1.0 and W <= 2.35 and W >= 2.15)
return False
def __isData3(self, W: float, Q2: float):
if self.name == "K+L":
return Q2 <= 3.45 and Q2 >= 1.8 and W <= 2.575 and W >= 1.63
elif self.name == "K+S0":
return Q2 <= 3.45 and Q2 >= 1.8 and W <= 2.575 and W >= 1.695
return False
def __isW1(self, W: float):
if self.name == "K+L":
return W <= 1.975 and W >= 1.65
elif self.name == "K+S0":
return W <= 2.05 and W >= 1.725
return False
def __isW2(self, W: float):
if self.name == "K+L":
return W >= 1.65 and W <= 2.35
elif self.name == "K+S0":
return W >= 1.75 and W <= 2.35
return False
def __isW3(self, W: float):
if self.name == "K+L":
return W <= 2.575 and W >= 1.63
elif self.name == "K+S0":
return W <= 2.575 and W >= 1.695
return False
def __isWforQ2inter(self, W: float, Q2: float):
if Q2 < 1.8:
if self.name == "K+L":
return W <= 2.575 and W >= 1.65
else:
if Q2 > 1.0:
return W <= 2.575 and W >= 1.75
else:
return W <= 2.575 and W >= 1.725
else:
if self.name == "K+L":
return W <= 2.575 and W >= 1.63
else:
return W <= 2.575 and W >= 1.695
def __isSigma(self, W: float):
if self.name == "K+L":
return W <= 2.18 and W >= 1.72
else:
return W <= 2.17 and W >= 1.78
def __Give_MinMaxE(self, W: float, Q2: float, zone: int):
result = {}
result["W"] = [W]
result["Q2"] = [Q2]
if zone == 1:
result["W_min"] = float(floor((W - 0.025)*20))/20 + 0.025
result["W_max"] = result["W_min"] + 0.05
if W < 1.725:
result["W_min"] = 1.65
result["W_max"] = 1.725
if W > 1.925:
result["W_min"] = 1.925
result["W_max"] = 1.975
result["Q2_min"] = 0.65
result["Q2_max"] = 1.0
result["E"] = 2.567
elif zone == 2:
result["Q2_min"] = float(floor((Q2 - 0.05)*2))/2 + 0.05
result["Q2_max"] = result["Q2_min"] + 0.5
if Q2 < 1.55:
result["Q2_min"] = 1.0
result["Q2_max"] = 1.55
if Q2 > 2.05:
result["Q2_min"] = 2.05
result["Q2_max"] = 2.55
result["W_min"] = int(1000*(float(floor((W - 0.05)*10))/10 + 0.05))/1000.0
result["W_max"] = result["W_min"] + 0.1
if abs(W - 2.15) < 1e-9:
result["W_min"] = 2.05
result["W_max"] = 2.15
if abs(W - 1.65) < 1e-9:
result["W_min"] = 1.65
result["W_max"] = 1.75
if abs(W - 1.75) < 1e-9:
result["W_min"] = 1.75
result["W_max"] = 1.85
if abs(W - 2.35) < 1e-9:
result["W_min"] = 2.25
result["W_max"] = 2.35
result["E"] = 4.056
elif zone == 3:
result["W_min"] = float(floor((W - 0.025)*20))/20 + 0.025
result["W_max"] = result["W_min"] + 0.05
if W < 1.675 and self.name == "K+L":
result["W_min"] = 1.63
result["W_max"] = 1.675
if W < 1.725 and self.name == "K+S0":
result["W_min"] = 1.695
result["W_max"] = 1.725
if W > 2.525:
result["W_min"] = 2.525
result["W_max"] = 2.575
if Q2 < 2.6:
result["Q2_min"] = 1.8
result["Q2_max"] = 2.6
if 2.6 <= Q2:
result["Q2_min"] = 2.6
result["Q2_max"] = 3.45
result["E"] = 5.499
result["W_min"] = float("{0:.3f}".format(result["W_min"]))
result["W_max"] = float("{0:.3f}".format(result["W_max"]))
result["Q2_min"] = float("{0:.2f}".format(result["Q2_min"]))
result["Q2_max"] = float("{0:.2f}".format(result["Q2_max"]))
W_min = result["W_min"]
W_max = result["W_max"]
Q2_min = result["Q2_min"]
Q2_max = result["Q2_max"]
result = [{'W0': W, 'Q20': Q2, 'W': result["W_min"], 'Q2': result["Q2_min"], 'E': result["E"]}, {'W0': W, 'Q20': Q2, 'W': result["W_max"], 'Q2': result["Q2_min"], 'E': result["E"]}, {
'W0': W, 'Q20': Q2, 'W': result["W_min"], 'Q2': result["Q2_max"], 'E': result["E"]}, {'W0': W, 'Q20': Q2, 'W': result["W_max"], 'Q2': result["Q2_max"], 'E': result["E"]}]
W_Q2 = pd.DataFrame({'W0': [W], 'Q20': [Q2], 'W_min': [W_min],
'Q2_min': [Q2_min], 'W_max': [W_max], 'Q2_max': [Q2_max]})
return result, W_Q2
def __giveData(self, data_table, zone: int):
buff = pd.DataFrame()
W_Q2 = pd.DataFrame()
for index, row in data_table.iterrows():
W = row['W']
Q2 = row['Q2']
prior, minor = self.__Give_MinMaxE(W, Q2, zone)
buff = pd.concat([buff, pd.DataFrame(prior)])
W_Q2 = pd.concat([W_Q2, minor], ignore_index=True)
result = buff.drop(columns=['E'])
buff = buff.drop(columns=['W0', 'Q20'])
buff = buff.groupby(['W', 'Q2'], as_index=False).mean()
out = pd.DataFrame()
for index, row in buff.iterrows():
out = pd.concat([out, self.__approx_cos_leg(self.Data.Data.loc[(abs(self.Data.Data['W'] - row['W']) < 1e-6) & (
abs(self.Data.Data['Q2'] - row['Q2']) < 1e-6) & (abs(self.Data.Data['E'] - row['E']) < 1e-5)])])
result.set_index(['W', 'Q2'], inplace=True, drop=True)
out.set_index(['W', 'Q2'], inplace=True, drop=True)
result = out.merge(result, on=['W', 'Q2']) # Check all indecies
result.reset_index(inplace=True)
result_final = pd.DataFrame()
W_Q2.set_index(['W_min', 'Q2_min', 'W_max', 'Q2_max'], inplace=True, drop=True)
W_Q2_dict = {}
for index, row in W_Q2.iterrows():
W_Q2_dict.setdefault(index, []).append([row['W0'], row['Q20']])
for i in W_Q2_dict.keys():
for cos_th in self.cos_th:
del buff
buff = pd.DataFrame()
buff = pd.concat([buff, (result.loc[(result['W'] == i[0]) & (result['Q2'] == i[1]) & (
result['cos_th'] == cos_th)]).drop(columns=['W0', 'Q20'])], ignore_index=True)
buff = pd.concat([buff, (result.loc[(result['W'] == i[0]) & (result['Q2'] == i[3]) & (
result['cos_th'] == cos_th)]).drop(columns=['W0', 'Q20'])], ignore_index=True)
buff = pd.concat([buff, (result.loc[(result['W'] == i[2]) & (result['Q2'] == i[1]) & (
result['cos_th'] == cos_th)]).drop(columns=['W0', 'Q20'])], ignore_index=True)
buff = pd.concat([buff, (result.loc[(result['W'] == i[2]) & (result['Q2'] == i[3]) & (
result['cos_th'] == cos_th)]).drop(columns=['W0', 'Q20'])], ignore_index=True)
buff.drop_duplicates(subset=['W', 'Q2', 'cos_th'], inplace=True)
buff.reset_index(inplace=True)
x = np.array(buff['W'])
y = np.array(buff['Q2'])
f1 = np.array(buff['St'])
df1 = np.array(buff['dSt'])
f2 = np.array(buff['Sl'])
df2 = np.array(buff['dSl'])
f3 = np.array(buff['Slt'].astype(np.float))
df3 = np.array(buff['dSlt'])
f4 = np.array(buff['Stt'].astype(np.float))
df4 = np.array(buff['dStt'])
St_int = interpolate.interp2d(x, y, f1, kind='linear', copy=False)
dSt_int = interpolate.interp2d(x, y, df1, kind='linear', copy=False)
Sl_int = interpolate.interp2d(x, y, f2, kind='linear', copy=False)
dSl_int = interpolate.interp2d(x, y, df2, kind='linear', copy=False)
Slt_int = interpolate.interp2d(x, y, f3, kind='linear', copy=False)
dSlt_int = interpolate.interp2d(x, y, df3, kind='linear', copy=False)
Stt_int = interpolate.interp2d(x, y, f4, kind='linear', copy=False)
dStt_int = interpolate.interp2d(x, y, df4, kind='linear', copy=False)
for [W, Q2] in W_Q2_dict[i]:
St = St_int(W, Q2).astype(np.float)[0]
dSt = dSt_int(W, Q2).astype(np.float)[0]
Sl = Sl_int(W, Q2).astype(np.float)[0]
dSl = dSl_int(W, Q2).astype(np.float)[0]
Slt = Slt_int(W, Q2).astype(np.float)[0]
dSlt = dSlt_int(W, Q2).astype(np.float)[0]
Stt = Stt_int(W, Q2).astype(np.float)[0]
dStt = dStt_int(W, Q2).astype(np.float)[0]