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matrix_coef.py
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matrix_coef.py
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import numpy as np
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
from matplotlib import cm
import matplotlib.patches as mpatches
import matplotlib.lines as mlines
from eft_coefficients import EftPredictions
from mg_calculations import wilson_coefficients, MG_SM, sig_SM
def main():
np.set_printoptions(edgeitems=3)
np.core.arrayprint._line_width = 120
eft = EftPredictions(wilson_coefficients, MG_SM, sig_SM)
#Plots with limit contours
make_plot1d(eft.S)
# make_plot2dC1C2(eft.S)
# make_plot2dC0C1(eft.S)
# make_plot3d(eft.S)
print eft.S
def C0(C0,s):
'''
Calculations of the tttt EFT cross section based on just one operator C0
:param C0:
:param s:
:return: sigma_tttt = sigma_tttt_SM + C_0*sigma_0 + C_0*C_0*sigma_00
'''
c = [C0,0.,0.,0.,0.]
row = [ sig_SM, c[0]*s[0], c[1]*s[1], c[2]*s[2], c[3]*s[3], c[4]*s[4],
(c[0]**2.)*s[5], (c[1]**2.)*s[6], (c[2]**2.)*s[7], (c[3]**2.)*s[8], (c[4]**2.)*s[9],
2.*c[0]*c[1]*s[10], 2.*c[0]*c[2]*s[11], 2.*c[0]*c[3]*s[12], 2.*c[0]*c[4]*s[13],
2.*c[1]*c[2]*s[14], 2.*c[1]*c[3]*s[15], 2.*c[1]*c[4]*s[16],
2.*c[2]*c[3]*s[17], 2.*c[2]*c[4]*s[18],
2.*c[3]*c[4]*s[19]]
return sum(row)
def C0C1(C0,C1,s):
'''
Calculations of the tttt EFT cross section based on just two operators C0, C1
:param C0:
:param s:
:return: sigma_tttt = sigma_tttt_SM + sum_i C_i*sigma_i + sum_ij C_i*C_j*sigma_ij, where i,j = 0,1
'''
c = [C0,C1,0.,0.,0.]
row = [ sig_SM, c[0]*s[0], c[1]*s[1], c[2]*s[2], c[3]*s[3], c[4]*s[4],
(c[0]**2.)*s[5], (c[1]**2.)*s[6], (c[2]**2.)*s[7], (c[3]**2.)*s[8], (c[4]**2.)*s[9],
2.*c[0]*c[1]*s[10], 2.*c[0]*c[2]*s[11], 2.*c[0]*c[3]*s[12], 2.*c[0]*c[4]*s[13],
2.*c[1]*c[2]*s[14], 2.*c[1]*c[3]*s[15], 2.*c[1]*c[4]*s[16],
2.*c[2]*c[3]*s[17], 2.*c[2]*c[4]*s[18],
2.*c[3]*c[4]*s[19]]
return sum(row)
def C1C2(C1,C2,s):
'''
Calculations of the tttt EFT cross section based on just two operators C1, C2
:param s:
:return: sigma_tttt = sigma_tttt_SM + sum_i C_i*sigma_i + sum_ij C_i*C_j*sigma_ij, where i,j = 0,1
'''
c = [0.,C1,C2,0.,0.]
row = [ sig_SM, c[0]*s[0], c[1]*s[1], c[2]*s[2], c[3]*s[3], c[4]*s[4],
(c[0]**2.)*s[5], (c[1]**2.)*s[6], (c[2]**2.)*s[7], (c[3]**2.)*s[8], (c[4]**2.)*s[9],
2.*c[0]*c[1]*s[10], 2.*c[0]*c[2]*s[11], 2.*c[0]*c[3]*s[12], 2.*c[0]*c[4]*s[13],
2.*c[1]*c[2]*s[14], 2.*c[1]*c[3]*s[15], 2.*c[1]*c[4]*s[16],
2.*c[2]*c[3]*s[17], 2.*c[2]*c[4]*s[18],
2.*c[3]*c[4]*s[19]]
return sum(row)
def make_plot1d(sigma):
# Constants definitions
expected_limit = 2.0*sig_SM
print sigma
# Solve for independent limits
#coefs = C0_independent_polynomial_coefficients(sigma)
#coefs[-1] = coefs[-1] - expected_limit
#print coefs
#print "Independent Expected limits for C0", np.roots(coefs)
#coefs = C1_independent_polynomial_coefficients(sigma)
#coefs[-1] = coefs[-1] - expected_limit
#print coefs
#print "Independent Expected limits for C1", np.roots(coefs)
#coefs = C2_independent_polynomial_coefficients(sigma)
#coefs[-1] = coefs[-1] - expected_limit
#print coefs
#print "Independent Expected limits for C2", np.roots(coefs)
#coefs = C3_independent_polynomial_coefficients(sigma)
#coefs[-1] = coefs[-1] - expected_limit
#print coefs
#print "Independent Expected limits for C3", np.roots(coefs)
#coefs = C4_independent_polynomial_coefficients(sigma)
#coefs[-1] = coefs[-1] - expected_limit
#print coefs
#print "Independent Expected limits for C4", np.roots(coefs)
# Plotting
########################################################
xlist = np.linspace(-3.0, 3.0, num=120)
f = np.vectorize( C0, excluded=set([1]))
ylist = f(xlist,sigma)
plt.rc('text', usetex=True)
plt.rcParams.update({'font.size': 20})
plt.figure()
plt.title('')
plt.plot(xlist,ylist,linewidth=2.0)
xband = np.linspace(-3.0, 3.0, 2)
yband = np.array([expected_limit, expected_limit])
band_half_w_1s_pos = np.array([(1.6)*sig_SM,(1.6)*sig_SM])
band_half_w_1s_neg = np.array([(1.)*sig_SM,(1.)*sig_SM])
band_half_w_2s_pos = np.array([(3.9)*sig_SM,(3.9)*sig_SM])
band_half_w_2s_neg = np.array([(1.52)*sig_SM,(1.52)*sig_SM])
plt.plot(xband, yband, 'k')
plt.fill_between(xband, yband-band_half_w_2s_neg, yband+band_half_w_2s_pos, facecolor='green')
plt.fill_between(xband, yband-band_half_w_1s_neg, yband+band_half_w_1s_pos, facecolor='yellow')
#
plt.axvline(x=-1.57,color='r',ymax=0.55,linestyle='--')
plt.axvline(x=-1.37,color='r',ymax=0.55)
plt.axvline(x=-1.16,color='r',ymax=0.55,linestyle='--')
plt.axvline(x=1.4,color='r',ymax=0.55,linestyle='--')
plt.axvline(x=1.2,color='r',ymax=0.55)
plt.axvline(x=1.05,color='r',ymax=0.55,linestyle='--')
plt.xlabel(r'$c_{O_{R}}$', labelpad=2)
plt.ylabel(r'$\sigma_{t\bar{t}t\bar{t}}$ (fb)')
# Theory band
plt.fill_between(xlist, ylist-0.15*ylist, ylist+0.15*ylist,alpha=0.5, edgecolor='#CC4F1B', facecolor='#FF9848')
two_s_band = mpatches.Patch(color='green', label=r'2 s.d.')
one_s_band = mpatches.Patch(color='yellow', label=r'1 s.d.')
th_band = mpatches.Patch(alpha=0.5, edgecolor='#CC4F1B', facecolor='#FF9848')
limit_line = mlines.Line2D([], [], color='black', label='Combined')
eft_line = mlines.Line2D([], [], color='blue', label='EFT')
plt.legend([eft_line, th_band, limit_line, one_s_band, two_s_band],['EFT', '15\% Th. Unc', 'Expected','1 s.d.','2 s.d.'],
loc='upper center',ncol=3,prop={'size':13})
plt.show()
def make_plot2dC0C1(sigma):
ylim = 3
xlist = np.linspace(-3.0, 3.0, num=120)
ylist = np.linspace(-ylim, ylim, num=120)
X, Y = np.meshgrid(xlist, ylist)
f = np.vectorize( C0C1, excluded=set([2]))
Z = f(X,Y,sigma)
plt.rc('text', usetex=True)
plt.rcParams.update({'font.size': 20})
fig, ax = plt.subplots()
#levels = [10.0, 20., 30., 40., 50., 70.]
levels = [40.,60.0, 70.]
contour = plt.contour(X, Y, Z, levels, colors='k')
plt.clabel(contour, colors = 'k', fmt = '%2.1f', fontsize=12)
level_expected = [2.0*sig_SM]
level_expectedUnc1Up = [3.0*sig_SM]
level_expectedUnc1Dw = [1.3*sig_SM]
contour_expected = plt.contour(X, Y, Z, level_expected, colors='k',linewidths=np.arange(3.9, 4, .5))
plt.clabel(contour_expected, colors = 'k', fontsize=12, fmt='Exp.')
contour_1Up = plt.contour(X, Y, Z, level_expectedUnc1Up, colors='k',linewidths=np.arange(3.9, 4, .5),linestyles='dashed')
plt.clabel(contour_1Up, colors = 'k', fontsize=12, fmt='+1 s.d.')
contour_1Dw = plt.contour(X, Y, Z, level_expectedUnc1Dw, colors='k',linewidths=np.arange(3.9, 4, .5),linestyles='dashed')
plt.clabel(contour_1Dw, colors = 'k', fontsize=12, fmt='-1 s.d.')
#marginal intervals
xmaginalDw = -1.387
line = plt.plot([xmaginalDw,xmaginalDw],[-3.,0.],'k-', linewidth=2)
xmaginalUp = 1.24
line = plt.plot([xmaginalUp,xmaginalUp],[-3.,0.],'k-', linewidth=2)
plt.text(-1.1, -2.9, 'Marginalized interval', fontsize=12)
line_interval = plt.plot([xmaginalDw,xmaginalUp],[-3.,-3.],'b-', linewidth=5)
ymaginalDw = -1.4
line = plt.plot([-3.,0.],[ymaginalDw,ymaginalDw],'k-', linewidth=2)
ymaginalUp = 1.26
line = plt.plot([-3.,0.],[ymaginalUp,ymaginalUp],'k-', linewidth=2)
plt.text(-2.9, 0.9, 'Marginalized interval', fontsize=12, rotation=-90)
line_interval = plt.plot([-3.,-3.],[ymaginalDw,ymaginalUp],'b-', linewidth=5)
#independent intervals
xmaginalDw = -1.387
xmaginalUp = 1.24
line = plt.plot([xmaginalDw,xmaginalUp],[0.,0.],'k-', linewidth=2)
#line = plt.plot([xmaginalUp,xmaginalUp],[ymaginalDw,ymaginalDw],'k-', linewidth=2)
#plt.text(-1.1, -2.9, 'Marginalized interval', fontsize=12)
#line_interval = plt.plot([xmaginalDw,xmaginalUp],[-3.,-3.],'b-', linewidth=5)
#ymaginalDw = -1.4
#line = plt.plot([-3.,0.],[ymaginalDw,ymaginalDw],'k-', linewidth=2)
#ymaginalUp = 1.26
#line = plt.plot([-3.,0.],[ymaginalUp,ymaginalUp],'k-', linewidth=2)
#plt.text(-2.9, 0.9, 'Marginalized interval', fontsize=12, rotation=-90)
#line_interval = plt.plot([-3.,-3.],[ymaginalDw,ymaginalUp],'b-', linewidth=5)
# contour_filled = plt.contourf(X, Y, Z, 100,cmap='RdYlBu')
contour_filled = plt.contourf(X, Y, Z, 100,cmap='YlOrBr')
color_bar = plt.colorbar(contour_filled)
color_bar.set_label('$\\sigma_{{ t\\bar{{t}}t\\bar{{t}} }}$ (fb)')
cbytick_obj = plt.getp(color_bar.ax.axes, 'yticklabels') #tricky
plt.setp(cbytick_obj)
plt.title('')
plt.xlabel(r'$C_{O_{R}}$')
plt.ylabel(r'$C_{O_{L}^{(1)}}$')
plt.subplots_adjust(left=0.19, bottom=0.15)
plt.show()
def make_plot2dC1C2(sigma):
xlist = np.linspace(-30.0, 30.0, num=120)
ylist = np.linspace(-30.0, 30.0, num=120)
X, Y = np.meshgrid(xlist, ylist)
f = np.vectorize( C1C2, excluded=set([2]))
Z = f(X,Y,sigma)
plt.rc('text', usetex=True)
plt.rcParams.update({'font.size': 20})
fig, ax = plt.subplots()
#levels = [10.0, 20., 30., 40., 50., 70.]
levels = [10.0, 70., 200.]
contour = plt.contour(X, Y, Z, levels, colors='k')
plt.clabel(contour, colors = 'k', fmt = '%2.1f', fontsize=12)
#level_expected = [2.0*sig_SM]
#level_expectedUnc = [1.3*sig_SM,3.0*sig_SM]
#contour_expected = plt.contour(X, Y, Z, level_expected, colors='r',linewidths=np.arange(3.9, 4, .5),linestyles='dashed')
#plt.clabel(contour_expected, colors = 'r', fontsize=12)
#contour_2016sl = plt.contour(X, Y, Z, level_expectedUnc, colors='r',linewidths=np.arange(3.9, 4, .5))
#plt.clabel(contour_2016sl, colors = 'r', fontsize=12)
contour_filled = plt.contourf(X, Y, Z, 100,cmap='RdYlBu')
color_bar = plt.colorbar(contour_filled)
color_bar.set_label('$\\sigma_{{ t\\bar{{t}}t\\bar{{t}} }}$ (fb)')
cbytick_obj = plt.getp(color_bar.ax.axes, 'yticklabels') #tricky
plt.setp(cbytick_obj)
plt.title('')
#plt.xlabel(r'$O_{R}$')
plt.xlabel(r'$C_{O_{L}^{(1)}}$')
plt.ylabel(r'$C_{O_{L}^{(8)}}$')
plt.show()
def make_plot3d(sigma):
from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
from matplotlib import cm
xlim_min, xlim_max = -4.0, 4.0
ylim_min, ylim_max = -4.0, 4.0
zlim_min, zlim_max = 0.0, 100.0
zoffset = -10
xmin, xmax = -3.0, 3.0
ymin, ymax = -3.0, 3.0
xlist = np.linspace(-3.0, 3.0, num=120)
ylist = np.linspace(-3.0, 3.0, num=120)
X, Y = np.meshgrid(xlist, ylist)
f = np.vectorize( C0C1, excluded=set([2]))
Z = f(X,Y,sigma)
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_surface(X, Y, Z, rstride=8, cstride=8, alpha=0.3)
csetz = ax.contourf(X, Y, Z, zdir='z', offset=zoffset, cmap=cm.coolwarm)
# csetx = ax.contour(X, Y, Z, [-2., 0., 2.], zdir='x', offset=ylim_min, label=[r'$C_{O_{R}}=0$',r'$C_{O_{R}}=1$',r'$C_{O_{R}}=2$'])
# csety = ax.contour(X, Y, Z, [-2., 0., 2.], zdir='y', offset=4)
levels = [10.0, 25., 50.]
contour = ax.contour(X, Y, Z, [levels[0]], offset=zoffset, colors='k')
# contour3d = [ax.contour(X, Y, Z, [level], offset=level, colors='k') for level in levels]
line_x_low = ax.plot([-1.4, -1.4], [ylim_min, ylim_max], [zoffset+0.01, zoffset+0.01], 'k')
line_x_high = ax.plot([1.4, 1.4], [ylim_min, ylim_max], [zoffset+0.01, zoffset+0.01], 'k')
line_y_low = ax.plot([xlim_min, xlim_max], [-1.4, -1.4], [zoffset+0.01, zoffset+0.01], 'k')
line_y_high = ax.plot([xlim_min, xlim_max], [1.4, 1.4], [zoffset+0.01, zoffset+0.01], 'k')
ax.set_xlabel(r'$C_{O_{R}}$')
ax.set_xlim(xlim_min, xlim_max)
ax.set_ylabel(r'$C_{O_{L}^{\left(1\right)}}$')
ax.set_ylim(ylim_min, ylim_max)
ax.set_zlabel(r'$\sigma_{t\bar{t}t\bar{t}}$ (fb)')
ax.set_zlim(zlim_min, zlim_max)
# lines = [mlines.Line2D([], [], color=csetx.collections[0].get_color()[0], label=r'$C_{O_{j}}=-2$'),
# mlines.Line2D([], [], color=csetx.collections[1].get_color()[0], label=r'$C_{O_{j}}=0$'),
# mlines.Line2D([], [], color=csetx.collections[2].get_color()[0], label=r'$C_{O_{j}}=2$')]
# plt.legend(handles=lines)
plt.show()
if __name__ == "__main__":
main()