def OSupperLimit(psr, GCGnoiseInv, ORF, OSsmbhb, ul_list=None,
far=None, drlist=None, tex=True, nlims=60):
if tex == True:
plt.rcParams['text.usetex'] = True
gam_bkgrd = np.linspace(1.01,6.99,nlims)
optStatList=[]
ct=0
for indx in gam_bkgrd:
optStatList.append( utils.optStat(psr, GCGnoiseInv, ORF, gam_gwb=indx)[:3] )
ct+=1
print "Finished {0}% of optimal-statistic upper-limit calculations...".format( 100.0*ct/(1.0*nlims) )
optStatList = np.array(optStatList)
fig, ax = plt.subplots()
stylelist = ['solid','dashed','dotted']
if ul_list is not None:
for ii in range(len(ul_list)):
ax.plot(gam_bkgrd, np.sqrt( optStatList[:,0] + optStatList[:,1]*np.sqrt(2.0)*( ss.erfcinv(2.0*(1.-ul_list[ii])) ) ),
linestyle=stylelist[ii], color='black', linewidth=3.0, label='$A_h$ {0}$\%$ upper-limit'.format(ul_list[ii]*100))
plt.hlines(y=np.sqrt( OSsmbhb[0] + OSsmbhb[1]*np.sqrt(2.0)*( ss.erfcinv(2.0*(1.-ul_list[ii])) ) ),
xmin=gam_bkgrd.min(), xmax=13./3., linewidth=3.0, linestyle='solid', color='red')
plt.vlines(x=13./3., ymin=0.0, ymax=np.sqrt( OSsmbhb[0] + OSsmbhb[1]*np.sqrt(2.0)*( ss.erfcinv(2.0*(1.-ul_list[ii])) ) ),
linewidth=3.0, linestyle='solid', color='red')
else:
for ii in range(len(drlist)):
ax.plot(gam_bkgrd, np.sqrt( optStatList[:,1]*np.sqrt(2.0)*( ss.erfcinv(2.0*far) - ss.erfcinv(2.0*drlist[ii]) ) ),
linestyle=stylelist[ii], color='black', linewidth=3.0, label='$A_h$ ({0}$\%$ FAR, {1}$\%$ DR)'.format(far*100,drlist[ii]*100))
plt.hlines(y=np.sqrt( OSsmbhb*np.sqrt(2.0)*( ss.erfcinv(2.0*far) - ss.erfcinv(2.0*drlist[ii]) ) ),
xmin=gam_bkgrd.min(), xmax=13./3., linewidth=3.0, linestyle='solid', color='red')
plt.vlines(x=13./3., ymin=0.0, ymax=np.sqrt( OSsmbhb*np.sqrt(2.0)*( ss.erfcinv(2.0*far) - ss.erfcinv(2.0*drlist[ii]) ) ),
linewidth=3.0, linestyle='solid', color='red')
ax.set_yscale('log')
ax.set_xlabel(r'$\gamma\equiv 3-2\alpha$', fontsize=20)
ax.set_ylabel(r'$A_h$', fontsize=20)
ax.minorticks_on()
plt.tick_params(labelsize=18)
plt.grid(which='major')
plt.grid(which='minor')
plt.title('Optimal-statistic bounds')
plt.legend(loc='lower left', shadow=True, frameon=True, prop={'size':15})
plt.show()
def OSupperLimit(psr,
GCGnoiseInv,
ORF,
OSsmbhb,
ul_list=None,
far=None,
drlist=None,
tex=True,
nlims=60):
if tex == True:
plt.rcParams['text.usetex'] = True
gam_bkgrd = np.linspace(1.01, 6.99, nlims)
optStatList = []
ct = 0
for indx in gam_bkgrd:
optStatList.append(
utils.optStat(psr, GCGnoiseInv, ORF, gam_gwb=indx)[:3])
ct += 1
print "Finished {0}% of optimal-statistic upper-limit calculations...".format(
100.0 * ct / (1.0 * nlims))
optStatList = np.array(optStatList)
fig, ax = plt.subplots()
stylelist = ['solid', 'dashed', 'dotted']
if ul_list is not None:
for ii in range(len(ul_list)):
ax.plot(
gam_bkgrd,
np.sqrt(optStatList[:, 0] + optStatList[:, 1] * np.sqrt(2.0) *
(ss.erfcinv(2.0 * (1. - ul_list[ii])))),
linestyle=stylelist[ii],
color='black',
linewidth=3.0,
label='$A_h$ {0}$\%$ upper-limit'.format(ul_list[ii] * 100))
plt.hlines(y=np.sqrt(OSsmbhb[0] + OSsmbhb[1] * np.sqrt(2.0) *
(ss.erfcinv(2.0 * (1. - ul_list[ii])))),
xmin=gam_bkgrd.min(),
xmax=13. / 3.,
linewidth=3.0,
linestyle='solid',
color='red')
plt.vlines(x=13. / 3.,
ymin=0.0,
ymax=np.sqrt(OSsmbhb[0] + OSsmbhb[1] * np.sqrt(2.0) *
(ss.erfcinv(2.0 * (1. - ul_list[ii])))),
linewidth=3.0,
linestyle='solid',
color='red')
else:
for ii in range(len(drlist)):
ax.plot(
gam_bkgrd,
np.sqrt(
optStatList[:, 1] * np.sqrt(2.0) *
(ss.erfcinv(2.0 * far) - ss.erfcinv(2.0 * drlist[ii]))),
linestyle=stylelist[ii],
color='black',
linewidth=3.0,
label='$A_h$ ({0}$\%$ FAR, {1}$\%$ DR)'.format(
far * 100, drlist[ii] * 100))
plt.hlines(y=np.sqrt(
OSsmbhb * np.sqrt(2.0) *
(ss.erfcinv(2.0 * far) - ss.erfcinv(2.0 * drlist[ii]))),
xmin=gam_bkgrd.min(),
xmax=13. / 3.,
linewidth=3.0,
linestyle='solid',
color='red')
plt.vlines(
x=13. / 3.,
ymin=0.0,
ymax=np.sqrt(
OSsmbhb * np.sqrt(2.0) *
(ss.erfcinv(2.0 * far) - ss.erfcinv(2.0 * drlist[ii]))),
linewidth=3.0,
linestyle='solid',
color='red')
ax.set_yscale('log')
ax.set_xlabel(r'$\gamma\equiv 3-2\alpha$', fontsize=20)
ax.set_ylabel(r'$A_h$', fontsize=20)
ax.minorticks_on()
plt.tick_params(labelsize=18)
plt.grid(which='major')
plt.grid(which='minor')
plt.title('Optimal-statistic bounds')
plt.legend(loc='lower left', shadow=True, frameon=True, prop={'size': 15})
plt.show()
tgrid = utils.makeTimeGrid(psr[ii], psr[ii])
#Cgwb_ML = utils.makeRedTDcov(Agwb_ML, 13./3., tgrid)
Cred = utils.makeRedTDcov(Ared_ML[ii], gam_red_ML[ii], tgrid)
Cdm = utils.makeDmTDcov(psr[ii], Adm_ML[ii], gam_dm_ML[ii], tgrid)
Cwhite = np.diag(psr[ii].toaerrs**2.0)
########
#GCGnoise = np.dot(psr[ii].G.T, np.dot(Cgwb_ML+Cred+Cdm+Cwhite, psr[ii].G))
GCGnoise = np.dot(psr[ii].G.T, np.dot(Cred+Cdm+Cwhite, psr[ii].G))
GCGnoise = np.nan_to_num(GCGnoise)
cho = sl.cho_factor(GCGnoise)
GCGnoiseInv.append(sl.cho_solve(cho, np.eye(len(GCGnoise))))
gam_bkgrd = 4.33333
optimalStat = utils.optStat(psr, GCGnoiseInv, HnD, gam_gwb=gam_bkgrd)
print "\n A^2 = {0}, std = {1}, SNR = {2}\n".format(optimalStat[0],optimalStat[1],optimalStat[2])
print "\n In this data, the minimum Ah of an SMBHB background that is required for 5% FAR and 68% DR is {0}\n".\
format(np.sqrt( optimalStat[1]*np.sqrt(2.0)*( ss.erfcinv(2.0*0.05) - ss.erfcinv(2.0*0.68) ) ))
print "\n In this data, the minimum Ah of an SMBHB background that is required for 5% FAR and 95% DR is {0}\n".\
format(np.sqrt( optimalStat[1]*np.sqrt(2.0)*( ss.erfcinv(2.0*0.05) - ss.erfcinv(2.0*0.95) ) ))
print "\n The 90% upper-limit on Ah is {0}\n".\
format(np.sqrt( optimalStat[0] + optimalStat[1]*np.sqrt(2.0)*( ss.erfcinv(2.0*(1.-0.90)) ) ))
print "\n The 95% upper-limit on Ah is {0}\n".\
format(np.sqrt( optimalStat[0] + optimalStat[1]*np.sqrt(2.0)*( ss.erfcinv(2.0*(1.-0.95)) ) ))
if args.make_plot:
tgrid = utils.makeTimeGrid(psr[ii], psr[ii])
#Cgwb_ML = utils.makeRedTDcov(Agwb_ML, 13./3., tgrid)
Cred = utils.makeRedTDcov(Ared_ML[ii], gam_red_ML[ii], tgrid)
Cdm = utils.makeDmTDcov(psr[ii], Adm_ML[ii], gam_dm_ML[ii], tgrid)
Cwhite = np.diag(psr[ii].toaerrs**2.0)
########
#GCGnoise = np.dot(psr[ii].G.T, np.dot(Cgwb_ML+Cred+Cdm+Cwhite, psr[ii].G))
GCGnoise = np.dot(psr[ii].G.T, np.dot(Cred + Cdm + Cwhite, psr[ii].G))
GCGnoise = np.nan_to_num(GCGnoise)
cho = sl.cho_factor(GCGnoise)
GCGnoiseInv.append(sl.cho_solve(cho, np.eye(len(GCGnoise))))
gam_bkgrd = 4.33333
optimalStat = utils.optStat(psr, GCGnoiseInv, HnD, gam_gwb=gam_bkgrd)
print "\n A^2 = {0}, std = {1}, SNR = {2}\n".format(optimalStat[0],
optimalStat[1],
optimalStat[2])
print "\n In this data, the minimum Ah of an SMBHB background that is required for 5% FAR and 68% DR is {0}\n".\
format(np.sqrt( optimalStat[1]*np.sqrt(2.0)*( ss.erfcinv(2.0*0.05) - ss.erfcinv(2.0*0.68) ) ))
print "\n In this data, the minimum Ah of an SMBHB background that is required for 5% FAR and 95% DR is {0}\n".\
format(np.sqrt( optimalStat[1]*np.sqrt(2.0)*( ss.erfcinv(2.0*0.05) - ss.erfcinv(2.0*0.95) ) ))
print "\n The 90% upper-limit on Ah is {0}\n".\
format(np.sqrt( optimalStat[0] + optimalStat[1]*np.sqrt(2.0)*( ss.erfcinv(2.0*(1.-0.90)) ) ))
print "\n The 95% upper-limit on Ah is {0}\n".\
format(np.sqrt( optimalStat[0] + optimalStat[1]*np.sqrt(2.0)*( ss.erfcinv(2.0*(1.-0.95)) ) ))
if args.make_plot:
