def upperLimitFunc(A, optstat_ref, nreal):
"""
Compute the value of the Optimal Statistic for different signal realizations
@param A: value of GWB amplitude
@param optstat_ref: value of optimal statistic with no injection
@param nreal: number of realizations
"""
count = 0
for ii in range(nreal):
# create residuals
inducedRes = PALutils.createGWB(psr, A, 4.3333)
Pinvr = []
Pinv = []
for ct, p in enumerate(psr):
# replace residuals in pulsar object
p.res = res[ct] + np.dot(R[ct], inducedRes[ct])
# determine injected amplitude by minimizing Likelihood function
c = np.dot(Dmatrix[ct], p.res)
f = lambda x: -PALutils.twoComponentNoiseLike(x, D[ct], c)
fbounded = minimize_scalar(f, bounds=(0, 1e-14, 3.0e-13), method='Brent')
Amp = np.abs(fbounded.x)
#print Amp
#Amp = A
# construct P^-1 r
Pinvr.append(c/(Amp**2 * D[ct] + 1))
Pinv.append(1/(Amp**2 * D[ct] + 1))
# construct optimal statstic
k = 0
top = 0
bot = 0
for ll in range(npsr):
for kk in range(ll+1, npsr):
# compute numerator of optimal statisic
top += ORF[k]/2 * np.dot(Pinvr[ll], np.dot(SIJ[k], Pinvr[kk]))
# compute trace term
bot += (ORF[k]/2)**2 * np.trace(np.dot((Pinv[ll]*SIJ[k].T).T, (Pinv[kk]*SIJ[k]).T))
# iterate counter
k += 1
# get optimal statistic and SNR
optStat = top/bot
snr = top/np.sqrt(bot)
# check to see if larger than in real data
if optStat > optstat_ref:
count += 1
# now get detection probability
detProb = count/nreal
print A, detProb
injAmp.append(A)
injDetProb.append(detProb)
return detProb - 0.95
