# carry out Fp search
if args.fpFlag:
print 'Beginning Fp Search with {0} pulsars, with frequency range {1} -- {2}'.format(npsr, f[0], f[-1])
fpstat = np.zeros(args.nfreqs)
for ii in range(args.nfreqs):
fpstat[ii] = PALLikelihoods.fpStat(psr, f[ii])
print 'Done Search. Computing False Alarm Probability'
# single template FAP
pf = np.array([PALutils.ptSum(npsr, fpstat[ii]) for ii in range(np.alen(f))])
# get total false alarm probability with trials factor
pfT = 1 - (1-pf)**np.alen(f)
# write results to file
if not os.path.exists(args.outDir):
os.makedirs(args.outDir)
# get filename from hdf5 file
fname = args.outDir + '/' + args.h5file.split('/')[-1].split('.')[0] + '.txt'
fout = open(fname, 'w')
print 'Writing results to file {0}'.format(fname)
for ii in range(np.alen(f)):
fout.write('%g %g %g\n'%(f[ii], fpstat[ii], pfT[ii]))
# carry out Fp search
if args.fpFlag:
print 'Beginning Fp Search with {0} pulsars, with frequency range {1} -- {2}'.format(
npsr, f[0], f[-1])
fpstat = np.zeros(args.nfreqs)
for ii in range(args.nfreqs):
fpstat[ii] = PALLikelihoods.fpStat(psr, f[ii])
print 'Done Search. Computing False Alarm Probability'
# single template FAP
pf = np.array(
[PALutils.ptSum(npsr, fpstat[ii]) for ii in range(np.alen(f))])
# get total false alarm probability with trials factor
pfT = 1 - (1 - pf)**np.alen(f)
# write results to file
if not os.path.exists(args.outDir):
os.makedirs(args.outDir)
# get filename from hdf5 file
fname = args.outDir + '/' + args.h5file.split('/')[-1].split(
'.')[0] + '.txt'
fout = open(fname, 'w')
print 'Writing results to file {0}'.format(fname)
for ii in range(np.alen(f)):
def upperLimitFunc(h, fstat_ref, freq, nreal, theta=None, phi=None, detect=False, \
dist=None):
"""
Compute the value of the fstat for a range of parameters, with fixed
amplitude over many realizations.
@param h: value of the strain amplitude to keep constant
@param fstat_ref: value of fstat for real data set
@param freq: GW frequency
@param nreal: number of realizations
"""
Tmaxyr = np.array([(p.toas.max() - p.toas.min())/3.16e7 for p in psr]).max()
count = 0
for ii in range(nreal):
# draw parameter values
gwtheta = np.arccos(np.random.uniform(-1, 1))
gwphi = np.random.uniform(0, 2*np.pi)
gwphase = np.random.uniform(0, 2*np.pi)
gwinc = np.arccos(np.random.uniform(-1, 1))
#gwpsi = np.random.uniform(-np.pi/4, np.pi/4)
gwpsi = np.random.uniform(0, np.pi)
# check to make sure source has not coalesced during observation time
coal = True
while coal:
gwmc = 10**np.random.uniform(7, 10)
tcoal = 2e6 * (gwmc/1e8)**(-5/3) * (freq/1e-8)**(-8/3)
if tcoal > Tmaxyr:
coal = False
# determine distance in order to keep strain fixed
gwdist = 4 * np.sqrt(2/5) * (gwmc*4.9e-6)**(5/3) * (np.pi*freq)**(2/3) / h
# convert back to Mpc
gwdist /= 1.0267e14
# check for fixed sky location
if theta is not None:
gwtheta = theta
if phi is not None:
gwphi = phi
if dist is not None:
gwdist = dist
gwmc = ((gwdist*1.0267e14)/4/np.sqrt(2/5)/(np.pi*freq)**(2/3)*h)**(3/5)/4.9e-6
# create residuals
for ct,p in enumerate(psr):
inducedRes = PALutils.createResiduals(p, gwtheta, gwphi, gwmc, gwdist, \
freq, gwphase, gwpsi, gwinc, evolve=True)
# replace residuals in pulsar object
noise = np.dot(L[ct], np.random.randn(L[ct].shape[0]))
p.res = np.dot(R[ct], noise+inducedRes)
# compute f-statistic
fpstat = PALLikelihoods.fpStat(psr, freq)
# check to see if larger than in real data
if detect:
if PALutils.ptSum(npsr, fpstat) < 1e-4:
count += 1
else:
if fpstat > fstat_ref:
count += 1
# now get detection probability
detProb = count/nreal
if args.dist:
print '%e %e %f\n'%(freq, gwmc, detProb)
else:
print freq, h, detProb
return detProb - 0.95
def upperLimitFunc(h, fstat_ref, freq, nreal, theta=None, phi=None, detect=False, \
dist=None):
"""
Compute the value of the fstat for a range of parameters, with fixed
amplitude over many realizations.
@param h: value of the strain amplitude to keep constant
@param fstat_ref: value of fstat for real data set
@param freq: GW frequency
@param nreal: number of realizations
"""
Tmaxyr = np.array([(p.toas.max() - p.toas.min()) / 3.16e7
for p in psr]).max()
count = 0
for ii in range(nreal):
# draw parameter values
gwtheta = np.arccos(np.random.uniform(-1, 1))
gwphi = np.random.uniform(0, 2 * np.pi)
gwphase = np.random.uniform(0, 2 * np.pi)
gwinc = np.arccos(np.random.uniform(-1, 1))
#gwpsi = np.random.uniform(-np.pi/4, np.pi/4)
gwpsi = np.random.uniform(0, np.pi)
# check to make sure source has not coalesced during observation time
coal = True
while coal:
gwmc = 10**np.random.uniform(7, 10)
tcoal = 2e6 * (gwmc / 1e8)**(-5 / 3) * (freq / 1e-8)**(-8 / 3)
if tcoal > Tmaxyr:
coal = False
# determine distance in order to keep strain fixed
gwdist = 4 * np.sqrt(
2 / 5) * (gwmc * 4.9e-6)**(5 / 3) * (np.pi * freq)**(2 / 3) / h
# convert back to Mpc
gwdist /= 1.0267e14
# check for fixed sky location
if theta is not None:
gwtheta = theta
if phi is not None:
gwphi = phi
if dist is not None:
gwdist = dist
gwmc = ((gwdist * 1.0267e14) / 4 / np.sqrt(2 / 5) /
(np.pi * freq)**(2 / 3) * h)**(3 / 5) / 4.9e-6
# create residuals
for ct, p in enumerate(psr):
inducedRes = PALutils.createResiduals(p, gwtheta, gwphi, gwmc, gwdist, \
freq, gwphase, gwpsi, gwinc, evolve=True)
# replace residuals in pulsar object
noise = np.dot(L[ct], np.random.randn(L[ct].shape[0]))
p.res = np.dot(R[ct], noise + inducedRes)
# compute f-statistic
fpstat = PALLikelihoods.fpStat(psr, freq)
# check to see if larger than in real data
if detect:
if PALutils.ptSum(npsr, fpstat) < 1e-4:
count += 1
else:
if fpstat > fstat_ref:
count += 1
# now get detection probability
detProb = count / nreal
if args.dist:
print '%e %e %f\n' % (freq, gwmc, detProb)
else:
print freq, h, detProb
return detProb - 0.95
