Adds initial results from AllSky MC study

Also adds data from directed study

Paper/AllSkyMC/generate_data.py

+import pyfstat
+import numpy as np
+import os
+import sys
+
+ID = sys.argv[1]
+outdir = sys.argv[2]
+
+label = 'run_{}'.format(ID)
+data_label = '{}_data'.format(label)
+results_file_name = '{}/MCResults_{}.txt'.format(outdir, ID)
+
+# Properties of the GW data
+sqrtSX = 2e-23
+tstart = 1000000000
+Tspan = 100*86400
+tend = tstart + Tspan
+
+# Fixed properties of the signal
+F0_center = 30
+F1_center = 1e-10
+F2 = 0
+tref = .5*(tstart+tend)
+
+
+VF0 = VF1 = 100
+DeltaF0 = VF0 * np.sqrt(3)/(np.pi*Tspan)
+DeltaF1 = VF1 * np.sqrt(45/4.)/(np.pi*Tspan**2)
+
+depths = np.linspace(100, 400, 7)
+
+run_setup = [((100, 0), 27, False),
+             ((100, 0), 15, False),
+             ((100, 0), 8, False),
+             ((100, 0), 4, False),
+             ((50, 50), 1, False)]
+
+DeltaAlpha = 0.05
+DeltaDelta = 0.05
+
+for depth in depths:
+    h0 = sqrtSX / float(depth)
+    r = np.random.uniform(0, 1)
+    theta = np.random.uniform(0, 2*np.pi)
+    F0 = F0_center + 3*np.sqrt(r)*np.cos(theta)/(np.pi**2 * Tspan**2)
+    F1 = F1_center + 45*np.sqrt(r)*np.sin(theta)/(4*np.pi**2 * Tspan**4)
+    Alpha = np.random.uniform(0, 2*np.pi)
+    Delta = np.arccos(2*np.random.uniform(0, 1)-1)-np.pi/2
+    fAlpha = np.random.uniform(0, 1)
+    Alpha_min = Alpha - DeltaAlpha*(1-fAlpha)
+    Alpha_max = Alpha + DeltaAlpha*fAlpha
+    fDelta = np.random.uniform(0, 1)
+    Delta_min = Delta - DeltaDelta*(1-fDelta)
+    Delta_max = Delta + DeltaDelta*fDelta
+
+    psi = np.random.uniform(-np.pi/4, np.pi/4)
+    phi = np.random.uniform(0, 2*np.pi)
+    cosi = np.random.uniform(-1, 1)
+
+    data = pyfstat.Writer(
+        label=data_label, outdir=outdir, tref=tref,
+        tstart=tstart, F0=F0, F1=F1, F2=F2, duration=Tspan, Alpha=Alpha,
+        Delta=Delta, h0=h0, sqrtSX=sqrtSX, psi=psi, phi=phi, cosi=cosi,
+        detector='H1,L1')
+    data.make_data()
+    predicted_twoF = data.predict_fstat()
+
+    theta_prior = {'F0': {'type': 'unif',
+                          'lower': F0-DeltaF0/2.,
+                          'upper': F0+DeltaF0/2.},
+                   'F1': {'type': 'unif',
+                          'lower': F1-DeltaF1/2.,
+                          'upper': F1+DeltaF1/2.},
+                   'F2': F2,
+                   'Alpha': {'type': 'unif',
+                             'lower': Alpha_min,
+                             'upper': Alpha_max},
+                   'Delta': {'type': 'unif',
+                             'lower': Delta_min,
+                             'upper': Delta_max},
+                   }
+
+    ntemps = 1
+    log10temperature_min = -1
+    nwalkers = 100
+
+    mcmc = pyfstat.MCMCFollowUpSearch(
+        label=label, outdir=outdir,
+        sftfilepath='{}/*{}*sft'.format(outdir, data_label),
+        theta_prior=theta_prior,
+        tref=tref, minStartTime=tstart, maxStartTime=tend,
+        nwalkers=nwalkers, ntemps=ntemps,
+        log10temperature_min=log10temperature_min)
+    mcmc.run(run_setup=run_setup, create_plots=False, log_table=False,
+             gen_tex_table=False)
+    d, maxtwoF = mcmc.get_max_twoF()
+    dF0 = F0 - d['F0']
+    dF1 = F1 - d['F1']
+    with open(results_file_name, 'a') as f:
+        f.write('{} {:1.8e} {:1.8e} {:1.8e} {:1.8e} {:1.8e}\n'
+                .format(depth, h0, dF0, dF1, predicted_twoF, maxtwoF))
+    os.system('rm {}/*{}*'.format(outdir, label))

Paper/AllSkyMC/generate_table.py

+import pyfstat
+import numpy as np
+
+outdir = 'data'
+
+label = 'AllSky'
+data_label = '{}_data'.format(label)
+
+# Properties of the GW data
+sqrtSX = 2e-23
+tstart = 1000000000
+Tspan = 100*86400
+tend = tstart + Tspan
+
+# Fixed properties of the signal
+F0_center = 30
+F1_center = 1e-10
+F2 = 0
+tref = .5*(tstart+tend)
+
+
+VF0 = VF1 = 100
+DeltaF0 = VF0 * np.sqrt(3)/(np.pi*Tspan)
+DeltaF1 = VF1 * np.sqrt(45/4.)/(np.pi*Tspan**2)
+
+depths = np.linspace(100, 400, 7)
+
+run_setup = [((100, 0), 27, False),
+             ((100, 0), 15, False),
+             ((100, 0), 8, False),
+             ((100, 0), 4, False),
+             ((50, 50), 1, False)]
+
+DeltaAlpha = 0.05
+DeltaDelta = 0.05
+
+depth = 100
+
+h0 = sqrtSX / float(depth)
+F0 = F0_center
+F1 = F1_center
+Alpha = 0
+Delta = 0
+Alpha_min = Alpha - DeltaAlpha/2
+Alpha_max = Alpha + DeltaAlpha/2
+Delta_min = Delta - DeltaDelta/2
+Delta_max = Delta + DeltaDelta/2
+
+psi = 0
+phi = 0
+cosi = 0
+
+data = pyfstat.Writer(
+    label=data_label, outdir=outdir, tref=tref,
+    tstart=tstart, F0=F0, F1=F1, F2=F2, duration=Tspan, Alpha=Alpha,
+    Delta=Delta, h0=h0, sqrtSX=sqrtSX, psi=psi, phi=phi, cosi=cosi,
+    detector='H1,L1')
+data.make_data()
+predicted_twoF = data.predict_fstat()
+
+theta_prior = {'F0': {'type': 'unif',
+                      'lower': F0-DeltaF0/2.,
+                      'upper': F0+DeltaF0/2.},
+               'F1': {'type': 'unif',
+                      'lower': F1-DeltaF1/2.,
+                      'upper': F1+DeltaF1/2.},
+               'F2': F2,
+               'Alpha': {'type': 'unif',
+                         'lower': Alpha_min,
+                         'upper': Alpha_max},
+               'Delta': {'type': 'unif',
+                         'lower': Delta_min,
+                         'upper': Delta_max},
+               }
+
+ntemps = 1
+log10temperature_min = -1
+nwalkers = 100
+
+mcmc = pyfstat.MCMCFollowUpSearch(
+    label=label, outdir=outdir,
+    sftfilepath='{}/*{}*sft'.format(outdir, data_label),
+    theta_prior=theta_prior,
+    tref=tref, minStartTime=tstart, maxStartTime=tend,
+    nwalkers=nwalkers, ntemps=ntemps,
+    log10temperature_min=log10temperature_min)
+mcmc.run(run_setup=run_setup)

Paper/AllSkyMC/plot_data.py

+import matplotlib.pyplot as plt
+import pandas as pd
+import numpy as np
+import os
+from tqdm import tqdm
+from oct2py import octave
+
+plt.style.use('paper')
+
+Tspan = 100 * 86400
+
+
+def Recovery(Tspan, Depth, twoFstar=60, detectors='H1,L1'):
+    numDetectors = len(detectors.split(','))
+    cmd = ("DetectionProbabilityStackSlide('Nseg', 1, 'Tdata', {},"
+           "'misHist', createDeltaHist(0), 'avg2Fth', {}, 'detectors', '{}',"
+           "'Depth', {})"
+           ).format(numDetectors*Tspan, twoFstar, detectors, Depth)
+    return octave.eval(cmd, verbose=False)
+
+
+def binomialConfidenceInterval(N, K, confidence=0.95):
+    cmd = '[fLow, fUpper] = binomialConfidenceInterval({}, {}, {})'.format(
+        N, K, confidence)
+    [l, u] =  octave.eval(cmd, verbose=False, return_both=True)[0].split('\n')
+    return float(l.split('=')[1]), float(u.split('=')[1])
+
+results_file_name = 'MCResults.txt'
+
+df = pd.read_csv(
+    results_file_name, sep=' ', names=['depth', 'h0', 'dF0', 'dF1',
+                                       'twoF_predicted', 'twoF'])
+
+twoFstar = 60
+depths = np.unique(df.depth.values)
+recovery_fraction = []
+recovery_fraction_CI = []
+for d in depths:
+    twoFs = df[df.depth == d].twoF.values
+    N = len(twoFs)
+    K = np.sum(twoFs > twoFstar)
+    print d, N, K
+    recovery_fraction.append(K/float(N))
+    [fLower, fUpper] = binomialConfidenceInterval(N, K)
+    recovery_fraction_CI.append([fLower, fUpper])
+
+yerr = np.abs(recovery_fraction - np.array(recovery_fraction_CI).T)
+fig, ax = plt.subplots()
+ax.errorbar(depths, recovery_fraction, yerr=yerr, fmt='sk', marker='s', ms=2,
+            capsize=1, capthick=0.5, elinewidth=0.5,
+            label='Monte-Carlo result')
+
+fname = 'analytic_data.txt'
+if os.path.isfile(fname):
+    depths_smooth, recovery_analytic = np.loadtxt(fname)
+else:
+    depths_smooth = np.linspace(10, 550, 100)
+    recovery_analytic = []
+    for d in tqdm(depths_smooth):
+        recovery_analytic.append(Recovery(Tspan, d, twoFstar))
+    np.savetxt(fname, np.array([depths_smooth, recovery_analytic]))
+depths_smooth = np.concatenate(([0], depths_smooth))
+recovery_analytic = np.concatenate(([1], recovery_analytic))
+ax.plot(depths_smooth, recovery_analytic, '-k', label='Theoretical maximum')
+
+
+ax.set_ylim(0, 1.05)
+ax.set_xlabel(r'Signal depth', size=10)
+ax.set_ylabel(r'Recovered fraction', size=10)
+ax.legend(loc=1, frameon=False)
+
+fig.tight_layout()
+fig.savefig('allsky_recovery.png')

Paper/AllSkyMC/repeat.sh

+#!/bin/bash
+
+. /home/gregory.ashton/lalsuite-install/etc/lalapps-user-env.sh
+export PATH="/home/gregory.ashton/anaconda2/bin:$PATH"
+export MPLCONFIGDIR=/home/gregory.ashton/.config/matplotlib
+
+rm /local/user/gregory.ashton/MCResults*txt 
+for ((n=0;n<10;n++))
+do
+/home/gregory.ashton/anaconda2/bin/python generate_data.py "$1" /local/user/gregory.ashton --quite --no-template-counting
+done
+cp /local/user/gregory.ashton/MCResults*txt /home/gregory.ashton/PyFstat/Paper/AllSkyMC/CollectedOutput

Paper/AllSkyMC/submitfile

+Executable= repeat.sh
+Arguments= $(Cluster)_$(Process)
+Universe=vanilla
+Input=/dev/null
+accounting_group = ligo.dev.o2.cw.explore.test
+Output=CollectedOutput/out.$(Process)
+Error=CollectedOutput/err.$(Process)
+Log=CollectedOutput/log.$(Process)
+request_cpus = 1
+request_memory = 16 GB
+
+Queue 10

Paper/AllSky_run_setup.tex

+\begin{tabular}{c|cccccc}
+Stage & $\Nseg$ & $\Tcoh^{\rm days}$ &$\Nsteps$ & $\V$ & $\Vsky$ & $\Vpe$ \\ \hline
+0 & 27 & 3.7 & 100 & 1.0 & 1.0 & 1.0 \\
+1 & 15 & 6.7 & 100 & 1.0 & 1.0 & 1.0 \\
+2 & 8 & 12.5 & 100 & 1.0 & 1.0 & 1.0 \\
+3 & 4 & 25.0 & 100 & 1.0 & 1.0 & 1.0 \\
+4 & 1 & 100.0 & 50,50 & 1.0 & 1.0 & 1.0 \\
+\end{tabular}