Adds directed MC results

Paper/DirectedMC/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
@@ -16,14 +24,13 @@ Alpha = 5e-3
 Delta = 6e-2
 tref = .5*(tstart+tend)
 
-data_label = 'temp_data_{}'.format(os.getpid())
-results_file_name = 'MCResults.txt'
 
 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, 250, 13)
+depths = np.linspace(100, 400, 7)
+depths = [125, 175]
 
 run_setup = [((10, 0), 16, False),
              ((10, 0), 5, False),
@@ -40,7 +47,7 @@ for depth in depths:
     cosi = np.random.uniform(-1, 1)
 
     data = pyfstat.Writer(
-        label=data_label, outdir='data', tref=tref,
+        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')
@@ -60,12 +67,13 @@ for depth in depths:
 
     ntemps = 1
     log10temperature_min = -1
-    nwalkers = 50
+    nwalkers = 100
     nsteps = [50, 50]
 
     mcmc = pyfstat.MCMCFollowUpSearch(
-        label='temp', outdir='data',
-        sftfilepath='data/*'+data_label+'*sft', theta_prior=theta_prior,
+        label=label, outdir=outdir,
+        sftfilepath='{}/*{}*sft'.format(outdir, data_label),
+        theta_prior=theta_prior,
         tref=tref, minStartTime=tstart, maxStartTime=tend, nsteps=nsteps,
         nwalkers=nwalkers, ntemps=ntemps,
         log10temperature_min=log10temperature_min)
@@ -77,4 +85,4 @@ for depth in depths:
     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 data/temp*')
+    os.system('rm {}/*{}*'.format(outdir, label))

Paper/DirectedMC/plot_data.py

 import matplotlib.pyplot as plt
 import pandas as pd
 import numpy as np
-import scipy.stats
+import os
+from tqdm import tqdm
+from oct2py import octave
+
+plt.style.use('paper')
 
 Tspan = 100 * 86400
 
 
-def Recovery(Tspan, Depth, twoFstar=60):
-    rho2 = 4*Tspan/25./Depth**2
-    twoF_Hs = scipy.stats.distributions.ncx2(df=4, nc=rho2)
-    return 1 - twoF_Hs.cdf(twoFstar)
+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'
 
@@ -20,26 +34,40 @@ df = pd.read_csv(
 twoFstar = 60
 depths = np.unique(df.depth.values)
 recovery_fraction = []
-recovery_fraction_std = []
+recovery_fraction_CI = []
 for d in depths:
     twoFs = df[df.depth == d].twoF.values
-    print d, len(twoFs)
-    n = float(len(twoFs))
-    rf = np.sum(twoFs > twoFstar) / n
-    rf_bars = [np.sum(np.concatenate((twoFs[:i-1], twoFs[i:]))>twoFstar)/(n-1)
-               for i in range(int(n))]
-    var = (n-1)/n * np.sum([(rf_bar - rf)**2 for rf_bar in rf_bars])
-    recovery_fraction.append(rf)
-    recovery_fraction_std.append(np.sqrt(var))
+    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=recovery_fraction_std)
-#ax.plot(depths, recovery_fraction)
+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')
+
 
-depths_smooth = np.linspace(min(depths), max(depths), 100)
-recovery_analytic = [Recovery(Tspan, d) for d in depths_smooth]
-ax.plot(depths_smooth, recovery_analytic)
+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)
 
-ax.set_xlabel(r'Signal depth', size=16)
-ax.set_ylabel('Recovered fraction [%]', size=12)
+fig.tight_layout()
 fig.savefig('directed_recovery.png')

Paper/DirectedMC/repeat.sh

-for ((n=0;n<100;n++))
+#!/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
-echo $n
-python generate_data.py --quite --no-template-counting
+/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/DirectedMC/CollectedOutput

Paper/DirectedMC/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 100