def isoDensityMap(isoroot):
isoDensity, isoDensityStd = loadIsotropicResults(isoroot)
# Calculate the average of the average density from the isotropic
# simulations.
avgIsoDensity = isoDensity.mean(axis=0)
stdIsoDensity = isoDensity.std(axis=0)
# Plot the maps
healpix.plot(avgIsoDensity, showdisks=True,
unit='Avg. Density [stars/deg^2]')
py.savefig(isoroot + '_avg.png')
healpix.plot(stdIsoDensity, showdisks=True,
unit='Std. Density [stars/deg^2]')
py.savefig(isoroot + '_std.png')
def isoDensityMap(isoroot):
isoDensity, isoDensityStd = loadIsotropicResults(isoroot)
# Calculate the average of the average density from the isotropic
# simulations.
avgIsoDensity = isoDensity.mean(axis=0)
stdIsoDensity = isoDensity.std(axis=0)
# Plot the maps
healpix.plot(avgIsoDensity,
showdisks=True,
unit='Avg. Density [stars/deg^2]')
py.savefig(isoroot + '_avg.png')
healpix.plot(stdIsoDensity,
showdisks=True,
unit='Std. Density [stars/deg^2]')
py.savefig(isoroot + '_std.png')
def distNormalVector(N, outdir):
incl = np.arccos(2.0 * scipy.rand(N) - 1.0)
omeg = scipy.rand(N) * 2.0 * math.pi
# Double check for random orientation
nside = 4
npix = healpy.nside2npix(nside)
hidx = healpy.ang2pix(nside, incl, omeg)
pdf = np.zeros(npix)
for hh in hidx:
pdf[hh] += 1
healpix.plot(pdf, unit='N stars')
py.savefig(outdir + 'heal_io_sim.png')
py.close()
incl = np.degrees(incl)
omeg = np.degrees(omeg)
return (incl, omeg)
def distNormalVector(N, outdir):
incl = np.arccos( 2.0 * scipy.rand(N) - 1.0 )
omeg = scipy.rand(N) * 2.0 * math.pi
# Double check for random orientation
nside = 4
npix = healpy.nside2npix(nside)
hidx = healpy.ang2pix(nside, incl, omeg)
pdf = np.zeros(npix)
for hh in hidx:
pdf[hh] += 1
healpix.plot(pdf, unit='N stars')
py.savefig(outdir + 'heal_io_sim.png')
py.close()
incl = np.degrees(incl)
omeg = np.degrees(omeg)
return (incl, omeg)
def probabilityMap(obsdir, isoroot):
"""
Read a healpix map of our observed density of normal vectors.
For each pixel in the map, calculate the probability distribution
for the corresponding pixel from isotropic simulations. This yields
a "probability map" indicating the probability that the observed
density of normal vectors could be the result of an isotropic
distribution of stars.
Parameters:
obsdir -- the directory to search for the disk.neighbor.dat file
isoroot -- the directory and root file name for the isotropic simulations.
an example would be 'iso_test/iso_d_avg_0.8_13.5_73_200_1000'
and all files with this root name will be included in the
isotropic simulations.
"""
Nside = 32
Npix = healpy.nside2npix(Nside)
# Load the observations
from papers import lu06yng as lu
obsDensity, obsDensityStd = lu.loadDiskDensity(Npix, orbDir=obsdir)
# Load results from the Isotropic Simulations
isoDensity, isoDensityStd = loadIsotropicResults(isoroot)
# Get the inclination and omegas for each pixel
pixIdx = np.arange(0, Npix)
(ipix, opix) = healpy.pix2ang(Nside, pixIdx)
ipix = np.degrees(ipix)
opix = np.degrees(opix)
# Construct a probability map and a gaussian significance map
probMap = np.zeros(Npix, dtype=float)
gsigMap = np.zeros(Npix, dtype=float)
# Calculate the values for each pixel.
for jj in range(Npix):
i = ipix[jj]
o = opix[jj]
density = obsDensity[jj]
probMap[jj] = probabilityFromMap(i,
o,
density,
isoDensity,
verbose=False)
# Calculate the average of the average density from the isotropic
# simulations.
avgIsoDensity = isoDensity[:, jj].mean()
stdIsoDensity = isoDensity[:, jj].std()
# Use the same definition as Bartko et al.
gsigMap[jj] = (density - avgIsoDensity) / stdIsoDensity
# Find the peak in the observations
peakIdx = obsDensity.argmax()
peakIncl = ipix[peakIdx]
peakOmeg = opix[peakIdx]
peakDens = obsDensity[peakIdx]
print 'Disk candidate: '
print ' inclination = %6.2f deg' % (peakIncl)
print ' Omega = %6.2f deg' % (peakOmeg)
print ' density = %9.5f stars/deg^2' % (peakDens)
print 'Probability of measuring this density or higher'
print 'from an isotropic distribution is:'
print ' Prob = %.2e' % (probMap[peakIdx])
probMapLog = np.ma.masked_where(probMap == 0, np.log10(probMap))
healpix.plot(probMapLog, showdisks=True, unit='Log Probabilty')
py.savefig(obsdir + 'iso_probability_map.png')
healpix.plot(gsigMap, showdisks=True, unit='normal sigma')
py.savefig(obsdir + 'iso_significance_map.png')
def probabilityMap(obsdir, isoroot):
"""
Read a healpix map of our observed density of normal vectors.
For each pixel in the map, calculate the probability distribution
for the corresponding pixel from isotropic simulations. This yields
a "probability map" indicating the probability that the observed
density of normal vectors could be the result of an isotropic
distribution of stars.
Parameters:
obsdir -- the directory to search for the disk.neighbor.dat file
isoroot -- the directory and root file name for the isotropic simulations.
an example would be 'iso_test/iso_d_avg_0.8_13.5_73_200_1000'
and all files with this root name will be included in the
isotropic simulations.
"""
Nside = 32
Npix = healpy.nside2npix(Nside)
# Load the observations
from papers import lu06yng as lu
obsDensity, obsDensityStd = lu.loadDiskDensity(Npix, orbDir=obsdir)
# Load results from the Isotropic Simulations
isoDensity, isoDensityStd = loadIsotropicResults(isoroot)
# Get the inclination and omegas for each pixel
pixIdx = np.arange(0, Npix)
(ipix, opix) = healpy.pix2ang(Nside, pixIdx)
ipix = np.degrees(ipix)
opix = np.degrees(opix)
# Construct a probability map and a gaussian significance map
probMap = np.zeros(Npix, dtype=float)
gsigMap = np.zeros(Npix, dtype=float)
# Calculate the values for each pixel.
for jj in range(Npix):
i = ipix[jj]
o = opix[jj]
density = obsDensity[jj]
probMap[jj] = probabilityFromMap(i, o, density, isoDensity,
verbose=False)
# Calculate the average of the average density from the isotropic
# simulations.
avgIsoDensity = isoDensity[:,jj].mean()
stdIsoDensity = isoDensity[:,jj].std()
# Use the same definition as Bartko et al.
gsigMap[jj] = (density - avgIsoDensity) / stdIsoDensity
# Find the peak in the observations
peakIdx = obsDensity.argmax()
peakIncl = ipix[peakIdx]
peakOmeg = opix[peakIdx]
peakDens = obsDensity[peakIdx]
print 'Disk candidate: '
print ' inclination = %6.2f deg' % (peakIncl)
print ' Omega = %6.2f deg' % (peakOmeg)
print ' density = %9.5f stars/deg^2' % (peakDens)
print 'Probability of measuring this density or higher'
print 'from an isotropic distribution is:'
print ' Prob = %.2e' % (probMap[peakIdx])
probMapLog = np.ma.masked_where(probMap == 0, np.log10(probMap))
healpix.plot(probMapLog, showdisks=True, unit='Log Probabilty')
py.savefig(obsdir + 'iso_probability_map.png')
healpix.plot(gsigMap, showdisks=True, unit='normal sigma')
py.savefig(obsdir + 'iso_significance_map.png')