def bar_detectability_convolve(parser,nconvsamples=1000,
dx=_XWIDTH/20.,dy=_YWIDTH/20.,
nx=100,ny=20,
ngrid=201,rrange=[0.7,1.3],
phirange=[-m.pi/2.,m.pi/2.],
saveDir='../bar/1dLarge/',
saveDirConv='../bar/1dLargeConv/'):
"""
NAME:
bar_detectability_convolve
PURPOSE:
analyze the detectability of the Hercules moving group in the
los-distribution around the Galaxy, convolving with distance
uncertainties
INPUT:
parser - from optparse
nconvsamples - number of samples to take to perform the convolution
nx - number of plots in the x-direction
ny - number of plots in the y direction
dx - x-spacing
dy - y-spacing
ngrid - number of gridpoints to evaluate the density on
rrange - range of Galactocentric radii to consider
phirange - range of Galactic azimuths to consider
saveDir - directory to save the pickles in
OUTPUT:
plot in plotfilename
HISTORY:
2010-05-09 - Written - Bovy (NYU)
"""
(options,args)= parser.parse_args()
if len(args) == 0:
parser.print_help()
return
vloslinspace= (-.9,.9,ngrid)
vloss= sc.linspace(*vloslinspace)
picklebasename= '1d_%i_%i_%i_%.1f_%.1f_%.1f_%.1f' % (nx,ny,ngrid,rrange[0],rrange[1],phirange[0],phirange[1])
#First load all of the precalculated velocity distributions
phis= sc.zeros(nx)
rs= sc.zeros(ny)
bisplphis= sc.zeros(nx*ny)
bisplrs= sc.zeros(nx*ny)
vlosds= sc.zeros((nx*ny,ngrid))
axivlosds= sc.zeros((nx*ny,ngrid))
for ii in range(nx):
for jj in range(ny):
thisR= (rrange[0]+(rrange[1]-rrange[0])/
(ny*_YWIDTH+(ny-1)*dy)*(jj*(_YWIDTH+dy)+_YWIDTH/2.))
thisphi= (phirange[0]+(phirange[1]-phirange[0])/
(nx*_XWIDTH+(nx-1)*dx)*(ii*(_XWIDTH+dx)+_XWIDTH/2.))
phis[ii]= thisphi
rs[jj]= thisR
bisplphis[ii*ny+jj]= thisphi
bisplrs[ii*ny+jj]= thisR
thissavefilename= os.path.join(saveDir,picklebasename+'_%i_%i.sav' %(ii,jj))
if os.path.exists(thissavefilename):
print "Restoring los-velocity distribution at %.2f, %.2f ..." %(thisR,thisphi)
savefile= open(thissavefilename,'r')
vlosd= pickle.load(savefile)
axivlosd= pickle.load(savefile)
savefile.close()
vlosds[ii*ny+jj,:]= vlosd
axivlosds[ii*ny+jj,:]= axivlosd
else:
print "Did not find the los-velocity distribution at at %.2f, %.2f ..." %(thisR,thisphi)
print "returning ..."
return
#Now convolve and calculate Kullback-Leibler divergence
picklebasename= '1d_%i_%i_%i_%.1f_%.1f_%.1f_%.1f_%.1f' % (nx,ny,ngrid,rrange[0],rrange[1],phirange[0],phirange[1],options.convolve)
detect= sc.zeros((nx,ny))
losd= sc.zeros((nx,ny))
for ii in range(nx):
for jj in range(ny):
if ii == 45 and jj == 13:
continue#BOVY: FIX FOR NOW
thisR= rs[jj]
thisphi= phis[ii]
thissavefilename= os.path.join(saveDirConv,picklebasename+'_%i_%i.sav' %(ii,jj))
if os.path.exists(thissavefilename):
print "Restoring convolved los-velocity distribution at %.2f, %.2f ..." %(thisR,thisphi)
savefile= open(thissavefilename,'r')
convvlosd= pickle.load(savefile)
convaxivlosd= pickle.load(savefile)
savefile.close()
else:
print "Calculating convolved los-velocity distribution at %.2f, %.2f ..." %(thisR,thisphi)
#los distance
losd[ii,jj]= m.sqrt(thisR**2.+1.-2.*thisR*m.cos(thisphi))
thislosd= losd[ii,jj]
#Galactic longitude
if 1./m.cos(thisphi) < thisR and m.cos(thisphi) > 0.:
thisl= m.pi-m.asin(thisR/thislosd*m.sin(thisphi))
else:
thisl= m.asin(thisR/thislosd*m.sin(thisphi))
convvlosd= sc.zeros(ngrid)
convaxivlosd= sc.zeros(ngrid)
broke= False
for kk in range(ngrid):
weights= invdist2(bisplrs[ii*ny+jj],bisplphis[ii*ny+jj],
bisplrs,bisplphis)
weights[sc.isinf(weights)]= sc.amax(weights[sc.isfinite(weights)])
splindx= (weights > 1./(thislosd*options.convolve*5.)**2.)
try:
tck= interpolate.bisplrep(bisplphis[splindx],
bisplrs[splindx],
vlosds[splindx,kk],
w=weights[splindx])
except TypeError:
#Trye interp2d?
broke= True
break
except ValueError:
splindx= (weights > 1./(2.*thislosd*options.convolve*5.)**2.)
try:
tck= interpolate.bisplrep(bisplphis[splindx],
bisplrs[splindx],
vlosds[splindx,kk],
w=weights[splindx])
except TypeError:
broke= True
break
except ValueError:
broke= True
break
#Now convolve
thisnsamples= 0
for ll in range(nconvsamples):
samplelosd= thislosd+stats.norm.rvs()*thislosd*options.convolve
sampleR, samplephi= dlToRphi(samplelosd,thisl)
addvlos= interpolate.bisplev(samplephi,sampleR,tck)
convvlosd[kk]+= addvlos
if not addvlos == 0.:
thisnsamples+= 1
convvlosd[kk]/= thisnsamples
try:
tck= interpolate.bisplrep(bisplphis[splindx],
bisplrs[splindx],
axivlosds[splindx,kk],
w=weights[splindx])
except TypeError:
broke= True
break
except ValueError:
splindx= (weights > 1./(2.*thislosd*options.convolve*5.)**2.)
try:
tck= interpolate.bisplrep(bisplphis[splindx],
bisplrs[splindx],
axivlosds[splindx,kk],
w=weights[splindx])
except TypeError:
broke= True
break
except ValueError:
broke= True
break
#Now convolve
thisnsamples= 0
for ll in range(nconvsamples):
samplelosd= thislosd+stats.norm.rvs()*thislosd*options.convolve
sampleR, samplephi= dlToRphi(samplelosd,thisl)
addvlos= interpolate.bisplev(samplephi,sampleR,tck)
convaxivlosd[kk]+= addvlos
if not addvlos == 0.:
thisnsamples+= 1
convaxivlosd[kk]/= thisnsamples
savefile= open(thissavefilename,'w')
pickle.dump(convvlosd,savefile)
pickle.dump(convaxivlosd,savefile)
savefile.close()
if broke:
continue#BOVY: FIX FOR NOW
ddx= 1./sc.sum(axivlosd)
#skipCenter
if not options.skipCenter == 0.:
skipIndx= (sc.fabs(vloss) < options.skipCenter)
indx= (sc.fabs(vloss) >= options.skipCenter)
convvlosd= convvlosd/sc.sum(convvlosd[indx])/ddx
convaxivlosd= convaxivlosd/sc.sum(convaxivlosd[indx])/ddx
convvlosd[skipIndx]= 1.
convaxivlosd[skipIndx]= 1.
convvlosd_zeroindx= (convvlosd == 0.)
convaxivlosd_zeroindx= (convaxivlosd == 0.)
convvlosd[convvlosd_zeroindx]= 1.
convaxivlosd[convvlosd_zeroindx]= 1.
convvlosd[convaxivlosd_zeroindx]= 1.
convaxivlosd[convaxivlosd_zeroindx]= 1.
detect[ii,jj]= probDistance.kullbackLeibler(convvlosd,convaxivlosd,
ddx,nan=True)
detect[(detect < 0)]= 0.
detect[(detect > 0.07)]= 0.
#Now plot
plot.bovy_print()
plot.bovy_dens2d(detect.T,origin='lower',#interpolation='nearest',
xlabel=r'$\mathrm{Galactocentric\ azimuth}\ [\mathrm{deg}]$',
ylabel=r'$\mathrm{Galactocentric\ radius}\ /R_0$',
cmap='gist_yarg',xrange=sc.array(phirange)*_RADTODEG,
yrange=rrange,
aspect=(phirange[1]-phirange[0])*_RADTODEG/(rrange[1]-rrange[0]))
#contour the los distance
levels= [2/8.2*(ii+1/2.) for ii in range(10)]
contour(losd.T,levels,colors='0.25',origin='lower',linestyles='--',
aspect=(phirange[1]-phirange[0])*_RADTODEG/(rrange[1]-rrange[0]),
extent=(phirange[0]*_RADTODEG,phirange[1]*_RADTODEG,
rrange[0],rrange[1]))
plot.bovy_end_print(args[0])
def bar_detectability(parser,
dx=_XWIDTH/20.,dy=_YWIDTH/20.,
nx=100,ny=20,
ngrid=201,rrange=[0.7,1.3],
phirange=[-m.pi/2.,m.pi/2.],
saveDir='../bar/1dLarge/'):
"""
NAME:
bar_detectability
PURPOSE:
analyze the detectability of the Hercules moving group in the
los-distribution around the Galaxy
INPUT:
nx - number of plots in the x-direction
ny - number of plots in the y direction
dx - x-spacing
dy - y-spacing
ngrid - number of gridpoints to evaluate the density on
rrange - range of Galactocentric radii to consider
phirange - range of Galactic azimuths to consider
saveDir - directory to save the pickles in
OUTPUT:
plot in plotfilename
HISTORY:
2010-05-09 - Written - Bovy (NYU)
"""
(options,args)= parser.parse_args()
if len(args) == 0:
parser.print_help()
return
if not options.convolve == None:
bar_detectability_convolve(parser,dx=dx,dy=dy,nx=nx,ny=ny,ngrid=ngrid,
rrange=rrange,phirange=phirange,
saveDir=saveDir)
return
vloslinspace= (-.9,.9,ngrid)
vloss= sc.linspace(*vloslinspace)
picklebasename= '1d_%i_%i_%i_%.1f_%.1f_%.1f_%.1f' % (nx,ny,ngrid,rrange[0],rrange[1],phirange[0],phirange[1])
detect= sc.zeros((nx,ny))
losd= sc.zeros((nx,ny))
gall= sc.zeros((nx,ny))
for ii in range(nx):
for jj in range(ny):
thisR= (rrange[0]+(rrange[1]-rrange[0])/
(ny*_YWIDTH+(ny-1)*dy)*(jj*(_YWIDTH+dy)+_YWIDTH/2.))
thisphi= (phirange[0]+(phirange[1]-phirange[0])/
(nx*_XWIDTH+(nx-1)*dx)*(ii*(_XWIDTH+dx)+_XWIDTH/2.))
thissavefilename= os.path.join(saveDir,picklebasename+'_%i_%i.sav' %(ii,jj))
if os.path.exists(thissavefilename):
print "Restoring los-velocity distribution at %.2f, %.2f ..." %(thisR,thisphi)
savefile= open(thissavefilename,'r')
vlosd= pickle.load(savefile)
axivlosd= pickle.load(savefile)
savefile.close()
else:
print "Did not find the los-velocity distribution at at %.2f, %.2f ..." %(thisR,thisphi)
print "returning ..."
return
ddx= 1./sc.sum(axivlosd)
#skipCenter
if not options.skipCenter == 0.:
skipIndx= (sc.fabs(vloss) < options.skipCenter)
indx= (sc.fabs(vloss) >= options.skipCenter)
vlosd= vlosd/sc.sum(vlosd[indx])/ddx
axivlosd= axivlosd/sc.sum(axivlosd[indx])/ddx
vlosd[skipIndx]= 1.
axivlosd[skipIndx]= 1.
vlosd_zeroindx= (vlosd == 0.)
axivlosd_zeroindx= (axivlosd == 0.)
vlosd[vlosd_zeroindx]= 1.
axivlosd[vlosd_zeroindx]= 1.
vlosd[axivlosd_zeroindx]= 1.
axivlosd[axivlosd_zeroindx]= 1.
detect[ii,jj]= probDistance.kullbackLeibler(vlosd,axivlosd,ddx,nan=True)
#los distance and Galactic longitude
d= m.sqrt(thisR**2.+1.-2.*thisR*m.cos(thisphi))
losd[ii,jj]= d
if 1./m.cos(thisphi) < thisR and m.cos(thisphi) > 0.:
l= m.pi-m.asin(thisR/d*m.sin(thisphi))
else:
l= m.asin(thisR/d*m.sin(thisphi))
gall[ii,jj]= l
#Find maximum, further than 3 kpc away
detectformax= detect.flatten()
detectformax[losd.flatten() < 3./8.2]= 0.
x= sc.argmax(detectformax)
indx = sc.unravel_index(x,detect.shape)
maxR= (rrange[0]+(rrange[1]-rrange[0])/
(ny*_YWIDTH+(ny-1)*dy)*(indx[1]*(_YWIDTH+dy)+_YWIDTH/2.))
maxphi= (phirange[0]+(phirange[1]-phirange[0])/
(nx*_XWIDTH+(nx-1)*dx)*(indx[0]*(_XWIDTH+dx)+_XWIDTH/2.))
print maxR, maxphi, losd[indx[0],indx[1]], detect[indx[0],indx[1]], gall[indx[0],indx[1]]*180./sc.pi
#Now plot
plot.bovy_print()
plot.bovy_dens2d(detect.T,origin='lower',#interpolation='nearest',
xlabel=r'$\mathrm{Galactocentric\ azimuth}\ [\mathrm{deg}]$',
ylabel=r'$\mathrm{Galactocentric\ radius}\ /R_0$',
cmap='gist_yarg',xrange=sc.array(phirange)*_RADTODEG,
yrange=rrange,
aspect=(phirange[1]-phirange[0])*_RADTODEG/(rrange[1]-rrange[0]))
#contour the los distance and gall
#plot.bovy_text(-22.,1.1,r'$\mathrm{apogee}$',color='w',
# rotation=105.)
plot.bovy_text(-18.,1.1,r'$\mathrm{APOGEE}$',color='w',
rotation=285.)
levels= [2/8.2*(ii+1/2.) for ii in range(10)]
contour(losd.T,levels,colors='0.25',origin='lower',linestyles='--',
aspect=(phirange[1]-phirange[0])*_RADTODEG/(rrange[1]-rrange[0]),
extent=(phirange[0]*_RADTODEG,phirange[1]*_RADTODEG,
rrange[0],rrange[1]))
gall[gall < 0.]+= sc.pi*2.
levels= [0.,sc.pi/2.,sc.pi,3.*sc.pi/2.]
contour(gall.T,levels,colors='w',origin='lower',linestyles='--',
aspect=(phirange[1]-phirange[0])*_RADTODEG/(rrange[1]-rrange[0]),
extent=(phirange[0]*_RADTODEG,phirange[1]*_RADTODEG,
rrange[0],rrange[1]))
levels= [-5/180.*sc.pi,250/180.*sc.pi]
contour(gall.T,levels,colors='w',origin='lower',linestyles='-.',
aspect=(phirange[1]-phirange[0])*_RADTODEG/(rrange[1]-rrange[0]),
extent=(phirange[0]*_RADTODEG,phirange[1]*_RADTODEG,
rrange[0],rrange[1]))
if options.skipCenter == 0.:
plot.bovy_text(r'$\mathrm{KL\ divergence\ / \ all}\ v_{\mathrm{los}}$',
title=True)
else:
plot.bovy_text(r'$\mathrm{KL\ divergence\ / }\ |v_{\mathrm{los}}| \geq %.2f \ v_0$' % options.skipCenter,
title=True)
plot.bovy_end_print(args[0])
