def bovy_dens2d(x,y, *args,**kwargs):
'''
wrapper around bovy_dens2d
hist_2d = bovy_dens2d(x,y, *args,**kwargs)
'''
try:
import bovy_plot
except ImportError:
print 'Import bovyplot failed'
if kwargs.has_key('xrange'):
xrange=kwargs['xrange']
kwargs.pop('xrange')
else:
xrange=[x.min(),x.max()]
if kwargs.has_key('yrange'):
yrange=kwargs['yrange']
kwargs.pop('yrange')
else:
yrange=[y.min(),y.max()]
ndata= len(x)
if kwargs.has_key('bins'):
bins= kwargs['bins']
kwargs.pop('bins')
else:
bins= round(0.3*sc.sqrt(ndata))
if kwargs.has_key('aspect'):
aspect= kwargs['aspect']
kwargs.pop('aspect')
else:
aspect= (xrange[1]-xrange[0])/(yrange[1]-yrange[0])
if kwargs.has_key('weights'):
weights= kwargs['weights']
kwargs.pop('weights')
else:
weights= None
if kwargs.has_key('levels'):
levels= kwargs['levels']
kwargs.pop('levels')
else:
levels= special.erf(0.5*sc.arange(1,4))
hh_2d, edges= sc.histogramdd(sc.array([x, y]).T,
bins=bins, range=[xrange ,yrange])
bovy_plot.bovy_dens2d(hh_2d.T,
contours=True,levels=levels,cntrmass=True,
cmap='gist_yarg',origin='lower',
xrange=xrange, yrange=yrange, aspect=aspect,
interpolation='nearest', retCumImage=True, **kwargs)
return hh_2d
def exNew(exclude=sc.array([1,2,3,4]),
plotfilename='exNew.png',nburn=20000,nsamples=200000,
parsigma=[5,.075,.01,1,.1],dsigma=1.):
"""exMix1: solve the new exercise using MCMC sampling
Input:
exclude - ID numbers to exclude from the analysis (can be None)
plotfilename - filename for the output plot
nburn - number of burn-in samples
nsamples - number of samples to take after burn-in
parsigma - proposal distribution width (Gaussian)
dsigma - divide uncertainties by this amount
Output:
plot
History:
2010-04-28 - Written - Bovy (NYU)
"""
sc.random.seed(1) #In the interest of reproducibility (if that's a word)
#Read the data
data= read_data('data_yerr.dat')
ndata= len(data)
if not exclude == None:
nsample= ndata- len(exclude)
else:
nsample= ndata
#First find the chi-squared solution, which we will use as an
#initial guess
#Put the data in the appropriate arrays and matrices
Y= sc.zeros(nsample)
X= sc.zeros(nsample)
A= sc.ones((nsample,2))
C= sc.zeros((nsample,nsample))
yerr= sc.zeros(nsample)
jj= 0
for ii in range(ndata):
if not exclude == None and sc.any(exclude == data[ii][0]):
pass
else:
Y[jj]= data[ii][1][1]
X[jj]= data[ii][1][0]
A[jj,1]= data[ii][1][0]
C[jj,jj]= data[ii][2]**2./dsigma**2.
yerr[jj]= data[ii][2]/dsigma
jj= jj+1
#Now compute the best fit and the uncertainties
bestfit= sc.dot(linalg.inv(C),Y.T)
bestfit= sc.dot(A.T,bestfit)
bestfitvar= sc.dot(linalg.inv(C),A)
bestfitvar= sc.dot(A.T,bestfitvar)
bestfitvar= linalg.inv(bestfitvar)
bestfit= sc.dot(bestfitvar,bestfit)
initialguess= sc.array([bestfit[0],bestfit[1],0.,sc.mean(Y),m.log(sc.var(Y))])#(m,b,Pb,Yb,Vb)
#With this initial guess start off the sampling procedure
initialX= objective(initialguess,X,Y,yerr)
currentX= initialX
bestX= initialX
bestfit= initialguess
currentguess= initialguess
naccept= 0
samples= []
samples.append(currentguess)
for jj in range(nburn+nsamples):
#Draw a sample from the proposal distribution
newsample= sc.zeros(5)
newsample[0]= currentguess[0]+stats.norm.rvs()*parsigma[0]
newsample[1]= currentguess[1]+stats.norm.rvs()*parsigma[1]
#newsample[2]= stats.uniform.rvs()
newsample[2]= currentguess[2]+stats.norm.rvs()*parsigma[2]
newsample[3]= currentguess[3]+stats.norm.rvs()*parsigma[3]
newsample[4]= currentguess[4]+stats.norm.rvs()*parsigma[4]
#Calculate the objective function for the newsample
newX= objective(newsample,X,Y,yerr)
#Accept or reject
#Reject with the appropriate probability
u= stats.uniform.rvs()
if u < m.exp(newX-currentX):
#Accept
currentX= newX
currentguess= newsample
naccept= naccept+1
if currentX > bestX:
bestfit= currentguess
bestX= currentX
samples.append(currentguess)
if double(naccept)/(nburn+nsamples) < .2 or double(naccept)/(nburn+nsamples) > .6:
print "Acceptance ratio was "+str(double(naccept)/(nburn+nsamples))
samples= sc.array(samples).T[:,nburn:-1]
print "Best-fit, overall"
print bestfit, sc.mean(samples[2,:]), sc.median(samples[2,:])
histmb,edges= sc.histogramdd(samples.T[:,0:2],bins=round(sc.sqrt(nsamples)/5.))
indxi= sc.argmax(sc.amax(histmb,axis=1))
indxj= sc.argmax(sc.amax(histmb,axis=0))
print "Best-fit, marginalized"
print edges[0][indxi-1], edges[1][indxj-1]
print edges[0][indxi], edges[1][indxj]
print edges[0][indxi+1], edges[1][indxj+1]
#2D histogram
plot.bovy_print()
levels= special.erf(0.5*sc.arange(1,4))
#xrange=[edges[0][0],edges[0][-1]]
#yrange=[edges[1][0],edges[1][-1]]
xrange=[-120,120]
yrange=[1.5,3.2]
histmb,edges= sc.histogramdd(samples.T[:,0:2],
range=[[-120,120],[1.5,3.2]],
bins=(round(sc.sqrt(nsamples)/5.)/(edges[0][-1]-edges[0][0])*(xrange[1]-xrange[0]),
round(sc.sqrt(nsamples)/5.)/(edges[1][-1]-edges[1][0])*(yrange[1]-yrange[0])))
aspect=(xrange[1]-xrange[0])/(yrange[1]-yrange[0])
plot.bovy_dens2d(histmb.T,origin='lower',cmap='gist_yarg',
contours=True,cntrmass=True,
xrange=xrange,yrange=yrange,
levels=levels,
aspect=aspect,
xlabel=r'$b$',ylabel=r'$m$')
if dsigma == 1.:
plot.bovy_text(r'$\mathrm{using\ correct\ data\ uncertainties}$',
top_right=True)
else:
plot.bovy_text(r'$\mathrm{using\ data\ uncertainties\ /\ 2}$',
top_right=True)
if dsigma == 1.:
plot.bovy_end_print('exNew1a.png')
else:
plot.bovy_end_print('exNew2a.png')
#Data with MAP line and sampling
plot.bovy_print()
bestb= edges[0][indxi]
bestm= edges[1][indxj]
xrange=[0,300]
yrange=[0,700]
plot.bovy_plot(xrange,bestm*sc.array(xrange)+bestb,'k-',
xrange=xrange,yrange=yrange,
xlabel=r'$x$',ylabel=r'$y$',zorder=2)
errorbar(X,Y,yerr,color='k',marker='o',color='k',linestyle='None',zorder=1)
for ii in range(10):
#Random sample
ransample= sc.floor((stats.uniform.rvs()*nsamples))
ransample= samples.T[ransample,0:2]
bestb= ransample[0]
bestm= ransample[1]
plot.bovy_plot(xrange,bestm*sc.array(xrange)+bestb,
overplot=True,xrange=xrange,yrange=yrange,
xlabel=r'$x$',ylabel=r'$y$',color='0.75',zorder=1)
if dsigma == 1.:
plot.bovy_text(r'$\mathrm{using\ correct\ data\ uncertainties}$',
top_right=True)
else:
plot.bovy_text(r'$\mathrm{using\ data\ uncertainties\ /\ 2}$',
top_right=True)
if dsigma == 1.:
plot.bovy_end_print('exNew1b.png')
else:
plot.bovy_end_print('exNew2b.png')
#Pb plot
plot.bovy_print()
plot.bovy_hist(samples.T[:,2],color='k',bins=round(sc.sqrt(nsamples)/5.),
xlabel=r'$P_\mathrm{b}$',normed=True,histtype='step',
range=[0,1])
if dsigma == 1.:
plot.bovy_text(r'$\mathrm{using\ correct\ data\ uncertainties}$',
top_right=True)
else:
plot.bovy_text(r'$\mathrm{using\ data\ uncertainties\ /\ 2}$',
top_right=True)
if dsigma == 1.:
plot.bovy_end_print('exNew1c.png')
else:
plot.bovy_end_print('exNew2c.png')
return
def exMix1(
exclude=None,
plotfilenameA="exMix1a.png",
plotfilenameB="exMix1b.png",
plotfilenameC="exMix1c.png",
nburn=20000,
nsamples=1000000,
parsigma=[5, 0.075, 0.2, 1, 0.1],
dsigma=1.0,
bovyprintargs={},
sampledata=None,
):
"""exMix1: solve exercise 5 (mixture model) using MCMC sampling
Input:
exclude - ID numbers to exclude from the analysis (can be None)
plotfilename* - filenames for the output plot
nburn - number of burn-in samples
nsamples - number of samples to take after burn-in
parsigma - proposal distribution width (Gaussian)
dsigma - divide uncertainties by this amount
Output:
plot
History:
2010-04-28 - Written - Bovy (NYU)
"""
sc.random.seed(-1) # In the interest of reproducibility (if that's a word)
# Read the data
data = read_data("data_yerr.dat")
ndata = len(data)
if not exclude == None:
nsample = ndata - len(exclude)
else:
nsample = ndata
# First find the chi-squared solution, which we will use as an
# initial guess
# Put the data in the appropriate arrays and matrices
Y = sc.zeros(nsample)
X = sc.zeros(nsample)
A = sc.ones((nsample, 2))
C = sc.zeros((nsample, nsample))
yerr = sc.zeros(nsample)
jj = 0
for ii in range(ndata):
if not exclude == None and sc.any(exclude == data[ii][0]):
pass
else:
Y[jj] = data[ii][1][1]
X[jj] = data[ii][1][0]
A[jj, 1] = data[ii][1][0]
C[jj, jj] = data[ii][2] ** 2.0 / dsigma ** 2.0
yerr[jj] = data[ii][2] / dsigma
jj = jj + 1
brange = [-120, 120]
mrange = [1.5, 3.2]
# This matches the order of the parameters in the "samples" vector
mbrange = [brange, mrange]
if sampledata is None:
sampledata = runSampler(X, Y, A, C, yerr, nburn, nsamples, parsigma, mbrange)
(histmb, edges, mbsamples, pbhist, pbedges) = sampledata
# Hack -- produce fake Pbad samples from Pbad histogram.
pbsamples = hstack([array([x] * N) for x, N in zip((pbedges[:-1] + pbedges[1:]) / 2, pbhist)])
indxi = sc.argmax(sc.amax(histmb, axis=1))
indxj = sc.argmax(sc.amax(histmb, axis=0))
print "Best-fit, marginalized"
print edges[0][indxi - 1], edges[1][indxj - 1]
print edges[0][indxi], edges[1][indxj]
print edges[0][indxi + 1], edges[1][indxj + 1]
# 2D histogram
plot.bovy_print(**bovyprintargs)
levels = special.erf(0.5 * sc.arange(1, 4))
xe = [edges[0][0], edges[0][-1]]
ye = [edges[1][0], edges[1][-1]]
aspect = (xe[1] - xe[0]) / (ye[1] - ye[0])
plot.bovy_dens2d(
histmb.T,
origin="lower",
cmap=cm.gist_yarg,
interpolation="nearest",
contours=True,
cntrmass=True,
extent=xe + ye,
levels=levels,
aspect=aspect,
xlabel=r"$b$",
ylabel=r"$m$",
)
xlim(brange)
ylim(mrange)
plot.bovy_end_print(plotfilenameA)
# Data with MAP line and sampling
plot.bovy_print(**bovyprintargs)
bestb = edges[0][indxi]
bestm = edges[1][indxj]
xrange = [0, 300]
yrange = [0, 700]
plot.bovy_plot(
xrange,
bestm * sc.array(xrange) + bestb,
"k-",
xrange=xrange,
yrange=yrange,
xlabel=r"$x$",
ylabel=r"$y$",
zorder=2,
)
errorbar(X, Y, yerr, marker="o", color="k", linestyle="None", zorder=1)
for m, b in mbsamples:
plot.bovy_plot(
xrange,
m * sc.array(xrange) + b,
overplot=True,
xrange=xrange,
yrange=yrange,
xlabel=r"$x$",
ylabel=r"$y$",
color="0.75",
zorder=1,
)
plot.bovy_end_print(plotfilenameB)
# Pb plot
if not "text_fontsize" in bovyprintargs:
bovyprintargs["text_fontsize"] = 11
plot.bovy_print(**bovyprintargs)
plot.bovy_hist(
pbsamples,
bins=round(sc.sqrt(nsamples) / 5.0),
xlabel=r"$P_\mathrm{b}$",
normed=True,
histtype="step",
range=[0, 1],
edgecolor="k",
)
ylim(0, 4.0)
if dsigma == 1.0:
plot.bovy_text(r"$\mathrm{using\ correct\ data\ uncertainties}$", top_right=True)
else:
plot.bovy_text(r"$\mathrm{using\ data\ uncertainties\ /\ 2}$", top_left=True)
plot.bovy_end_print(plotfilenameC)
return sampledata
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])
def exMix1(exclude=None,
plotfilenameA='exMix1a.png',
plotfilenameB='exMix1b.png',
plotfilenameC='exMix1c.png',
nburn=20000,
nsamples=1000000,
parsigma=[5, .075, .2, 1, .1],
dsigma=1.,
bovyprintargs={},
sampledata=None):
"""exMix1: solve exercise 5 (mixture model) using MCMC sampling
Input:
exclude - ID numbers to exclude from the analysis (can be None)
plotfilename* - filenames for the output plot
nburn - number of burn-in samples
nsamples - number of samples to take after burn-in
parsigma - proposal distribution width (Gaussian)
dsigma - divide uncertainties by this amount
Output:
plot
History:
2010-04-28 - Written - Bovy (NYU)
"""
sc.random.seed(-1) #In the interest of reproducibility (if that's a word)
#Read the data
data = read_data('data_yerr.dat')
ndata = len(data)
if not exclude == None:
nsample = ndata - len(exclude)
else:
nsample = ndata
#First find the chi-squared solution, which we will use as an
#initial guess
#Put the data in the appropriate arrays and matrices
Y = sc.zeros(nsample)
X = sc.zeros(nsample)
A = sc.ones((nsample, 2))
C = sc.zeros((nsample, nsample))
yerr = sc.zeros(nsample)
jj = 0
for ii in range(ndata):
if not exclude == None and sc.any(exclude == data[ii][0]):
pass
else:
Y[jj] = data[ii][1][1]
X[jj] = data[ii][1][0]
A[jj, 1] = data[ii][1][0]
C[jj, jj] = data[ii][2]**2. / dsigma**2.
yerr[jj] = data[ii][2] / dsigma
jj = jj + 1
brange = [-120, 120]
mrange = [1.5, 3.2]
# This matches the order of the parameters in the "samples" vector
mbrange = [brange, mrange]
if sampledata is None:
sampledata = runSampler(X, Y, A, C, yerr, nburn, nsamples, parsigma,
mbrange)
(histmb, edges, mbsamples, pbhist, pbedges) = sampledata
# Hack -- produce fake Pbad samples from Pbad histogram.
pbsamples = hstack([
array([x] * N)
for x, N in zip((pbedges[:-1] + pbedges[1:]) / 2, pbhist)
])
indxi = sc.argmax(sc.amax(histmb, axis=1))
indxj = sc.argmax(sc.amax(histmb, axis=0))
print "Best-fit, marginalized"
print edges[0][indxi - 1], edges[1][indxj - 1]
print edges[0][indxi], edges[1][indxj]
print edges[0][indxi + 1], edges[1][indxj + 1]
#2D histogram
plot.bovy_print(**bovyprintargs)
levels = special.erf(0.5 * sc.arange(1, 4))
xe = [edges[0][0], edges[0][-1]]
ye = [edges[1][0], edges[1][-1]]
aspect = (xe[1] - xe[0]) / (ye[1] - ye[0])
plot.bovy_dens2d(histmb.T,
origin='lower',
cmap=cm.gist_yarg,
interpolation='nearest',
contours=True,
cntrmass=True,
extent=xe + ye,
levels=levels,
aspect=aspect,
xlabel=r'$b$',
ylabel=r'$m$')
xlim(brange)
ylim(mrange)
plot.bovy_end_print(plotfilenameA)
#Data with MAP line and sampling
plot.bovy_print(**bovyprintargs)
bestb = edges[0][indxi]
bestm = edges[1][indxj]
xrange = [0, 300]
yrange = [0, 700]
plot.bovy_plot(xrange,
bestm * sc.array(xrange) + bestb,
'k-',
xrange=xrange,
yrange=yrange,
xlabel=r'$x$',
ylabel=r'$y$',
zorder=2)
errorbar(X, Y, yerr, marker='o', color='k', linestyle='None', zorder=1)
for m, b in mbsamples:
plot.bovy_plot(xrange,
m * sc.array(xrange) + b,
overplot=True,
xrange=xrange,
yrange=yrange,
xlabel=r'$x$',
ylabel=r'$y$',
color='0.75',
zorder=1)
plot.bovy_end_print(plotfilenameB)
#Pb plot
if not 'text_fontsize' in bovyprintargs:
bovyprintargs['text_fontsize'] = 11
plot.bovy_print(**bovyprintargs)
plot.bovy_hist(pbsamples,
bins=round(sc.sqrt(nsamples) / 5.),
xlabel=r'$P_\mathrm{b}$',
normed=True,
histtype='step',
range=[0, 1],
edgecolor='k')
ylim(0, 4.)
if dsigma == 1.:
plot.bovy_text(r'$\mathrm{using\ correct\ data\ uncertainties}$',
top_right=True)
else:
plot.bovy_text(r'$\mathrm{using\ data\ uncertainties\ /\ 2}$',
top_left=True)
plot.bovy_end_print(plotfilenameC)
return sampledata