def distanceIntegrand(dist,cosb,Gsamples,rmcenter,onlygreen):
# Calculate the density
densmap= densprofiles.healpixelate(dist,densprofiles.expdisk,
[1./3.,1./0.3],nside=_NSIDE,
nest=False)
# Load the dust map
if onlygreen:
combinedmap= dust.load_green15(dist,nest=False,nside_out=_NSIDE)
combinedmap[combinedmap == healpy.UNSEEN]= 0.
else:
combinedmap= dust.load_combined(dist,nest=False,nside_out=_NSIDE)
# Sample over the distribution of MG
combinedmask= numpy.zeros_like(combinedmap)
G0= 0.68+dust.dist2distmod(dist)
for jj in range(_NGSAMPLES):
combinedmask+= ((combinedmap > (_GMIN-G0-Gsamples[jj]+0.68))\
*(combinedmap < (_GMAX-G0-Gsamples[jj]+0.68))).astype('float')
combinedmask/= _NGSAMPLES
if True or dust.dist2distmod(dist) == 9.5 or dust.dist2distmod(dist) == 10.5:
print numpy.sum(combinedmask)
print dust.dist2distmod(dist), numpy.sum(cosb*densmap*combinedmask)
# If rmcenter, rm the center of the MW
if rmcenter:
theta, phi= healpy.pixelfunc.pix2ang(_NSIDE,
numpy.arange(healpy.pixelfunc.nside2npix(_NSIDE)),
nest=False)
combinedmask[((phi < 25.*_DEGTORAD)+(phi > (360.-25.)*_DEGTORAD))\
*(numpy.fabs(numpy.pi/2.-theta) < 25.*_DEGTORAD)]= 0.
# Compute cross correlation
return float(numpy.sum(cosb*densmap*combinedmask))
def distanceIntegrand(dist, cosb, Gsamples, rmcenter, onlygreen):
# Calculate the density
densmap = densprofiles.healpixelate(dist,
densprofiles.expdisk,
[1. / 3., 1. / 0.3],
nside=_NSIDE,
nest=False)
# Load the dust map
if onlygreen:
combinedmap = dust.load_green15(dist, nest=False, nside_out=_NSIDE)
combinedmap[combinedmap == healpy.UNSEEN] = 0.
else:
combinedmap = dust.load_combined(dist, nest=False, nside_out=_NSIDE)
# Sample over the distribution of MG
combinedmask = numpy.zeros_like(combinedmap)
G0 = 0.68 + dust.dist2distmod(dist)
for jj in range(_NGSAMPLES):
combinedmask+= ((combinedmap > (_GMIN-G0-Gsamples[jj]+0.68))\
*(combinedmap < (_GMAX-G0-Gsamples[jj]+0.68))).astype('float')
combinedmask /= _NGSAMPLES
if True or dust.dist2distmod(dist) == 9.5 or dust.dist2distmod(
dist) == 10.5:
print numpy.sum(combinedmask)
print dust.dist2distmod(dist), numpy.sum(cosb * densmap * combinedmask)
# If rmcenter, rm the center of the MW
if rmcenter:
theta, phi = healpy.pixelfunc.pix2ang(
_NSIDE,
numpy.arange(healpy.pixelfunc.nside2npix(_NSIDE)),
nest=False)
combinedmask[((phi < 25.*_DEGTORAD)+(phi > (360.-25.)*_DEGTORAD))\
*(numpy.fabs(numpy.pi/2.-theta) < 25.*_DEGTORAD)]= 0.
# Compute cross correlation
return float(numpy.sum(cosb * densmap * combinedmask))
def plot_dust_gaia(dist, plotname):
# Load the dust map
green15map = dust.load_combined(dist, nest=True, nside_out=_NSIDE)
dm = dust.dist2distmod(dist)
green15map[green15map == healpy.UNSEEN] = -1.
print "%i are NaN" % (numpy.sum(numpy.isnan(green15map)))
#theta, phi= healpy.pixelfunc.pix2ang(_NSIDE,numpy.arange(healpy.pixelfunc.nside2npix(_NSIDE)),nest=True)
#print (numpy.pi/2.-theta)[numpy.isnan(green15map)]/numpy.pi*180.
#print phi[numpy.isnan(green15map)]/numpy.pi*180.
# plot it
healpy.visufunc.mollview(green15map,
nest=True,
xsize=4000,
min=0.,
max=round(10. * (20. - dm - 0.68)) / 10.,
format=r'$%g$',
cmap='gist_yarg',
title="",
unit='$A_G\,(\mathrm{mag})$')
# Plot outline of Marshall et al.
ls = numpy.linspace(-100.125, 100.125, 1001)
healpy.visufunc.projplot(ls, ls * 0. - 10.125, 'k--', lw=1.2, lonlat=True)
healpy.visufunc.projplot(ls, ls * 0. + 10.125, 'k--', lw=1.2, lonlat=True)
bs = numpy.linspace(-10.125, 10.125, 1001)
healpy.visufunc.projplot(bs * 0. - 100.125, bs, 'k--', lw=1.2, lonlat=True)
healpy.visufunc.projplot(bs * 0. + 100.125, bs, 'k--', lw=1.2, lonlat=True)
# Plot boundary of Green et al. map, dec > -30.
ras = numpy.linspace(0., 360., 1001)
decs = ras * 0. - 30.
lbs = bovy_coords.radec_to_lb(ras, decs, degree=True)
ls = lbs[:, 0]
bs = lbs[:, 1]
# rm those within Marshall et al.
keepIndx = True - ((ls > 259.875) * (numpy.fabs(bs) < 10.125) +
(ls < 100.125) * (numpy.fabs(bs) < 10.125))
ls = ls[keepIndx]
bs = bs[keepIndx]
healpy.visufunc.projplot(ls, bs, 'k-.', lw=1.2, lonlat=True)
# Labels
healpy.visufunc.projtext(350.,
-8.,
r'$\mathrm{Marshall\ et\ al.\ (2006)}$',
lonlat=True,
size=13.)
healpy.visufunc.projtext(10.,
-60.,
r'$\mathrm{Drimmel\ et\ al.\ (2003)}$',
lonlat=True,
size=13.)
healpy.visufunc.projtext(160.,
40.,
r'$\mathrm{Green\ et\ al.\ (2015)}$',
lonlat=True,
size=13.)
bovy_plot.bovy_end_print(plotname)
def plot_dust(dist,plotname):
# Load the dust map
green15map= dust.load_green15(dist,nest=True,nside_out=_NSIDE)
dm= dust.dist2distmod(dist)
green15map[green15map == healpy.UNSEEN]= -1.
# plot it
healpy.visufunc.mollview(green15map,
nest=True,
xsize=4000,min=0.,
max=round(10.*(12.8-dm+1.49))/10.,
format=r'$%g$',
title=r'$\mathrm{Extinction\ to\ %.1f\,kpc}$' % dist,
cmap='gist_yarg',
unit='$A_H\,(\mathrm{mag})$')
bovy_plot.bovy_end_print(plotname)
def plot_dust_gaia(dist,plotname):
# Load the dust map
green15map= dust.load_combined(dist,nest=True,nside_out=_NSIDE)
dm= dust.dist2distmod(dist)
green15map[green15map == healpy.UNSEEN]= -1.
print "%i are NaN" % (numpy.sum(numpy.isnan(green15map)))
#theta, phi= healpy.pixelfunc.pix2ang(_NSIDE,numpy.arange(healpy.pixelfunc.nside2npix(_NSIDE)),nest=True)
#print (numpy.pi/2.-theta)[numpy.isnan(green15map)]/numpy.pi*180.
#print phi[numpy.isnan(green15map)]/numpy.pi*180.
# plot it
healpy.visufunc.mollview(green15map,
nest=True,
xsize=4000,min=0.,
max=round(10.*(20.-dm-0.68))/10.,
format=r'$%g$',
cmap='gist_yarg',
title="",
unit='$A_G\,(\mathrm{mag})$')
# Plot outline of Marshall et al.
ls= numpy.linspace(-100.125,100.125,1001)
healpy.visufunc.projplot(ls,ls*0.-10.125,'k--',lw=1.2,lonlat=True)
healpy.visufunc.projplot(ls,ls*0.+10.125,'k--',lw=1.2,lonlat=True)
bs= numpy.linspace(-10.125,10.125,1001)
healpy.visufunc.projplot(bs*0.-100.125,bs,'k--',lw=1.2,lonlat=True)
healpy.visufunc.projplot(bs*0.+100.125,bs,'k--',lw=1.2,lonlat=True)
# Plot boundary of Green et al. map, dec > -30.
ras= numpy.linspace(0.,360.,1001)
decs= ras*0.-30.
lbs= bovy_coords.radec_to_lb(ras,decs,degree=True)
ls= lbs[:,0]
bs= lbs[:,1]
# rm those within Marshall et al.
keepIndx= True-((ls > 259.875)*(numpy.fabs(bs) < 10.125)
+(ls < 100.125)*(numpy.fabs(bs) < 10.125))
ls= ls[keepIndx]
bs= bs[keepIndx]
healpy.visufunc.projplot(ls,bs,'k-.',lw=1.2,lonlat=True)
# Labels
healpy.visufunc.projtext(350.,-8.,r'$\mathrm{Marshall\ et\ al.\ (2006)}$',
lonlat=True,size=13.)
healpy.visufunc.projtext(10.,-60.,r'$\mathrm{Drimmel\ et\ al.\ (2003)}$',
lonlat=True,size=13.)
healpy.visufunc.projtext(160.,40.,r'$\mathrm{Green\ et\ al.\ (2015)}$',
lonlat=True,size=13.)
bovy_plot.bovy_end_print(plotname)
def distanceIntegrandHires(dist, theta, phi, cosb, Gsamples, dmap):
# Calculate the density
densmap = densprofiles.expdisk(phi,
numpy.pi / 2. - theta,
dist * numpy.ones(len(theta)),
glon=True,
params=[1. / 3., 1. / 0.3])
# Distance pixel
tpix = numpy.argmin(numpy.fabs(dist - _HIRESGREEN15DISTS))
dmap = dmap[:, tpix]
# Sample over the distribution of MG
combinedmask = numpy.zeros_like(dmap)
G0 = 0.68 + dust.dist2distmod(dist)
#if dust.dist2distmod(dist) == 9.5 or dust.dist2distmod(dist) == 10.5:
# print numpy.sum(numpy.isnan(combinedmap))
for jj in range(_NGSAMPLES):
combinedmask+= ((dmap > (_GMIN-G0-Gsamples[jj]+0.68))\
*(dmap < (_GMAX-G0-Gsamples[jj]+0.68))).astype('float')
combinedmask /= _NGSAMPLES
#if dust.dist2distmod(dist) == 9.5 or dust.dist2distmod(dist) == 10.5:
# print numpy.sum(combinedmask)
# print dust.dist2distmod(dist), numpy.sum(cosb*densmap*combinedmask)
# Compute cross correlation
return float(numpy.sum(cosb * densmap * combinedmask))
def plot_distanceintegral_fewfields(savename, plotname, apogee=False):
#ls and bs of the patches
ls = [280., 30., 12., 37.5, 90., 127.5, 30., 60., 20., -20., -40.]
bs = [45., 4., 2., 0., 0., 0., 0., 0., 0., 0., 0.]
radius = 1.49
locs = [4214, 4244, 4378, 4312, 4242, 4318, 4240, 4241] # for apogee
# If we are doing APOGEE selection, load the APOGEE selection function
if apogee:
selectFile = '../savs/selfunc-nospdata.sav'
if os.path.exists(selectFile):
with open(selectFile, 'rb') as savefile:
apo = pickle.load(savefile)
if os.path.exists(savename):
with open(savename, 'rb') as savefile:
area = pickle.load(savefile)
if apogee:
area_cdens = pickle.load(savefile)
else:
if not apogee:
# For samping over the absolute magnitude distribution
iso = gaia_rc.load_iso()
Gsamples = gaia_rc.sample_Gdist(iso, n=_NGSAMPLES)
# Loop through each distance slice
area = numpy.zeros((len(ls), len(dust._GREEN15DISTS)))
if apogee:
area_cdens = numpy.zeros((len(ls), len(dust._GREEN15DISTS)))
for ii, dist in enumerate(dust._GREEN15DISTS):
print "Working on distance %i: %f" % (ii, dist)
G0 = 0.68 + dust.dist2distmod(dist)
H0 = -1.49 + dust.dist2distmod(dist)
# Load the dust map
combinedmap = dust.load_combined(dist,
nest=False,
nside_out=_NSIDE)
# Loop through a few patches
theta, phi = healpy.pixelfunc.pix2ang(
_NSIDE,
numpy.arange(healpy.pixelfunc.nside2npix(_NSIDE)),
nest=False)
cosb = numpy.sin(theta)
for ff, (ll, bb) in enumerate(zip(ls, bs)):
if ff >= len(ls) - 3 * apogee: break
vec = healpy.pixelfunc.ang2vec((90. - bb) * _DEGTORAD,
ll * _DEGTORAD)
ipixs = healpy.query_disc(_NSIDE,
vec,
radius * _DEGTORAD,
inclusive=False,
nest=False)
ipixIndx = numpy.in1d(numpy.arange(
healpy.pixelfunc.nside2npix(_NSIDE)),
ipixs,
assume_unique=True)
# Calculate the density
densmap = densprofiles.expdisk(phi[ipixIndx],
numpy.pi / 2. - theta[ipixIndx],
dist * numpy.ones(len(ipixs)),
glon=True,
params=[1. / 3., 1. / 0.3])
combinedmask = numpy.zeros(len(ipixs))
tcombinedmap = combinedmap[ipixIndx]
if apogee:
# Loop through the three cohorts
for c in ['short', 'medium', 'long']:
hmin = apo.Hmin(locs[ff], cohort=c)
hmax = apo.Hmax(locs[ff], cohort=c)
combinedmask+= ((tcombinedmap > (hmin-H0))\
*(tcombinedmap < (hmax-H0))).astype('float')*apo(locs[ff],hmin+0.01)
else:
for jj in range(_NGSAMPLES):
combinedmask+= ((tcombinedmap > (_GMIN-G0-Gsamples[jj]+0.68))\
*(tcombinedmap < (_GMAX-G0-Gsamples[jj]+0.68))).astype('float')
combinedmask /= _NGSAMPLES
# Compute cross correlation
area[ff,ii]= float(numpy.sum(cosb[ipixIndx]*densmap\
*combinedmask))
if apogee:
# Also store the approximation that the density is constant
cdens = densprofiles.expdisk(ll * _DEGTORAD,
bb * _DEGTORAD,
dist,
glon=True,
params=[1. / 3., 1. / 0.3])
area_cdens[ff,ii]= float(numpy.sum(cosb[ipixIndx]*cdens\
*combinedmask))
if apogee:
save_pickles(savename, area, area_cdens)
else:
save_pickles(savename, area)
# Plot the power spectrum
if True:
bovy_plot.bovy_print(fig_height=3.)
matplotlib.rcParams['text.latex.preamble'] = [r"\usepackage{yfonts}"]
colors = [
'b', 'g', 'r', 'c', 'gold', 'm', 'k', 'orange', 'y', 'b', 'g'
]
lss = ['-', '-', '-', '-', '-', '-', '-', '-', '-', '--', '--']
for ff in range(len(ls)):
if ff >= len(ls) - 3 * apogee: break
psdx, psd = signal.periodogram(
area[ff] * dust._GREEN15DISTS**3. /
numpy.sum(area[ff] * dust._GREEN15DISTS**3.),
fs=1. / (dust._GREEN15DISTMODS[1] - dust._GREEN15DISTMODS[0]),
detrend=lambda x: x,
scaling='spectrum')
bovy_plot.bovy_plot(psdx[1:],
psd[1:],
'-',
loglog=True,
xlabel=r'$2\pi\,k_\mu\,(\mathrm{mag}^{-1})$',
ylabel=r'$P_k$',
xrange=[0.04, 4.],
color=colors[ff],
ls=lss[ff],
overplot=ff > 0)
if ff == 0:
bovy_plot.bovy_text(
r'$\mathrm{normalized}\ D^3\,\nu_*(\mu|\theta)\,\textswab{S}(\mu)$',
bottom_left=True,
size=16.)
bovy_plot.bovy_end_print(plotname)
else:
bovy_plot.bovy_print(fig_height=3.)
matplotlib.rcParams['text.latex.preamble'] = [r"\usepackage{yfonts}"]
for ff in range(len(ls)):
if ff >= len(ls) - 3 * apogee: break
bovy_plot.bovy_plot(
dust._GREEN15DISTMODS,
area[ff] * dust._GREEN15DISTS**3.,
'k-',
xlabel=r'$\mu\,(\mathrm{mag}^{-1})$',
ylabel=r'$D^3\,\nu_*(\mu|\theta)\,\textswab{S}(\mu)$')
bovy_plot.bovy_end_print(plotname)
for ff in range(len(ls)):
if ff >= len(ls) - 3 * apogee: break
spl = interpolate.InterpolatedUnivariateSpline(dust._GREEN15DISTMODS,
area[ff] *
dust._GREEN15DISTS**3.,
k=5)
fthder = [spl.derivatives(dm)[4] for dm in dust._GREEN15DISTMODS]
print "Simpson error (%f,%f)= %g, volume = %g" % (
ls[ff], bs[ff], 0.5**4. / 180. * numpy.mean(numpy.fabs(fthder)) /
integrate.simps(area[ff] * dust._GREEN15DISTS**3., dx=0.5),
numpy.sum(area[ff] * dust._GREEN15DISTS**3.))
return None
def plot_powspec(dist,basename,plotname):
# Density
G0= 0.68+dust.dist2distmod(dist)
densname= basename+'_D%.1f_denscl.sav' % dist
if not os.path.exists(densname):
densmap= densprofiles.healpixelate(dist,densprofiles.expdisk,
[1./3.,1./0.3],nside=_NSIDE,
nest=False)
denscl= healpy.sphtfunc.anafast(densmap,pol=False)
densmap2= densprofiles.healpixelate(dist,densprofiles.expdisk,
[1./2.,1./0.9],nside=_NSIDE,
nest=False)
denscl2= healpy.sphtfunc.anafast(densmap2,pol=False)
ell= numpy.arange(len(denscl))
save_pickles(densname,ell,denscl,densmap,denscl2,densmap2)
else:
with open(densname,'rb') as savefile:
ell= pickle.load(savefile)
denscl= pickle.load(savefile)
densmap= pickle.load(savefile)
denscl2= pickle.load(savefile)
densmap2= pickle.load(savefile)
# dust map Cl and cross-power with dens
combinedname= basename+'_D%.1f_combinedcl.sav' % dist
bestfitloaded= False
if os.path.exists(combinedname):
with open(combinedname,'rb') as savefile:
ell= pickle.load(savefile)
combinedcl= pickle.load(savefile)
combinedcr= pickle.load(savefile)
combinedmcl= pickle.load(savefile)
combinedmcr= pickle.load(savefile)
combinedmcr2= pickle.load(savefile)
bestfitloaded= True
if not bestfitloaded:
# do the best-fit
combinedmap= dust.load_combined(dist,nest=False,nside_out=_NSIDE)
print numpy.sum(numpy.isnan(combinedmap))
combinedmap[numpy.isnan(combinedmap)]= 0.
# Sample over the distribution of MG
combinedmask= numpy.zeros_like(combinedmap)
iso= gaia_rc.load_iso()
Gsamples= gaia_rc.sample_Gdist(iso,n=_NGSAMPLES)
print "Computing effective selection function"
for jj in range(_NGSAMPLES):
combinedmask+= ((combinedmap > (_GMIN-G0-Gsamples[jj]+0.68))\
*(combinedmap < (_GMAX-G0-Gsamples[jj]+0.68))).astype('float')
combinedmask/= _NGSAMPLES
print "Computing Cl of extinction map"
combinedcl= healpy.sphtfunc.anafast(combinedmap,pol=False)
print "Computing cross of extinction map w/ densmap"
combinedcr= healpy.sphtfunc.anafast(combinedmap,map2=densmap,pol=False)
print "Computing Cl of effective selection function"
combinedmcl= healpy.sphtfunc.anafast(combinedmask,pol=False)
print "Computing cross of effective selection function w/ densmap"
combinedmcr= healpy.sphtfunc.anafast(combinedmask,map2=densmap,pol=False)
print "Computing cross of effective selection function w/ densmap2"
combinedmcr2= healpy.sphtfunc.anafast(combinedmask,map2=densmap2,pol=False)
# Save
save_pickles(combinedname,ell,combinedcl,combinedcr,
combinedmcl,combinedmcr,combinedmcr2)
gc.collect()
# Plot (2l+1)Cl!!
# Can smooth the masked power spectrum, perhaps underplot the non-smoothed in gray
# sp= interpolate.UnivariateSpline(numpy.log(ell)[1:],numpy.log(combinedmcl)[1:],k=3,s=300.)
# sp= interpolate.UnivariateSpline(numpy.log(ell)[1:],numpy.log(numpy.fabs(combinedmcr))[1:],k=3,s=10000.)
# First plot the power-spectrum, then the cross-correlation, then the
# cumulative sum
bovy_plot.bovy_print(fig_height=3.)
yrange=[10.**-12.,20.],
line1= bovy_plot.bovy_plot(ell[1:],
(2.*ell[1:]+1.)*combinedcl[1:],
'k-',loglog=True,
ylabel=r'$(2\ell+1)\,C_\ell$',
xrange=[0.5,20000],
yrange=yrange,
zorder=3)
line2= bovy_plot.bovy_plot(ell[2::2],
(2.*ell[2::2]+1.)*denscl[2::2],
'b-',overplot=True)
line3= bovy_plot.bovy_plot(ell[1:],
(2.*ell[1:]+1.)*combinedmcl[1:],
'r-',overplot=True)
# Add legend
if dist == 5.:
pyplot.legend((line2[0],line1[0],line3[0]),
(r'$\mathrm{exp.\ disk\ w/}$'+'\n'+r'$h_R = 3\,\mathrm{kpc},$'+'\n'+r'$h_Z = 0.3\,\mathrm{kpc}$',
r'$\mathrm{extinction\ map}$',
r'$\mathrm{effective\ selection\ function}$'),
loc='lower left',bbox_to_anchor=(.02,.02),
numpoints=8,
prop={'size':14},
frameon=False)
bovy_plot.bovy_text(r'$\mathrm{power\ spectrum}$',top_right=True,size=16.)
nullfmt = NullFormatter() # no labels
pyplot.gca().xaxis.set_major_formatter(nullfmt)
bovy_plot.bovy_end_print(plotname)
# Cross-correlation
bovy_plot.bovy_print(fig_height=3.)
line1= bovy_plot.bovy_plot(ell[1:],
(2.*ell[1:]+1.)*numpy.fabs(combinedcr[1:]),
'k-',loglog=True,
ylabel=r'$(2\ell+1)\,C^{\mathrm{cross}}_\ell$',
xrange=[0.5,20000],
yrange=yrange,
zorder=1)
line2= bovy_plot.bovy_plot(ell[1:],
(2.*ell[1:]+1.)*numpy.fabs(combinedmcr[1:]),
'r-',overplot=True,zorder=2)
# Add legend
if dist == 5.:
pyplot.legend((line1[0],line2[0]),
(r'$\mathrm{extinction\ map}$',
r'$\mathrm{effective\ selection}$'+'\n'+r'$\mathrm{function}$'),
loc='lower left',bbox_to_anchor=(.02,.02),
numpoints=8,
prop={'size':14},
frameon=False)
bovy_plot.bovy_text(r'$\mathrm{cross\ power\ spectrum\ w/\ density}$',top_right=True,size=16.)
#sp= interpolate.UnivariateSpline(numpy.log(ell)[1:],
# numpy.log(numpy.fabs(combinedmcr))[1:],
# k=3,s=100000.)
#bovy_plot.bovy_plot(ell[1:],
# 10.*(2.*ell[1:]+1.)*numpy.exp(sp(numpy.log(ell[1:]))),
# 'r-',overplot=True,zorder=2)
pyplot.gca().xaxis.set_major_formatter(nullfmt)
bovy_plot.bovy_end_print(plotname.replace('powspec','crosspowspec'))
effvol= numpy.sum((2.*ell+1.)*combinedmcr)
#effvol2= numpy.sum((2.*ell+1.)*combinedmcr2)
matplotlib.rcParams['text.latex.preamble']=[r"\usepackage{yfonts}"]
line1= bovy_plot.bovy_plot(ell[1:],
numpy.fabs(numpy.log(effvol)
-numpy.log(numpy.cumsum((2.*ell+1.)*combinedmcr)))[1:],
'k-',loglog=True,
xlabel=r'$\ell$',
ylabel=r'$\left|\Delta\ln\sum_{\ell}\sum_{m}\nu_{*,\ell m}\,\textswab{S}_{\ell m}\right|$',
xrange=[0.5,20000],
yrange=[2.*10.**-13.,20.],
zorder=3)
"""
line2= bovy_plot.bovy_plot(ell[1:],
numpy.fabs(numpy.log(effvol)
-numpy.log(numpy.cumsum((2.*ell+1.)*combinedmcr))
-numpy.log(effvol2)
+numpy.log(numpy.cumsum((2.*ell+1.)*combinedmcr2)))[1:],
'k--',loglog=True,
overplot=True,zorder=2)
# Add legend
pyplot.legend((line1[0],line2[0]),
(r'$\mathrm{exp.\ disk\ top\ panel}$',
r'$\mathrm{relative\ wrt\ exp.\ disk\ w/}$'+'\n'+
r'$h_R = 2\,\mathrm{kpc}, h_Z = 0.9\,\mathrm{kpc}$'),
loc='lower right',#bbox_to_anchor=(.91,.375),
numpoints=8,
prop={'size':14},
frameon=False)
"""
if dist == 5.:
bovy_plot.bovy_text(r'$\mathrm{error\ in}\ \ln\ \mathrm{effective\ area}$',top_right=True,size=16.)
bovy_plot.bovy_end_print(plotname.replace('powspec','cumulcrosspowspec'))
return None
def plot_powspec(dist, basename, plotname):
# Density
G0 = 0.68 + dust.dist2distmod(dist)
densname = basename + '_D%.1f_denscl.sav' % dist
if not os.path.exists(densname):
densmap = densprofiles.healpixelate(dist,
densprofiles.expdisk,
[1. / 3., 1. / 0.3],
nside=_NSIDE,
nest=False)
denscl = healpy.sphtfunc.anafast(densmap, pol=False)
densmap2 = densprofiles.healpixelate(dist,
densprofiles.expdisk,
[1. / 2., 1. / 0.9],
nside=_NSIDE,
nest=False)
denscl2 = healpy.sphtfunc.anafast(densmap2, pol=False)
ell = numpy.arange(len(denscl))
save_pickles(densname, ell, denscl, densmap, denscl2, densmap2)
else:
with open(densname, 'rb') as savefile:
ell = pickle.load(savefile)
denscl = pickle.load(savefile)
densmap = pickle.load(savefile)
denscl2 = pickle.load(savefile)
densmap2 = pickle.load(savefile)
# dust map Cl and cross-power with dens
combinedname = basename + '_D%.1f_combinedcl.sav' % dist
bestfitloaded = False
if os.path.exists(combinedname):
with open(combinedname, 'rb') as savefile:
ell = pickle.load(savefile)
combinedcl = pickle.load(savefile)
combinedcr = pickle.load(savefile)
combinedmcl = pickle.load(savefile)
combinedmcr = pickle.load(savefile)
combinedmcr2 = pickle.load(savefile)
bestfitloaded = True
if not bestfitloaded:
# do the best-fit
combinedmap = dust.load_combined(dist, nest=False, nside_out=_NSIDE)
print numpy.sum(numpy.isnan(combinedmap))
combinedmap[numpy.isnan(combinedmap)] = 0.
# Sample over the distribution of MG
combinedmask = numpy.zeros_like(combinedmap)
iso = gaia_rc.load_iso()
Gsamples = gaia_rc.sample_Gdist(iso, n=_NGSAMPLES)
print "Computing effective selection function"
for jj in range(_NGSAMPLES):
combinedmask+= ((combinedmap > (_GMIN-G0-Gsamples[jj]+0.68))\
*(combinedmap < (_GMAX-G0-Gsamples[jj]+0.68))).astype('float')
combinedmask /= _NGSAMPLES
print "Computing Cl of extinction map"
combinedcl = healpy.sphtfunc.anafast(combinedmap, pol=False)
print "Computing cross of extinction map w/ densmap"
combinedcr = healpy.sphtfunc.anafast(combinedmap,
map2=densmap,
pol=False)
print "Computing Cl of effective selection function"
combinedmcl = healpy.sphtfunc.anafast(combinedmask, pol=False)
print "Computing cross of effective selection function w/ densmap"
combinedmcr = healpy.sphtfunc.anafast(combinedmask,
map2=densmap,
pol=False)
print "Computing cross of effective selection function w/ densmap2"
combinedmcr2 = healpy.sphtfunc.anafast(combinedmask,
map2=densmap2,
pol=False)
# Save
save_pickles(combinedname, ell, combinedcl, combinedcr, combinedmcl,
combinedmcr, combinedmcr2)
gc.collect()
# Plot (2l+1)Cl!!
# Can smooth the masked power spectrum, perhaps underplot the non-smoothed in gray
# sp= interpolate.UnivariateSpline(numpy.log(ell)[1:],numpy.log(combinedmcl)[1:],k=3,s=300.)
# sp= interpolate.UnivariateSpline(numpy.log(ell)[1:],numpy.log(numpy.fabs(combinedmcr))[1:],k=3,s=10000.)
# First plot the power-spectrum, then the cross-correlation, then the
# cumulative sum
bovy_plot.bovy_print(fig_height=3.)
yrange = [10.**-12., 20.],
line1 = bovy_plot.bovy_plot(ell[1:], (2. * ell[1:] + 1.) * combinedcl[1:],
'k-',
loglog=True,
ylabel=r'$(2\ell+1)\,C_\ell$',
xrange=[0.5, 20000],
yrange=yrange,
zorder=3)
line2 = bovy_plot.bovy_plot(ell[2::2],
(2. * ell[2::2] + 1.) * denscl[2::2],
'b-',
overplot=True)
line3 = bovy_plot.bovy_plot(ell[1:], (2. * ell[1:] + 1.) * combinedmcl[1:],
'r-',
overplot=True)
# Add legend
if dist == 5.:
pyplot.legend(
(line2[0], line1[0], line3[0]),
(r'$\mathrm{exp.\ disk\ w/}$' + '\n' +
r'$h_R = 3\,\mathrm{kpc},$' + '\n' + r'$h_Z = 0.3\,\mathrm{kpc}$',
r'$\mathrm{extinction\ map}$',
r'$\mathrm{effective\ selection\ function}$'),
loc='lower left',
bbox_to_anchor=(.02, .02),
numpoints=8,
prop={'size': 14},
frameon=False)
bovy_plot.bovy_text(r'$\mathrm{power\ spectrum}$',
top_right=True,
size=16.)
nullfmt = NullFormatter() # no labels
pyplot.gca().xaxis.set_major_formatter(nullfmt)
bovy_plot.bovy_end_print(plotname)
# Cross-correlation
bovy_plot.bovy_print(fig_height=3.)
line1 = bovy_plot.bovy_plot(ell[1:], (2. * ell[1:] + 1.) *
numpy.fabs(combinedcr[1:]),
'k-',
loglog=True,
ylabel=r'$(2\ell+1)\,C^{\mathrm{cross}}_\ell$',
xrange=[0.5, 20000],
yrange=yrange,
zorder=1)
line2 = bovy_plot.bovy_plot(ell[1:], (2. * ell[1:] + 1.) *
numpy.fabs(combinedmcr[1:]),
'r-',
overplot=True,
zorder=2)
# Add legend
if dist == 5.:
pyplot.legend((line1[0], line2[0]),
(r'$\mathrm{extinction\ map}$',
r'$\mathrm{effective\ selection}$' + '\n' +
r'$\mathrm{function}$'),
loc='lower left',
bbox_to_anchor=(.02, .02),
numpoints=8,
prop={'size': 14},
frameon=False)
bovy_plot.bovy_text(r'$\mathrm{cross\ power\ spectrum\ w/\ density}$',
top_right=True,
size=16.)
#sp= interpolate.UnivariateSpline(numpy.log(ell)[1:],
# numpy.log(numpy.fabs(combinedmcr))[1:],
# k=3,s=100000.)
#bovy_plot.bovy_plot(ell[1:],
# 10.*(2.*ell[1:]+1.)*numpy.exp(sp(numpy.log(ell[1:]))),
# 'r-',overplot=True,zorder=2)
pyplot.gca().xaxis.set_major_formatter(nullfmt)
bovy_plot.bovy_end_print(plotname.replace('powspec', 'crosspowspec'))
effvol = numpy.sum((2. * ell + 1.) * combinedmcr)
#effvol2= numpy.sum((2.*ell+1.)*combinedmcr2)
matplotlib.rcParams['text.latex.preamble'] = [r"\usepackage{yfonts}"]
line1 = bovy_plot.bovy_plot(
ell[1:],
numpy.fabs(
numpy.log(effvol) -
numpy.log(numpy.cumsum((2. * ell + 1.) * combinedmcr)))[1:],
'k-',
loglog=True,
xlabel=r'$\ell$',
ylabel=
r'$\left|\Delta\ln\sum_{\ell}\sum_{m}\nu_{*,\ell m}\,\textswab{S}_{\ell m}\right|$',
xrange=[0.5, 20000],
yrange=[2. * 10.**-13., 20.],
zorder=3)
"""
line2= bovy_plot.bovy_plot(ell[1:],
numpy.fabs(numpy.log(effvol)
-numpy.log(numpy.cumsum((2.*ell+1.)*combinedmcr))
-numpy.log(effvol2)
+numpy.log(numpy.cumsum((2.*ell+1.)*combinedmcr2)))[1:],
'k--',loglog=True,
overplot=True,zorder=2)
# Add legend
pyplot.legend((line1[0],line2[0]),
(r'$\mathrm{exp.\ disk\ top\ panel}$',
r'$\mathrm{relative\ wrt\ exp.\ disk\ w/}$'+'\n'+
r'$h_R = 2\,\mathrm{kpc}, h_Z = 0.9\,\mathrm{kpc}$'),
loc='lower right',#bbox_to_anchor=(.91,.375),
numpoints=8,
prop={'size':14},
frameon=False)
"""
if dist == 5.:
bovy_plot.bovy_text(
r'$\mathrm{error\ in}\ \ln\ \mathrm{effective\ area}$',
top_right=True,
size=16.)
bovy_plot.bovy_end_print(plotname.replace('powspec', 'cumulcrosspowspec'))
return None
def plot_distanceintegral_fewfields(savename,plotname,apogee=False):
#ls and bs of the patches
ls= [280.,30.,12.,37.5,90.,127.5,30.,60.,20.,-20.,-40.]
bs= [45.,4.,2.,0.,0.,0.,0.,0.,0.,0.,0.]
radius= 1.49
locs= [4214,4244,4378,4312,4242,4318,4240,4241] # for apogee
# If we are doing APOGEE selection, load the APOGEE selection function
if apogee:
selectFile= '../savs/selfunc-nospdata.sav'
if os.path.exists(selectFile):
with open(selectFile,'rb') as savefile:
apo= pickle.load(savefile)
if os.path.exists(savename):
with open(savename,'rb') as savefile:
area= pickle.load(savefile)
if apogee:
area_cdens= pickle.load(savefile)
else:
if not apogee:
# For samping over the absolute magnitude distribution
iso= gaia_rc.load_iso()
Gsamples= gaia_rc.sample_Gdist(iso,n=_NGSAMPLES)
# Loop through each distance slice
area= numpy.zeros((len(ls),len(dust._GREEN15DISTS)))
if apogee:
area_cdens= numpy.zeros((len(ls),len(dust._GREEN15DISTS)))
for ii,dist in enumerate(dust._GREEN15DISTS):
print "Working on distance %i: %f" % (ii,dist)
G0= 0.68+dust.dist2distmod(dist)
H0= -1.49+dust.dist2distmod(dist)
# Load the dust map
combinedmap= dust.load_combined(dist,nest=False,nside_out=_NSIDE)
# Loop through a few patches
theta, phi= healpy.pixelfunc.pix2ang(_NSIDE,
numpy.arange(healpy.pixelfunc.nside2npix(_NSIDE)),
nest=False)
cosb= numpy.sin(theta)
for ff,(ll,bb) in enumerate(zip(ls,bs)):
if ff >= len(ls)-3*apogee: break
vec= healpy.pixelfunc.ang2vec((90.-bb)*_DEGTORAD,ll*_DEGTORAD)
ipixs= healpy.query_disc(_NSIDE,vec,radius*_DEGTORAD,
inclusive=False,nest=False)
ipixIndx= numpy.in1d(numpy.arange(healpy.pixelfunc.nside2npix(_NSIDE)),
ipixs,assume_unique=True)
# Calculate the density
densmap= densprofiles.expdisk(phi[ipixIndx],
numpy.pi/2.-theta[ipixIndx],
dist*numpy.ones(len(ipixs)),
glon=True,
params=[1./3.,1./0.3])
combinedmask= numpy.zeros(len(ipixs))
tcombinedmap= combinedmap[ipixIndx]
if apogee:
# Loop through the three cohorts
for c in ['short','medium','long']:
hmin= apo.Hmin(locs[ff],cohort=c)
hmax= apo.Hmax(locs[ff],cohort=c)
combinedmask+= ((tcombinedmap > (hmin-H0))\
*(tcombinedmap < (hmax-H0))).astype('float')*apo(locs[ff],hmin+0.01)
else:
for jj in range(_NGSAMPLES):
combinedmask+= ((tcombinedmap > (_GMIN-G0-Gsamples[jj]+0.68))\
*(tcombinedmap < (_GMAX-G0-Gsamples[jj]+0.68))).astype('float')
combinedmask/= _NGSAMPLES
# Compute cross correlation
area[ff,ii]= float(numpy.sum(cosb[ipixIndx]*densmap\
*combinedmask))
if apogee:
# Also store the approximation that the density is constant
cdens= densprofiles.expdisk(ll*_DEGTORAD,bb*_DEGTORAD,dist,
glon=True,
params=[1./3.,1./0.3])
area_cdens[ff,ii]= float(numpy.sum(cosb[ipixIndx]*cdens\
*combinedmask))
if apogee:
save_pickles(savename,area,area_cdens)
else:
save_pickles(savename,area)
# Plot the power spectrum
if True:
bovy_plot.bovy_print(fig_height=3.)
matplotlib.rcParams['text.latex.preamble']=[r"\usepackage{yfonts}"]
colors=['b','g','r','c','gold','m','k','orange','y','b','g']
lss=['-','-','-','-','-','-','-','-','-','--','--']
for ff in range(len(ls)):
if ff >= len(ls)-3*apogee: break
psdx, psd= signal.periodogram(area[ff]*dust._GREEN15DISTS**3./numpy.sum(area[ff]*dust._GREEN15DISTS**3.),
fs=1./(dust._GREEN15DISTMODS[1]-dust._GREEN15DISTMODS[0]),
detrend=lambda x: x,scaling='spectrum')
bovy_plot.bovy_plot(psdx[1:],psd[1:],
'-',loglog=True,
xlabel=r'$2\pi\,k_\mu\,(\mathrm{mag}^{-1})$',
ylabel=r'$P_k$',
xrange=[0.04,4.],
color=colors[ff],ls=lss[ff],
overplot=ff > 0)
if ff == 0:
bovy_plot.bovy_text(r'$\mathrm{normalized}\ D^3\,\nu_*(\mu|\theta)\,\textswab{S}(\mu)$',
bottom_left=True,size=16.)
bovy_plot.bovy_end_print(plotname)
else:
bovy_plot.bovy_print(fig_height=3.)
matplotlib.rcParams['text.latex.preamble']=[r"\usepackage{yfonts}"]
for ff in range(len(ls)):
if ff >= len(ls)-3*apogee: break
bovy_plot.bovy_plot(dust._GREEN15DISTMODS,
area[ff]*dust._GREEN15DISTS**3.,
'k-',
xlabel=r'$\mu\,(\mathrm{mag}^{-1})$',
ylabel=r'$D^3\,\nu_*(\mu|\theta)\,\textswab{S}(\mu)$')
bovy_plot.bovy_end_print(plotname)
for ff in range(len(ls)):
if ff >= len(ls)-3*apogee: break
spl= interpolate.InterpolatedUnivariateSpline(dust._GREEN15DISTMODS,
area[ff]*dust._GREEN15DISTS**3.,
k=5)
fthder= [spl.derivatives(dm)[4] for dm in dust._GREEN15DISTMODS]
print "Simpson error (%f,%f)= %g, volume = %g" % (ls[ff],bs[ff],0.5**4./180.*numpy.mean(numpy.fabs(fthder))/integrate.simps(area[ff]*dust._GREEN15DISTS**3.,dx=0.5),numpy.sum(area[ff]*dust._GREEN15DISTS**3.))
return None