def distanceAreaIntegrand(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)
if dust.dist2distmod(dist) == 9.5 or dust.dist2distmod(dist) == 10.5:
print numpy.sum(numpy.isnan(combinedmap))
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 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 (cosb * densmap * combinedmask)
def distanceAreaIntegrand(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)
if dust.dist2distmod(dist) == 9.5 or dust.dist2distmod(dist) == 10.5:
print numpy.sum(numpy.isnan(combinedmap))
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 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 (cosb*densmap*combinedmask)
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
