"""

Purpose:

create simulated S_{1/2} from input power spectrum

Note:

this calculates Jmn every time it is run so should not be used for ensembles

Procedure:

simulates full sky CMB, measures S_{1/2}

Inputs:

ell: the l values for the power spectrum

Cl: the power spectrum

lmax: the maximum ell value to use in calculation

Default: 100

cutSky: set to True to convert to real space, apply mask, etc.

Default: False

Note: true option not yet implemented

Returns:

simulated S_{1/2}

"""

# get Jmn matrix for harmonic space S_{1/2} calc.

myJmn = getJmn(lmax=lmax)[2:,2:] # do not include monopole, dipole

#alm_prim,alm_late = hp.synalm((primCl,lateCl,crossCl),lmax=lmax,new=True)

almSim = hp.synalm(Cl,lmax=lmax) # question: does this need to start at ell[0]=1?

ClSim = hp.alm2cl(almSim)

"""

Purpose:

create p-value using ensemble and reference point

Inputs:

myArray: numpy array containing ensemble values

threshold: value to compare to ensemble to calculate p-value of

Returns:

the p-value

"""

nUnder = 0 # will also include nEqual

nOver = 0

for sim in myArray:

if sim > threshold:

nOver += 1

else:

nUnder += 1

#print "nUnder: ",nUnder,", nOver: ",nOver

cutSky=True,myNSIDE=128,newSC2=True,saveFile='simpleSonehalfC2.npy',

nGrid=100):

"""

Purpose:

function for testing S_{1/2} calculations

Inputs:

nSims: the number of simulations to do

Overriden if newSC2 = False

Default: 100

lmax: the highest l to use in the calculation

Default: 100

lmin: the lowest l to use in the calculation

Default: 2

partialMax: the maximum l to use for partial Sonehalf plots

must be more than lmin

Overriden if newSC2 = False

Default: 4

useCLASS: set to 1 to use CLASS Cl, 0 for CAMB

Default: 1

useLensing: set to 1 to use lensed Cls

Default: 1

cutSky: set to True to do cut-sky sims

Default: True

myNSIDE: HEALPix parameter for simulated maps if cutSky=True

Default: 128

newSC2: set to True to simulate new ensemble and save S,C2 results

in file, False to skip simulation and load previous results

If false, values of nSims and partialMax will come from file

Default: True

saveFile: filename to save S,C2 result if newSC2 is true, to load if false

Default: 'simpleSonehalfC2.npy'

nGrid: to pass to plot2Ddist; controls grid for binning for contours

Default: 100

"""

# get power spectrum

# starts with ell[0]=2

ell,fullCl,primCl,lateCl,crossCl = gcp.loadCls(useCLASS=useCLASS,useLensing=useLensing)

# fill beginning with zeros

startEll = int(ell[0])

ell = np.append(np.arange(startEll),ell)

Cl = np.append(np.zeros(startEll),fullCl)

#conv = ell*(ell+1)/(2*np.pi)

# Note: optimizeSx2 includes a multiplication of Cl by (beam*window)**2 at this point,

# but in this program I'm omitting it. Why? Effects are small, esp. at low ell

# get Jmn matrix for harmonic space S_{1/2} calc.

myJmn = getJmn(lmax=lmax) # do not include monopole, dipole

if cutSky:

# yeah.. disk access is annoying so...

RAMdisk = '/Volumes/ramdisk/'

ClTempFile = RAMdisk+'tempCl.fits'

mapTempFile = RAMdisk+'tempMap.fits'

mapDegFile = RAMdisk+'smicaMapDeg.fits' #created by sim_stats.getSMICA

maskDegFile = RAMdisk+'maskMapDeg.fits' #created by sim_stats.getSMICA

# create RAM Disk for SpICE and copy these files there using bash

RAMsize = 4 #Mb

ramDiskOutput = subprocess.check_output('./ramdisk.sh create '+str(RAMsize), shell=True)

print ramDiskOutput

diskID = ramDiskOutput[31:41] # this might not grab the right part; works for '/dev/disk1'

subprocess.call('cp smicaMapDeg.fits '+RAMdisk, shell=True)

subprocess.call('cp maskMapDeg.fits ' +RAMdisk, shell=True)

ispice(mapDegFile,ClTempFile,maskfile1=maskDegFile,subav="YES",subdipole="YES")

Clsmica = hp.read_cl(ClTempFile)

else:

ClTempFile = 'tempCl.fits'

mapTempFile = 'tempMap.fits'

mapDegFile = 'smicaMapDeg.fits' #created by sim_stats.getSMICA

maskDegFile = 'maskMapDeg.fits' #created by sim_stats.getSMICA

ispice(mapDegFile,ClTempFile,subav="YES",subdipole="YES")

Clsmica = hp.read_cl(ClTempFile)

# collect results

if newSC2:

sEnsemblePartial = np.zeros([nSims,partialMax+1])

C2Ensemble = np.zeros(nSims)

for i in range(nSims):

print "starting sim ",i+1," of ",nSims,"... "

almSim = hp.synalm(Cl,lmax=lmax) # should start with ell[0] = 0

if cutSky:

mapSim = hp.alm2map(almSim,myNSIDE,lmax=lmax)

hp.write_map(mapTempFile,mapSim)

ispice(mapTempFile,ClTempFile,maskfile1=maskDegFile,subav="YES",subdipole="YES")

ClSim = hp.read_cl(ClTempFile)

else:

ClSim = hp.alm2cl(almSim)

for myLmin in range(lmin,partialMax+1):

sEnsemblePartial[i,myLmin] = np.dot(ClSim[myLmin:lmax+1],

np.dot(myJmn[myLmin:,myLmin:],ClSim[myLmin:lmax+1]))

C2Ensemble[i] = ClSim[2]

# save results

np.save(saveFile,np.hstack((np.array([C2Ensemble]).T,sEnsemblePartial)) )

else: # load from file

sEnsemblePartial = np.load(saveFile)

C2Ensemble = sEnsemblePartial[:,0]

sEnsemblePartial = sEnsemblePartial[:,1:]

nSims = sEnsemblePartial.shape[0]

partialMax = sEnsemblePartial.shape[1]-1

if cutSky:

# free the RAM used by SpICE's RAM disk

ramDiskOutput = subprocess.check_output('./ramdisk.sh delete '+diskID, shell=True)

print ramDiskOutput

# plot results

print 'plotting S_{1/2} distributions... '

#myBins = np.logspace(2,7,100)

myBins = np.logspace(2,6,100)

#plt.axvline(x=6763,color='b',linewidth=3,label='SMICA inpainted')

#plt.axvline(x=2145,color='g',linewidth=3,label='SMICA masked')

#plt.hist(sEnsembleFull,bins=myBins,color='b',histtype='step',label='full sky')

#plt.hist(sEnsembleCut, bins=myBins,color='g',histtype='step',label='cut sky')

myColors = ('g','b','r','c','m','k')#need more? prob. not.

myLines = ('-','--','-.')#need more?

for myEll in range(lmin,partialMax+1):

plt.hist(sEnsemblePartial[:,myEll],bins=myBins,histtype='step',

label=r'sims: $\ell_{\rm min}$ = '+str(myEll),

color=myColors[myEll-lmin],linestyle=myLines[myEll-lmin],linewidth=2)

Sonehalf = np.dot(Clsmica[myEll:lmax+1],

np.dot(myJmn[myEll:,myEll:],Clsmica[myEll:lmax+1])) *1e24

plt.axvline(x=Sonehalf,linewidth=3,label=r'SMICA: $\ell_{\rm min}$='+str(myEll),

color=myColors[myEll-lmin],linestyle=myLines[myEll-lmin])

# calculate and print p-value

pval = pValue(sEnsemblePartial[:,myEll],Sonehalf)

print 'l_min: ',myEll,', Sonehalf: ',Sonehalf,', p-value: ',pval

plt.gca().set_xscale("log")

plt.legend()

myfs = 16 # font size for labels

plt.xlabel(r'$S_{1/2} (\mu K^4)$',fontsize=myfs)

plt.ylabel('Counts',fontsize=myfs)

plt.xlim((500,10**6))

if cutSky:

sName = ' cut-sky'

else:

sName = ' full-sky'

#plt.title(r'$S_{1/2}$ of '+str(nSims)+sName+' simulated CMBs')

plt.show()

print 'plotting C_2 vs. S_{1/2} histogram... '

SMICAvals = (np.log10(2145),171.8) # KLUDGE!!! #moved to earlier in program

SonehalfLabel = "$log_{10}(\ S_{1/2}\ /\ (\mu K)^4\ )$"

C2Label = "$C_2\ /\ (\mu K)^2$"

C2Label3 = "$C_2\ /\ (10^3 (\mu K)^2)$"

log10SonehalfEnsemble = np.log10(sEnsemblePartial[:,lmin])

myBinsLog10S = np.linspace(2,6,100)

myBinsC2 = np.linspace(0,3000,100)

cmap = cm.magma#Greens#Blues

plt.hist2d(log10SonehalfEnsemble,C2Ensemble,bins=[myBinsLog10S,myBinsC2],cmap=cmap)

plt.plot(SMICAvals[0],SMICAvals[1],'cD')

plt.colorbar()

#myfs = 16 # font size for labels

plt.xlabel(SonehalfLabel,fontsize=myfs)

plt.ylabel(C2Label,fontsize=myfs)

plt.show()

print 'plotting C_2 vs. S_{1/2} contours... '

H,xedges,yedges=np.histogram2d(log10SonehalfEnsemble,C2Ensemble,bins=(myBinsLog10S,myBinsC2))

H = H.T # Let each row list bins with common y range

myXedges = (xedges[1:]+xedges[:-1])/2 #find midpoint of linspace for plotting

myYedges = (yedges[1:]+yedges[:-1])/2

hMax = np.max(H)

#levels = [hMax*0.0009,hMax*0.009,hMax*0.09,hMax*0.9,hMax]

#levels = [hMax*0.01,hMax*0.05,hMax*0.1,hMax*0.5,hMax*0.9,hMax]

levels = np.logspace(np.log10(0.01*hMax),np.log10(0.9*hMax),5)

norm = cm.colors.Normalize(vmax=abs(H).max(),vmin=0)

#cmap = cm.PRGn

#plt.figure()

#plt.imshow(H,origin='lower',norm=norm,cmap=cmap)#,extent=extent) #extent is a coordinate zoom

#plt.imshow(H,norm=norm,cmap=cmap,extent=(2,6,0,3000)) #should match linspace above

#v = plt.axis()

CS = plt.contour(myXedges,myYedges,H,levels,colors='k',thickness=2)

plt.clabel(CS, inline=1, fontsize=10)

#plt.axis(v)

plt.colorbar()

#plt.title('do i want a title here?')

plt.xlim(2.8,5.8)

#myfs = 16 # font size for labels

plt.xlabel(SonehalfLabel,fontsize=myfs)

plt.ylabel(C2Label,fontsize=myfs)

plt.plot(SMICAvals[0],SMICAvals[1],'cD')

plt.show()

print 'plotting corner plot... '

toPlot = np.vstack((log10SonehalfEnsemble,C2Ensemble))

toPlot = toPlot.T

figure = corner.corner(toPlot,labels=[SonehalfLabel,C2Label],

show_titles=False,truths=SMICAvals,

range=((2.5,6),(0,3000)),label_kwargs={'fontsize':myfs} )

plt.show()

print 'plotting contours again but now using plot2Ddist (please wait)... '

doTime = True

startTime = time.time()

scatterstyle = {'color':'r','alpha':0.5}

styleargs = {'color':'k','scatterstyle':scatterstyle}

bw_method = 0.05 #'scott'

axSize= "20%" #1.5

nstart=600

# create separate figures to contain separate plots

"""plt.figure(1)

ax1=plt.gca()

plt.figure(2)

ax2=plt.gca()

plt.figure(3)

ax3=plt.gca()"""

#fig = plt.figure() #should be the same one used by plot2Ddist

# divide C2Ensemble by 1000 since that is approximate factor between ranges of C2,Sonehalf

# presumably useful for accuracy in contour plotting via kernel density estimation

fig1,axeslist = plot2Ddist.plot2Ddist([log10SonehalfEnsemble,C2Ensemble/1000],

truevalues=[SMICAvals[0],SMICAvals[1]/1000],

labels=[SonehalfLabel,C2Label3],contourNGrid=nGrid,

bw_method=bw_method,axSize=axSize,nstart=nstart,

returnfigure=True,**styleargs)

#bw_method=bw_method,axSize=axSize,axeslist=[ax1,ax2,ax3],**styleargs)

ax1,ax2,ax3=axeslist

timeInterval1 = time.time()-startTime

if doTime:

print 'time elapsed: ',int(timeInterval1),' seconds'

print 'starting second plot2Ddist call... '

ax1.set_xlim(left=2.9,right=6.1)

ax1.set_ylim(top=5.5)

ax1.plot(SMICAvals[0],SMICAvals[1]/1000,'cD')

#inset plot

left, bottom, width, height = [0.2, 0.4, 0.3, 0.3]

ax4 = fig1.add_axes([left,bottom,width,height])

#ax4.plot(range(10))

plt.figure(5)

ax5=plt.gca()

plt.figure(6)

ax6=plt.gca()

plot2Ddist.plot2Ddist([log10SonehalfEnsemble,C2Ensemble/1000],

truevalues=[SMICAvals[0],SMICAvals[1]/1000],

contourNGrid=nGrid,

bw_method=bw_method,axSize=axSize,nstart=nstart,

axeslist=[ax4,ax5,ax6],contourFractions=[0.91,0.93,0.95,0.97,0.99],

labelcontours=False,**styleargs)

timeInterval2 = time.time()-startTime

if doTime:

print 'time elapsed for both: ',int(timeInterval2),' seconds'

ax4.set_xlim(left=3.15,right=3.45)

ax4.set_ylim(top=0.5)

ax4.plot(SMICAvals[0],SMICAvals[1]/1000,'cD')

ax4.xaxis.set_ticks((3.2,3.3,3.4))

#plt.figure(1)

#plt.xlim(2.9,6.1)

#plt.ylim(-0.03,5.5)

plt.show()

# calculate and print 1D p-values

pValueS12 = pValue(log10SonehalfEnsemble,SMICAvals[0])

pValueC2 = pValue(C2Ensemble,SMICAvals[1])

print 'S_{1/2} p-value = ',pValueS12

print 'C_2 p-value = ',pValueC2