def test(useCLASS=1,
useLensing=1,
classCamb=1,
nSims=1000,
lmax=100,
lmin=2,
newSMICA=False,
newDeg=False,
suppressC2=False,
suppFactor=0.23,
filterC2=False,
filtFacLow=0.1,
filtFacHigh=0.2,
R1=False):
"""
code for testing the other functions in this module
Inputs:
useCLASS: set to 1 to use CLASS, 0 to use CAMB
CLASS Cl has early/late split at z=50
CAMB Cl has ISWin/out split: ISWin: 0.4<z<0.75, ISWout: the rest
Note: CAMB results include primary in ISWin and ISWout (not as intended)
default: 1
useLensing: set to 1 to use lensed Cl, 0 for non-lensed
default: 1
classCamb: if 1: use the CAMB format of CLASS output, if 0: use CLASS format
Note: parameter not used if useCLASS = 0
default: 1
nSims: the number of simulations to do for ensemble
default: 1000
lmax: the highest l to include in Legendre transforms
default: 100
lmin: the lowest l to include in S_{1/2} = CIC calculations
default: 2
newSMICA: set to True to recalculate SMICA results
default: False
newDeg: set to True to recalculate map and mask degredations
(only if newSMICA is also True)
default: False
suppressC2: set to True to suppress theoretical C_2 (quadrupole) by
suppFactor before creating a_lm.s
Default: False
suppFactor: multiplies C_2 if suppressC2 is True
Default: 0.23 # from Tegmark et. al. 2003, figure 13 (WMAP)
filterC2 : set to true to filter simulated CMBs after spice calculates
cut sky C_l. Sims will pass filter if C_2 * filtFacLow < C_2^sim <
C_2 * filtFacHigh.
Default: False
filtFacLow,filtFacHigh: defines C_2 range for passing simulated CMBs
Default: 0.1,0.2
R1: set to True to use SMICA and Mask R1. Otherwise, R2 used.
Only affects calculation of newly degraded map.
Default: False
"""
# load data
ell, fullCl, primCl, lateCl, crossCl = gcp.loadCls(useCLASS=useCLASS,
useLensing=useLensing,
classCamb=classCamb)
# fill beginning with zeros
startEll = int(ell[0])
ell = np.append(np.arange(startEll), ell)
fullCl = np.append(np.zeros(startEll), fullCl)
primCl = np.append(np.zeros(startEll), primCl)
lateCl = np.append(np.zeros(startEll), lateCl)
crossCl = np.append(np.zeros(startEll), crossCl)
# suppress C_2 to see what happens in enesmble
if suppressC2:
fullCl[2] *= suppFactor
primCl[2] *= suppFactor
lateCl[2] *= suppFactor
crossCl[2] *= suppFactor
conv = ell * (ell + 1) / (2 * np.pi)
#print ell,conv #ell[0]=2.0
"""
# verify statistical properties of alm realizations
nSims = 1000
lmax = 100
Clprim_sum = np.zeros(lmax+1)
Cllate_sum = np.zeros(lmax+1)
Clcros_sum = np.zeros(lmax+1) # prim x late
for nSim in range(nSims):
print 'starting sim ',nSim+1, ' of ',nSims
#alm_prim,alm_late = getAlms(A_lij,lmax=lmax) #AKW method defunct
# see if synalm can do it
alm_prim,alm_late = hp.synalm((primCl,lateCl,crossCl),lmax=lmax,new=True)
Clprim_sum = Clprim_sum + hp.alm2cl(alm_prim)
Cllate_sum = Cllate_sum + hp.alm2cl(alm_late)
Clcros_sum = Clcros_sum + hp.alm2cl(alm_prim,alm_late)
Cl_prim_avg = Clprim_sum/nSims
Cl_late_avg = Cllate_sum/nSims
Cl_cros_avg = Clcros_sum/nSims
doPlot = True
if doPlot:
plt.plot(ell[:lmax+1],Cl_prim_avg*conv[:lmax+1])
plt.plot(ell[:lmax+1],primCl[:lmax+1]*conv[:lmax+1])
plt.title('primary')
plt.ylabel('D_l')
plt.show()
plt.plot(ell[:lmax+1],Cl_late_avg*conv[:lmax+1])
plt.plot(ell[:lmax+1],lateCl[:lmax+1]*conv[:lmax+1])
plt.title('late')
plt.ylabel('D_l')
plt.show()
plt.plot(ell[:lmax+1],Cl_cros_avg*conv[:lmax+1])
plt.plot(ell[:lmax+1],crossCl[:lmax+1]*conv[:lmax+1])
plt.title('cross')
plt.ylabel('D_l')
plt.show()
"""
# get covariances from SMICA map and mask
theta_i = 0.0 #degrees
theta_f = 180.0 #degrees
nSteps = 1800
#lmax = 100
""" # don't want anafast after all
# get unmasked and masked SMICA covariances
# note: getSMICA uses linspace in theta for thetaArray
#newSMICA = False#True
thetaArray2, C_SMICA, C_SMICAmasked, S_SMICAnomask, S_SMICAmasked = \
getSMICA(theta_i=theta_i,theta_f=theta_f,nSteps=nSteps,lmax=lmax,lmin=lmin,
newSMICA=newSMICA,newDeg=newDeg,useSPICE=False,R1=R1)
print ''
print 'S_{1/2}(anafast): SMICA, no mask: ',S_SMICAnomask,', masked: ',S_SMICAmasked
print ''
"""
# get C_l from SPICE to compare to above method
# note: getSMICA uses linspace in theta for thetaArray
#newSMICA = False#True
thetaArray2sp, C_SMICAsp, C_SMICAmaskedsp, S_SMICAnomasksp, S_SMICAmaskedsp = \
getSMICA(theta_i=theta_i,theta_f=theta_f,nSteps=nSteps,lmax=lmax,lmin=lmin,
newSMICA=newSMICA,newDeg=newDeg,useSPICE=True,R1=R1)
print ''
print 'S_{1/2}(spice): SMICA, no mask: ', S_SMICAnomasksp, ', masked: ', S_SMICAmaskedsp
print ''
# Find S_{1/2} in real space to compare methods
nTerms = 10000
#SSnm2 = SOneHalf(thetaArray2, C_SMICA, nTerms=nTerms)
#SSmd2 = SOneHalf(thetaArray2, C_SMICAmasked, nTerms=nTerms)
SSnm2sp = SOneHalf(thetaArray2sp, C_SMICAsp, nTerms=nTerms)
SSmd2sp = SOneHalf(thetaArray2sp, C_SMICAmaskedsp, nTerms=nTerms)
# create ensemble of realizations and gather statistics
covEnsembleFull = np.zeros([nSims, nSteps + 1]) # for maskless
covEnsembleCut = np.zeros([nSims, nSteps + 1]) # for masked
sEnsembleFull = np.zeros(nSims)
sEnsembleCut = np.zeros(nSims)
covTheta = np.array([])
#nSims = 1000
# apply beam and pixel window functions to power spectra
# note: to ignore the non-constant pixel shape, W(l) must be > B(l)
# however, this is not true for NSIDE=128 and gauss_beam(5')
# Here I ignore this anyway and proceed
myNSIDE = 128 # must be same NSIDE as in getSMICA function
Wpix = hp.pixwin(myNSIDE)
Bsmica = hp.gauss_beam(5. / 60 * np.pi / 180) # 5 arcmin
WlMax = Wpix.size
if WlMax < lmax:
print 'die screaming!!!'
return 0
primCl = primCl[:WlMax] * (Wpix * Bsmica)**2
lateCl = lateCl[:WlMax] * (Wpix * Bsmica)**2
crossCl = crossCl[:WlMax] * (Wpix * Bsmica)**2
# note: i tried sims without this scaling, and results seemed the same at a glance
# collect simulated Cl for comparison to model
Clsim_full_sum = np.zeros(lmax + 1)
# get Jmn matrix for harmonic space S_{1/2} calc.
myJmn = getJmn(lmax=lmax)
# set up ramdisk for SpICE
# super lame that spice needs to read/write from disk, but here goes...
RAMdisk = '/Volumes/ramdisk/'
ClTempFile = RAMdisk + 'tempCl.fits'
mapTempFile = RAMdisk + 'tempMap.fits'
mapDegFile = RAMdisk + 'smicaMapDeg.fits' # this should have been created by sims.getSMICA
maskDegFile = RAMdisk + 'maskMapDeg.fits' # this should have been created by sims.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)
doTime = True # to time the run and print output
startTime = time.time()
#for nSim in range(nSims):
nSim = 0
while nSim < nSims:
print 'starting sim ', nSim + 1, ' of ', nSims
alm_prim, alm_late = hp.synalm((primCl, lateCl, crossCl),
lmax=lmax,
new=True)
# calculate C(theta) of simulation
Clsim_prim = hp.alm2cl(alm_prim)
Clsim_late = hp.alm2cl(alm_late)
Clsim_cros = hp.alm2cl(alm_prim, alm_late)
Clsim_full = Clsim_prim + 2 * Clsim_cros + Clsim_late
# use Cl_sim_full to omit prim/late distinction for now
# start with a mask
# -> for optional C2 filtering based on cut sky map
# alm2map should create map with default RING ordering
# pixel window and beam already accounted for in true Cls
#mapSim = hp.alm2map(alm_prim+alm_late,myNSIDE,lmax=lmax,pixwin=True,sigma=5./60*np.pi/180)
mapSim = hp.alm2map(alm_prim + alm_late, myNSIDE, lmax=lmax)
hp.write_map(mapTempFile, mapSim)
ispice(mapTempFile,
ClTempFile,
maskfile1=maskDegFile,
subav="YES",
subdipole="YES")
Cl_masked = hp.read_cl(ClTempFile)
ell2 = np.arange(Cl_masked.shape[0])
# Check for low power of cut sky C_2
if (filterC2 == True and fullCl[2] * filtFacHigh > Cl_masked[2] and
Cl_masked[2] > fullCl[2] * filtFacLow) or filterC2 == False:
# note: getCovar uses linspace in x for thetaArray
thetaArray, cArray2 = getCovar(ell2[:lmax + 1],
Cl_masked[:lmax + 1],
theta_i=theta_i,
theta_f=theta_f,
nSteps=nSteps,
lmin=lmin)
covEnsembleCut[nSim] = cArray2
# S_{1/2}
sEnsembleCut[nSim] = np.dot(
Cl_masked[lmin:lmax + 1],
np.dot(myJmn[lmin:, lmin:], Cl_masked[lmin:lmax + 1]))
doPlot = False #True
if doPlot:
plt.plot(thetaArray, cArray)
plt.xlabel('theta (degrees)')
plt.ylabel('C(theta)')
plt.title('covariance of CMB simulation ' + str(nSim + 1))
plt.show()
# now without the mask
# uses the same sims that passed the C2 filter
Clsim_full_sum += Clsim_full
# note: getCovar uses linspace in x for thetaArray
thetaArray, cArray = getCovar(ell[:lmax + 1],
Clsim_full[:lmax + 1],
theta_i=theta_i,
theta_f=theta_f,
nSteps=nSteps,
lmin=lmin)
covEnsembleFull[nSim] = cArray
covTheta = thetaArray
# S_{1/2}
sEnsembleFull[nSim] = np.dot(
Clsim_full[lmin:],
np.dot(myJmn[lmin:, lmin:], Clsim_full[lmin:]))
nSim += 1
if doTime:
print 'time elapsed: ', int(
(time.time() - startTime) / 60.), ' minutes'
# free the RAM used by SpICE's RAM disk
ramDiskOutput = subprocess.check_output('./ramdisk.sh delete ' + diskID,
shell=True)
print ramDiskOutput
avgEnsembleFull = np.average(covEnsembleFull, axis=0)
stdEnsembleFull = np.std(covEnsembleFull, axis=0)
# do I need a better way to describe confidence interval?
avgEnsembleCut = np.average(covEnsembleCut, axis=0)
stdEnsembleCut = np.std(covEnsembleCut, axis=0)
Clsim_full_avg = Clsim_full_sum / nSims
# save results
saveFile1 = "simStatResultC.npy"
np.save(
saveFile1,
np.vstack((thetaArray, avgEnsembleFull, stdEnsembleFull,
avgEnsembleCut, stdEnsembleCut)))
saveFile2 = "simStatC_SMICA.npy"
np.save(saveFile2, np.vstack((thetaArray2sp, C_SMICAsp, C_SMICAmaskedsp)))
saveFile3 = "simStatResultS.npy"
np.save(
saveFile3,
np.vstack((np.hstack((np.array(S_SMICAnomasksp), sEnsembleFull)),
np.hstack((np.array(S_SMICAmaskedsp), sEnsembleCut)))))
doPlot = True
if doPlot:
print 'plotting C_l... '
#print ell.size,conv.size,primCl.size,crossCl.size,lateCl.size
plt.plot(ell[:lmax + 1],
conv[:lmax + 1] * (primCl + 2 * crossCl + lateCl)[:lmax + 1],
label='model D_l')
plt.plot(ell[:lmax + 1],
conv[:lmax + 1] * Clsim_full_avg,
label='ensemble average D_l')
plt.legend()
plt.show()
makePlots(saveFile1=saveFile1,
saveFile2=saveFile2,
saveFile3=saveFile3)
# S_{1/2} output
print ''
print 'using CIC method: '
#print 'S_{1/2}(anafast): SMICA, no mask: ',S_SMICAnomask,', masked: ',S_SMICAmasked
print 'S_{1/2}(spice): SMICA, no mask: ', S_SMICAnomasksp, ', masked: ', S_SMICAmaskedsp
print ''
print 'using CCdx method: '
#print 'S_{1/2}(anafast): SMICA, no mask: ',SSnm2,', masked: ',SSmd2
print 'S_{1/2}(spice): SMICA, no mask: ', SSnm2sp, ', masked: ', SSmd2sp
print ''
def test(useCLASS=1,
useLensing=1,
classCamb=1,
nSims=1000,
lmax=100,
lmin=2,
newSMICA=False,
newDeg=False,
suppressC2=False,
suppFactor=0.23):
"""
code for testing the other functions in this module
Inputs:
useCLASS: set to 1 to use CLASS, 0 to use CAMB
CLASS Cl has early/late split at z=50
CAMB Cl has ISWin/out split: ISWin: 0.4<z<0.75, ISWout: the rest
Note: CAMB results include primary in ISWin and ISWout (not as intended)
default: 1
useLensing: set to 1 to use lensed Cl, 0 for non-lensed
default: 1
classCamb: if 1: use the CAMB format of CLASS output, if 0: use CLASS format
Note: parameter not used if useCLASS = 0
default: 1
nSims: the number of simulations to do for ensemble
default: 1000
lmax: the highest l to include in Legendre transforms
default: 100
lmin: the lowest l to include in S_{1/2} = CIC calculations
default: 2
newSMICA: set to True to recalculate SMICA results
default: False
newDeg: set to True to recalculate map and mask degredations
(only if newSMICA is also True)
default: False
suppressC2: set to True to suppress theoretical C_2 by suppFactor
before creating a_lm.s
Default: False
suppFactor: multiplies C_2 if suppressC2 is True
Default: 0.23 # from Tegmark et. al. 2003, figure 13 (WMAP)
"""
##############################################################################
# load theoretical power spectra
# load data
ell, fullCl, primCl, lateCl, crossCl = gcp.loadCls(useCLASS=useCLASS,
useLensing=useLensing,
classCamb=classCamb)
# fill beginning with zeros
startEll = int(ell[0])
ell = np.append(np.arange(startEll), ell)
fullCl = np.append(np.zeros(startEll), fullCl)
primCl = np.append(np.zeros(startEll), primCl)
lateCl = np.append(np.zeros(startEll), lateCl)
crossCl = np.append(np.zeros(startEll), crossCl)
# suppress C_2 to see what happens in enesmble
#suppressC2 = False
#suppFactor = 0.23 # from Tegmark et. al. 2003, figure 13 (WMAP)
if suppressC2:
fullCl[2] *= suppFactor
primCl[2] *= suppFactor
lateCl[2] *= suppFactor
crossCl[2] *= suppFactor
conv = ell * (ell + 1) / (2 * np.pi)
#print ell,conv #ell[0]=2.0
# apply beam and pixel window functions to power spectra
# note: to ignore the non-constant pixel shape, W(l) must be > B(l)
# however, this is not true for NSIDE=128 and gauss_beam(5')
# Here I ignore this anyway and proceed
myNSIDE = 128 # must be same NSIDE as in sims.getSMICA function
Wpix = hp.pixwin(myNSIDE)
Bsmica = hp.gauss_beam(5. / 60 * np.pi / 180) # 5 arcmin
WlMax = Wpix.size
if WlMax < lmax:
print 'die screaming!!!'
return 0
fullCl = fullCl[:WlMax] * (Wpix * Bsmica)**2
primCl = primCl[:WlMax] * (Wpix * Bsmica)**2
lateCl = lateCl[:WlMax] * (Wpix * Bsmica)**2
crossCl = crossCl[:WlMax] * (Wpix * Bsmica)**2
# note: i tried sims without this scaling, and results seemed the same at a glance
##############################################################################
# load SMICA data, converted to C(theta), via SpICE
if newSMICA:
theta_i = 0.0 #degrees
theta_f = 180.0 #degrees
nSteps = 1800
thetaArray2sp, C_SMICAsp, C_SMICAmaskedsp, S_SMICAnomasksp, S_SMICAmaskedsp = \
sims.getSMICA(theta_i=theta_i,theta_f=theta_f,nSteps=nSteps,lmax=lmax,lmin=lmin,
newSMICA=newSMICA,newDeg=newDeg,useSPICE=True)
# filenames for SpICE to use
# super lame that spice needs to read/write from disk, but here goes...
RAMdisk = '/Volumes/ramdisk/'
ClTempFile = RAMdisk + 'tempCl.fits'
mapTempFile = RAMdisk + 'tempMap.fits'
mapDegFile = RAMdisk + 'smicaMapDeg.fits' # this should have been created by sims.getSMICA
maskDegFile = RAMdisk + 'maskMapDeg.fits' # this should have been created by sims.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")
ClsmicaCut = hp.read_cl(ClTempFile)
# find S_{1/2} for SMICA. Should actually optimize but see what happens here first.
#myJmn = legprodint.getJmn(endX=0.5,lmax=lmax,doSave=False)
#Ssmica = np.dot(ClsmicaCut[lmin:lmax+1],np.dot(myJmn[lmin:,lmin:],
# ClsmicaCut[lmin:lmax+1]))*1e24 #K^4 to microK^4
##############################################################################
# create ensemble of realizations and gather statistics
spiceMax = myNSIDE * 3 # should be lmax+1 for SpICE
ClEnsembleCut = np.zeros([nSims, spiceMax])
simEll = np.arange(spiceMax)
doTime = True # to time the run and print output
startTime = time.time()
for nSim in range(nSims):
print 'starting masked Cl sim ', nSim + 1, ' of ', nSims
alm_prim, alm_late = hp.synalm((primCl, lateCl, crossCl),
lmax=lmax,
new=True)
mapSim = hp.alm2map(alm_prim + alm_late, myNSIDE, lmax=lmax)
hp.write_map(mapTempFile, mapSim)
ispice(mapTempFile,
ClTempFile,
maskfile1=maskDegFile,
subav="YES",
subdipole="YES")
ClEnsembleCut[nSim] = hp.read_cl(ClTempFile)
doPlot = False #True
if doPlot:
gcp.showCl(simEll[:lmax + 1],
ClEnsembleCut[nSim, :lmax + 1],
title='power spectrum of simulation ' + str(nSim + 1))
timeInterval1 = time.time() - startTime
if doTime: print 'time elapsed: ', int(timeInterval1 / 60.), ' minutes'
# free the RAM used by SpICE's RAM disk
ramDiskOutput = subprocess.check_output('./ramdisk.sh delete ' + diskID,
shell=True)
print ramDiskOutput
# put SMICA in as 0th member of the ensemble; 1e12 to convert K^2 to microK^2
ClEnsembleCut = np.vstack((ClsmicaCut * 1e12, ClEnsembleCut))
nSims += 1
##############################################################################
# create S(x) for each C_l, using interpolation
nXvals = 181
thetaVals = np.linspace(0, 180, nXvals) # one degree intervals
xVals = np.cos(thetaVals * np.pi / 180)
Jmnx = np.empty([nXvals, lmax + 1, lmax + 1])
for index, xVal in enumerate(xVals):
Jmnx[index] = legprodint.getJmn(endX=xVal, lmax=lmax, doSave=False)
SxToInterpolate = np.empty(nXvals)
# create list of functions
dummy = lambda x: x**2
SofXList = [dummy for i in range(nSims)]
for nSim in range(nSims):
print 'starting S(x) sim ', nSim + 1, ' of ', nSims
for index, xVal in enumerate(xVals):
SxToInterpolate[index] = np.dot(
ClEnsembleCut[nSim, lmin:lmax + 1],
np.dot(Jmnx[index, lmin:, lmin:],
ClEnsembleCut[nSim, lmin:lmax + 1]))
SofX = interp1d(xVals, SxToInterpolate)
#SofXList = SofXList.append(SofX)
# Apparently appending a function to an empty list is not allowed. Instead:
SofXList[nSim] = SofX
#print SofXList#[nSim]
doPlot = False #True
if doPlot:
nplotx = (nXvals - 1) * 10 + 1
plotTheta = np.linspace(0, 180, nplotx)
plotx = np.cos(plotTheta * np.pi / 180)
plotS = SofXList[nSim](plotx)
plt.plot(plotx, plotS)
plt.title('S(x) for simulation ' + str(nSim + 1))
plt.show()
doPlot = True
if doPlot:
for nSim in range(nSims):
nplotx = (nXvals - 1) * 10 + 1
plotTheta = np.linspace(0, 180, nplotx)
plotx = np.cos(plotTheta * np.pi / 180)
plotS = SofXList[nSim](plotx)
plt.plot(plotx, plotS, label='sim ' + str(nSim + 1))
#plt.legend()
plt.title('S(x) for ' + str(nSims) + ' simulations')
plt.xlabel('x')
plt.ylabel('S_x')
plt.show()
##############################################################################
# create Pval(x) for each S(x), using ensemble
# Pval: probability of result equal to or more extreme
# create list of functions
PvalOfXList = [dummy for i in range(nSims)]
for nSim in range(nSims):
print 'starting Pval(x) sim ', nSim + 1, ' of ', nSims
def PvalOfX(x):
nUnder = 0 # will also include nEqual
nOver = 0
threshold = SofXList[nSim](x)
for nSim2 in range(nSims):
Sx = SofXList[nSim2](x)
if Sx > threshold:
nOver += 1
#print "Over! mySx: ",Sx,", threshold: ",threshold
else:
nUnder += 1
#print "Under! mySx: ",Sx,", threshold: ",threshold
#print "nUnder: ",nUnder,", nOver: ",nOver
return nUnder / float(nUnder + nOver)
PvalOfXList[nSim] = PvalOfX
##############################################################################
# find global minimum for each Pval(x)
# simply use same xVals as above, at one degree intervals
# if there are equal p-values along the range, the one with the highest xVal
# will be reported
PvalMinima = np.empty(nSims)
xValMinima = np.empty(nSims)
doTime = True # to time the run and print output
startTime = time.time()
for nSim in range(nSims):
print 'starting minimum Pval(x) search for sim ', nSim + 1, ' of ', nSims
PvalOfX = PvalOfXList[nSim]
#print 'function: ',PvalOfX
PvalMinima[nSim] = PvalOfX(1.0)
xValMinima[nSim] = 1.0
Pvals = np.empty(nXvals)
for index, xVal in enumerate(
xVals): # will start from 1 and go down to -1
myPval = PvalOfX(xVal)
Pvals[index] = myPval
#print "nSim: ",nSim,", n: ",index,", myPval: ",myPval,", PvalMinima[nSim]: ",PvalMinima[nSim]
if myPval < PvalMinima[
nSim] and xVal > -0.999: #avoid the instabililility
PvalMinima[nSim] = myPval
xValMinima[nSim] = xVal
#print 'nSim: ',nSim+1,', new x for minimum Pval: ',xVal
#raw_input("Finished sim "+str(nSim+1)+" of "+str(nSims)+". Press enter to continue")
doPlot = True #False#True
if doPlot: # and np.random.uniform() < 0.1: #randomly choose about 1/10 of them
plt.plot(xVals, Pvals)
plt.vlines(xValMinima[nSim], 0, 1)
plt.xlabel('x = cos(theta), min at ' + str(xValMinima[nSim]))
plt.ylabel('P-value')
plt.title('P-values for simulation ' + str(nSim + 1) + ' of ' +
str(nSims) + ', p_min = ' + str(PvalMinima[nSim]))
plt.xlim(-1.05, 1.05)
plt.ylim(-0.05, 1.05)
plt.show()
timeInterval2 = time.time() - startTime
if doTime: print 'time elapsed: ', int(timeInterval2 / 60.), ' minutes'
"""
# A MYSTERY! Something about the following code causes Pvals to always take
# the values of PvalOfXList[nSims](xVals) WTF? Omit for now.
# Testing seems to indicate that PvalOfXList functions still have different
# locations in memory, but they all seem to be evaluating the same.
# However, when the previous block of code is copied to come again after
# this one, it behaves properly again.
# see how well it did
doPlot = False#True
if doPlot:
nPlots = 10
for nPlot in range(nPlots):
print 'plot ',nPlot+1,' of ',nPlots
toPlot = nPlot#np.random.randint(0,high=nSims)
#for nSim in range(nSims):
Pvals = np.empty(nXvals)
PvalOfX = PvalOfXList[nPlot]
print 'function: ',PvalOfX
for index, xVal in enumerate(xVals):
Pvals[index] = PvalOfX(xVal)
#print index,Pvals[index]
#print Pvals
plt.plot(xVals,Pvals)
plt.vlines(xValMinima[toPlot],0,1)
plt.xlabel('x = cos(theta), min at '+str(xValMinima[toPlot]))
plt.ylabel('P-value')
plt.title('P-values for simulation '+str(toPlot+1)+' of '+str(nSims))
plt.show()
"""
##############################################################################
# create distribution of S(xValMinima)
SxEnsembleMin = np.empty(nSims)
for nSim in range(nSims):
SxEnsembleMin[nSim] = SofXList[nSim](xValMinima[nSim])
# extract SMICA result
Ssmica = SxEnsembleMin[0]
##############################################################################
# plot/print results
print 'plotting S_x distribution... '
myBins = np.logspace(1, 7, 100)
plt.axvline(x=Ssmica, color='g', linewidth=3, label='SMICA masked')
plt.hist(SxEnsembleMin[1:], bins=myBins, histtype='step', label='cut sky')
# [1:] to omit SMICA value
plt.gca().set_xscale("log")
plt.legend()
plt.xlabel('S_x (microK^4)')
plt.ylabel('Counts')
plt.title('S_x of ' + str(nSims - 1) +
' simulated CMBs') #-1 due to SMICA in zero position
plt.show()
print ' '
print 'nSims = ', nSims - 1
print 'time interval 1: ', timeInterval1, 's, time interval 2: ', timeInterval2, 's'
print ' => ', timeInterval1 / (nSims - 1), ' s/sim, ', timeInterval2 / (
nSims - 1), ' s/sim'
print 'SMICA optimized S_x: S = ',Ssmica,', for x = ',xValMinima[0], \
', with p-value ',PvalMinima[0]
print ' '
print 'step 3: profit'
print ''
def test(nSims=100,
lmax=100,
lmin=2,
partialMax=4,
useCLASS=1,
useLensing=1,
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
print ''
def test(useCLASS=1,
useLensing=1,
classCamb=1,
nSims=1000,
lmax=100,
lmin=2,
newSMICA=False,
newDeg=False,
suppressC2=False,
suppFactor=0.23,
filterC2=False,
filtFacLow=0.1,
filtFacHigh=0.2,
doCovar=False):
"""
code for testing the other functions in this module
Inputs:
useCLASS: set to 1 to use CLASS, 0 to use CAMB
CLASS Cl has early/late split at z=50
CAMB Cl has ISWin/out split: ISWin: 0.4<z<0.75, ISWout: the rest
Note: CAMB results include primary in ISWin and ISWout (not as intended)
default: 1
useLensing: set to 1 to use lensed Cl, 0 for non-lensed
default: 1
classCamb: if 1: use the CAMB format of CLASS output, if 0: use CLASS format
Note: parameter not used if useCLASS = 0
default: 1
nSims: the number of simulations to do for ensemble
default: 1000
lmax: the highest l to include in Legendre transforms
default: 100
lmin: the lowest l to include in S_{1/2} = CIC calculations
default: 2
newSMICA: set to True to recalculate SMICA results
default: False
newDeg: set to True to recalculate map and mask degredations
(only if newSMICA is also True)
default: False
suppressC2: set to True to suppress theoretical C_2 (quadrupole) by
suppFactor before creating a_lm.s
Default: False
suppFactor: multiplies C_2 if suppressC2 is True
Default: 0.23 # from Tegmark et. al. 2003, figure 13 (WMAP)
filterC2 : set to true to filter simulated CMBs after spice calculates
cut sky C_l. Sims will pass filter if C_2 * filtFacLow < C_2^sim <
C_2 * filtFacHigh.
Default: False
filtFacLow,filtFacHigh: defines C_2 range for passing simulated CMBs
Default: 0.1,0.2
doCovar: set to True to calculate C(theta) and S_{1/2} distritutions for ensemble
Note: meant to capture functionality from sim_stats.py; ZK 2016.11.13
Default: False
"""
##############################################################################
# load theoretical power spectra
# load data
ell, fullCl, primCl, lateCl, crossCl = gcp.loadCls(useCLASS=useCLASS,
useLensing=useLensing,
classCamb=classCamb)
# fill beginning with zeros
startEll = int(ell[0])
ell = np.append(np.arange(startEll), ell)
fullCl = np.append(np.zeros(startEll), fullCl)
primCl = np.append(np.zeros(startEll), primCl)
lateCl = np.append(np.zeros(startEll), lateCl)
crossCl = np.append(np.zeros(startEll), crossCl)
# suppress C_2 to see what happens in enesmble
if suppressC2:
fullCl[2] *= suppFactor
primCl[2] *= suppFactor
lateCl[2] *= suppFactor
crossCl[2] *= suppFactor
conv = ell * (ell + 1) / (2 * np.pi)
#print ell,conv #ell[0]=2.0
# apply beam and pixel window functions to power spectra
# note: to ignore the non-constant pixel shape, W(l) must be > B(l)
# however, this is not true for NSIDE=128 and gauss_beam(5')
# Here I ignore this anyway and proceed
myNSIDE = 128 # must be same NSIDE as in sims.getSMICA function
Wpix = hp.pixwin(myNSIDE)
Bsmica = hp.gauss_beam(5. / 60 * np.pi / 180) # 5 arcmin
WlMax = Wpix.size
if WlMax < lmax:
print 'die screaming!!!'
return 0
fullCl = fullCl[:WlMax] * (Wpix * Bsmica)**2
primCl = primCl[:WlMax] * (Wpix * Bsmica)**2
lateCl = lateCl[:WlMax] * (Wpix * Bsmica)**2
crossCl = crossCl[:WlMax] * (Wpix * Bsmica)**2
# note: i tried sims without this scaling, and results seemed the same at a glance
##############################################################################
# load SMICA data, converted to C_l, via SpICE
if newSMICA or doCovar:
theta_i = 0.0 #degrees
theta_f = 180.0 #degrees
nSteps = 1800
thetaArray2sp, C_SMICAsp, C_SMICAmaskedsp, S_SMICAnomasksp, S_SMICAmaskedsp = \
sims.getSMICA(theta_i=theta_i,theta_f=theta_f,nSteps=nSteps,lmax=lmax,lmin=lmin,
newSMICA=newSMICA,newDeg=newDeg,useSPICE=True)
# filenames for SpICE to use
# super lame that spice needs to read/write from disk, but here goes...
RAMdisk = '/Volumes/ramdisk/'
ClTempFile = RAMdisk + 'tempCl.fits'
mapTempFile = RAMdisk + 'tempMap.fits'
mapDegFile = RAMdisk + 'smicaMapDeg.fits' # this should have been created by sims.getSMICA
maskDegFile = RAMdisk + 'maskMapDeg.fits' # this should have been created by sims.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")
ClsmicaCut = hp.read_cl(ClTempFile)
# find S_{1/2} for SMICA. Should actually optimize but see what happens here first.
if doCovar:
myJmn = legprodint.getJmn(endX=0.5, lmax=lmax, doSave=False)
#Ssmica = np.dot(ClsmicaCut[lmin:lmax+1],np.dot(myJmn[lmin:,lmin:],
# ClsmicaCut[lmin:lmax+1]))*1e24 #K^4 to microK^4
##############################################################################
# create ensemble of realizations and gather statistics
spiceMax = myNSIDE * 3 # should be lmax+1 for SpICE
ClEnsembleCut = np.zeros([nSims, spiceMax])
if doCovar:
ClEnsembleFull = np.zeros([nSims, lmax + 1])
simEll = np.arange(spiceMax)
# option for creating C(\theta) and S_{1/2} ensembles
if doCovar:
cEnsembleCut = np.zeros([nSims, nSteps + 1])
cEnsembleFull = np.zeros([nSims, nSteps + 1])
sEnsembleCut = np.zeros(nSims)
sEnsembleFull = np.zeros(nSims)
doTime = True # to time the run and print output
startTime = time.time()
#for nSim in range(nSims):
nSim = 0
while nSim < nSims:
print 'starting masked Cl sim ', nSim + 1, ' of ', nSims
alm_prim, alm_late = hp.synalm((primCl, lateCl, crossCl),
lmax=lmax,
new=True)
mapSim = hp.alm2map(alm_prim + alm_late, myNSIDE, lmax=lmax)
hp.write_map(mapTempFile, mapSim)
if doCovar:
ClEnsembleFull[nSim] = hp.alm2cl(alm_prim + alm_late)
ispice(mapTempFile,
ClTempFile,
maskfile1=maskDegFile,
subav="YES",
subdipole="YES")
ClEnsembleCut[nSim] = hp.read_cl(ClTempFile)
# Check for low power of cut sky C_2
if (filterC2 == True
and fullCl[2] * filtFacHigh > ClEnsembleCut[nSim, 2]
and ClEnsembleCut[nSim, 2] > fullCl[2] * filtFacLow
) or filterC2 == False:
doPlot = False #True
if doPlot:
gcp.showCl(simEll[:lmax + 1],
ClEnsembleCut[nSim, :lmax + 1],
title='power spectrum of simulation ' +
str(nSim + 1))
if doCovar:
# note: getCovar uses linspace in x for thetaArray
thetaArray, cArray = sims.getCovar(simEll[:lmax + 1],
ClEnsembleCut[nSim, :lmax +
1],
theta_i=theta_i,
theta_f=theta_f,
nSteps=nSteps,
lmin=lmin)
cEnsembleCut[nSim] = cArray
thetaArray, cArray = sims.getCovar(simEll[:lmax + 1],
ClEnsembleFull[nSim, :lmax +
1],
theta_i=theta_i,
theta_f=theta_f,
nSteps=nSteps,
lmin=lmin)
cEnsembleFull[nSim] = cArray
# S_{1/2}
sEnsembleCut[nSim] = np.dot(
ClEnsembleCut[nSim, lmin:lmax + 1],
np.dot(myJmn[lmin:, lmin:], ClEnsembleCut[nSim,
lmin:lmax + 1]))
sEnsembleFull[nSim] = np.dot(
ClEnsembleFull[nSim, lmin:lmax + 1],
np.dot(myJmn[lmin:, lmin:], ClEnsembleFull[nSim,
lmin:lmax + 1]))
nSim += 1
timeInterval1 = time.time() - startTime
if doTime: print 'time elapsed: ', int(timeInterval1 / 60.), ' minutes'
# free the RAM used by SpICE's RAM disk
ramDiskOutput = subprocess.check_output('./ramdisk.sh delete ' + diskID,
shell=True)
print ramDiskOutput
# put SMICA in as 0th member of the ensemble; 1e12 to convert K^2 to microK^2
ClEnsembleCut = np.vstack((ClsmicaCut * 1e12, ClEnsembleCut))
nSims += 1
##############################################################################
# create S(x) for each C_l, using interpolation
nXvals = 181
thetaVals = np.linspace(0, 180, nXvals) # one degree intervals
xVals = np.cos(thetaVals * np.pi / 180)
Jmnx = np.empty([nXvals, lmax + 1, lmax + 1])
for index, xVal in enumerate(xVals):
Jmnx[index] = legprodint.getJmn(endX=xVal, lmax=lmax, doSave=False)
SxToInterpolate = np.empty(nXvals)
# create list of functions
#dummy = lambda x: x**2
#SofXList = [dummy for i in range(nSims)]
# here is where this program starts to diverge from the purely python version
# create array to hold S_x values
SxValsArray = np.empty([nSims, nXvals])
for nSim in range(nSims):
print 'starting S(x) sim ', nSim + 1, ' of ', nSims
for index, xVal in enumerate(xVals): #not using xVal?
SxToInterpolate[index] = np.dot(
ClEnsembleCut[nSim, lmin:lmax + 1],
np.dot(Jmnx[index, lmin:, lmin:],
ClEnsembleCut[nSim, lmin:lmax + 1]))
#SofX = interp1d(xVals,SxToInterpolate)
#SofXList[nSim] = SofX
SxValsArray[nSim] = SxToInterpolate
"""
#print SofXList#[nSim]
doPlot=False#True
if doPlot:
nplotx = (nXvals-1)*10+1
plotTheta = np.linspace(0,180,nplotx)
plotx = np.cos(plotTheta*np.pi/180)
plotS = SofXList[nSim](plotx)
plt.plot(plotx,plotS)
plt.title('S(x) for simulation '+str(nSim+1))
plt.show()
doPlot = False#True
if doPlot:
for nSim in range(nSims):
nplotx = (nXvals-1)*10+1
plotTheta = np.linspace(0,180,nplotx)
plotx = np.cos(plotTheta*np.pi/180)
plotS = SofXList[nSim](plotx)
plt.plot(plotx,plotS,label='sim '+str(nSim+1))
#plt.plot(xVals,SxValsArray[nSim],label='sim '+str(nSim+1))
#plt.legend()
plt.title('S(x) for '+str(nSims)+ 'simulations')
plt.xlabel('x')
plt.ylabel('S_x')
plt.show()
"""
# Kludge for extracting the S(x) ensemble to disk for Jackknife testing later
saveAndExit = False #True
saveAndExitFile = 'SofXEnsemble.npy'
if saveAndExit:
np.save(saveAndExitFile, np.vstack((xVals, SxValsArray)))
print 'saving file ', saveAndExitFile, ' and exiting.'
return 0
##############################################################################
# send data to c library function in optimizeSx.so
xStart = -1.0
xEnd = 1.0
nSearch = 181 # same num as nXvals for now, but spaced equally in x, not theta
PvalMinima = np.empty(nSims) # for return values
XvalMinima = np.empty(nSims) # for return values
doTime = True # to time the run and print output
startTime = time.time()
optSx(xVals, nXvals, SxValsArray, nSims, xStart, xEnd, nSearch, PvalMinima,
XvalMinima)
timeInterval2 = time.time() - startTime
if doTime: print 'time elapsed: ', int(timeInterval2 / 60.), ' minutes'
##############################################################################
# create distribution of S(XvalMinima)
SxEnsembleMin = np.empty(nSims)
for nSim in range(nSims):
# need to interpolate since optSx uses interpolation
SofX = interp1d(xVals, SxValsArray[nSim])
SxEnsembleMin[nSim] = SofX(XvalMinima[nSim])
##############################################################################
# save S_x, P(x), x results
saveFile = "optSxResult.npy"
np.save(saveFile, np.vstack((PvalMinima, XvalMinima, SxEnsembleMin)))
saveFileC2 = "optSxC2.npy"
np.save(saveFileC2, ClEnsembleCut[:, 2]) #for C_2
# save C(theta) and S{1/2} results
if doCovar:
avgEnsembleFull = np.average(cEnsembleFull, axis=0)
stdEnsembleFull = np.std(cEnsembleFull, axis=0)
# do I need a better way to describe confidence interval?
avgEnsembleCut = np.average(cEnsembleCut, axis=0)
stdEnsembleCut = np.std(cEnsembleCut, axis=0)
saveFile1 = "simStatResultC.npy"
np.save(
saveFile1,
np.vstack((thetaArray, avgEnsembleFull, stdEnsembleFull,
avgEnsembleCut, stdEnsembleCut)))
saveFile2 = "simStatC_SMICA.npy"
np.save(saveFile2,
np.vstack((thetaArray2sp, C_SMICAsp, C_SMICAmaskedsp)))
saveFile3 = "simStatResultS.npy"
np.save(
saveFile3,
np.vstack((np.hstack((np.array(S_SMICAnomasksp), sEnsembleFull)),
np.hstack((np.array(S_SMICAmaskedsp), sEnsembleCut)))))
##############################################################################
# plot/print results
makePlots(saveFile=saveFile, suppressC2=suppressC2)
#makeCornerPlot(saveFile=saveFile,suppressC2=suppressC2)
makeCornerPlotSmall(saveFile=saveFile, suppressC2=suppressC2)
c2pval = makeC2Plot(saveFile=saveFileC2)
if doCovar:
sims.makePlots(saveFile1=saveFile1,
saveFile2=saveFile2,
saveFile3=saveFile3)
pv = PvalPval(saveFile=saveFile)
print ' '
print 'nSims = ', nSims - 1
print 'time interval 1: ', timeInterval1, 's, time interval 2: ', timeInterval2, 's'
print ' => ', timeInterval1 / (nSims - 1), ' s/sim, ', timeInterval2 / (
nSims - 1), ' s/sim'
print 'SMICA optimized S_x: S = ',SxEnsembleMin[0],', for x = ',XvalMinima[0], \
', with p-value ',PvalMinima[0]
print 'P-value of P-value for SMICA: ', pv
print ' '
print 'p-value of C_2^SMICA in distribution: ', c2pval
print ' '
print 'step 3: profit'
print ''
def test(useCLASS=1,
useLensing=1,
classCamb=1,
nSims=1000,
lmax=3,
lmin=2,
newSMICA=True,
newDeg=False):
"""
code for testing the other functions in this module
Inputs:
useCLASS: set to 1 to use CLASS, 0 to use CAMB
CLASS Cl has early/late split at z=50
CAMB Cl has ISWin/out split: ISWin: 0.4<z<0.75, ISWout: the rest
Note: CAMB results include primary in ISWin and ISWout (not as intended)
default: 1
useLensing: set to 1 to use lensed Cl, 0 for non-lensed
default: 1
classCamb: if 1: use the CAMB format of CLASS output, if 0: use CLASS format
Note: parameter not used if useCLASS = 0
default: 1
nSims: the number of simulations to do for ensemble
default: 1000
lmax: the highest l to include in Legendre transforms
default: 3
lmin: the lowest l to include in S_{1/2} = CIC calculations
default: 2
newSMICA: set to True to recalculate SMICA results
default: True
newDeg: set to True to recalculate map and mask degredations
default: False
"""
##############################################################################
# load theoretical power spectra
# load data
ell, fullCl, primCl, lateCl, crossCl = gcp.loadCls(useCLASS=useCLASS,
useLensing=useLensing,
classCamb=classCamb)
# fill beginning with zeros
startEll = ell[0]
ell = np.append(np.arange(startEll), ell)
fullCl = np.append(np.zeros(startEll), fullCl)
primCl = np.append(np.zeros(startEll), primCl)
lateCl = np.append(np.zeros(startEll), lateCl)
crossCl = np.append(np.zeros(startEll), crossCl)
# suppress C_2 to see what happens in enesmble
suppressC2 = False
suppFactor = 0.23 # from Tegmark et. al. 2003, figure 13 (WMAP)
if suppressC2:
fullCl[2] *= suppFactor
primCl[2] *= suppFactor
lateCl[2] *= suppFactor
crossCl[2] *= suppFactor
conv = ell * (ell + 1) / (2 * np.pi)
#print ell,conv #ell[0]=2.0
# apply beam and pixel window functions to power spectra
# note: to ignore the non-constant pixel shape, W(l) must be > B(l)
# however, this is not true for NSIDE=128 and gauss_beam(5')
# Here I ignore this anyway and proceed
myNSIDE = 128 # must be same NSIDE as in sims.getSMICA function
Wpix = hp.pixwin(myNSIDE)
Bsmica = hp.gauss_beam(5. / 60 * np.pi / 180) # 5 arcmin
WlMax = Wpix.size
if WlMax < lmax:
print 'die screaming!!!'
return 0
fullCl = fullCl[:WlMax] * (Wpix * Bsmica)**2
primCl = primCl[:WlMax] * (Wpix * Bsmica)**2
lateCl = lateCl[:WlMax] * (Wpix * Bsmica)**2
crossCl = crossCl[:WlMax] * (Wpix * Bsmica)**2
# note: i tried sims without this scaling, and results seemed the same at a glance
# extract the part I want
myL = ell[:lmax]
myCl = fullCl[:lmax]
##############################################################################
# load SMICA data and filter out all but low-l a_lm.s
theta_i = 0.0 #degrees
theta_f = 180.0 #degrees
nSteps = 1800
# default: lmax=3,lmin=2
#newSMICA = True # so I don't use lmax=100 from previous calc.
thetaArray2sp, C_SMICAsp, C_SMICAmaskedsp, S_SMICAnomasksp, S_SMICAmaskedsp = \
sims.getSMICA(theta_i=theta_i,theta_f=theta_f,nSteps=nSteps,lmax=lmax,lmin=lmin,
newSMICA=newSMICA,newDeg=newDeg,useSPICE=True)
##############################################################################
# create ensemble of realizations and gather statistics
covEnsembleFull = np.zeros([nSims, nSteps + 1]) # for maskless
covEnsembleCut = np.zeros([nSims, nSteps + 1]) # for masked
sEnsembleFull = np.zeros(nSims)
sEnsembleCut = np.zeros(nSims)
covTheta = np.array([])
# get Jmn matrix for harmonic space S_{1/2} calc.
myJmn = getJmn(lmax=lmax)
doTime = True # to time the run and print output
startTime = time.time()
for nSim in range(nSims):
print 'starting sim ', nSim + 1, ' of ', nSims
alm_prim, alm_late = hp.synalm((primCl, lateCl, crossCl),
lmax=lmax,
new=True)
# calculate C(theta) of simulation
Clsim_prim = hp.alm2cl(alm_prim)
Clsim_late = hp.alm2cl(alm_late)
Clsim_cros = hp.alm2cl(alm_prim, alm_late)
Clsim_full = Clsim_prim + 2 * Clsim_cros + Clsim_late
# use Cl_sim_full to omit prim/late distinction for now
#Clsim_full_sum += Clsim_full
# first without mask
# note: getCovar uses linspace in x for thetaArray
thetaArray, cArray = sims.getCovar(ell[:lmax + 1],
Clsim_full[:lmax + 1],
theta_i=theta_i,
theta_f=theta_f,
nSteps=nSteps,
lmin=lmin)
covEnsembleFull[nSim] = cArray
covTheta = thetaArray
# S_{1/2}
sEnsembleFull[nSim] = np.dot(
Clsim_full[lmin:], np.dot(myJmn[lmin:, lmin:], Clsim_full[lmin:]))
# now with a mask
# should have default RING ordering
# pixel window and beam already accounted for in true Cls
#mapSim = hp.alm2map(alm_prim+alm_late,myNSIDE,lmax=lmax,pixwin=True,sigma=5./60*np.pi/180)
mapSim = hp.alm2map(alm_prim + alm_late, myNSIDE, lmax=lmax)
# super lame that spice needs to read/write from disk, but here goes...
mapTempFile = 'tempMap.fits'
ClTempFile = 'tempCl.fits'
maskDegFile = 'maskMapDeg.fits' # this should have been created by sims.getSMICA
hp.write_map(mapTempFile, mapSim)
ispice(mapTempFile,
ClTempFile,
maskfile1=maskDegFile,
subav="YES",
subdipole="YES")
Cl_masked = hp.read_cl(ClTempFile)
ell2 = np.arange(Cl_masked.shape[0])
# note: getCovar uses linspace in x for thetaArray
thetaArray, cArray2 = sims.getCovar(ell2[:lmax + 1],
Cl_masked[:lmax + 1],
theta_i=theta_i,
theta_f=theta_f,
nSteps=nSteps,
lmin=lmin)
covEnsembleCut[nSim] = cArray2
# S_{1/2}
sEnsembleCut[nSim] = np.dot(
Cl_masked[lmin:lmax + 1],
np.dot(myJmn[lmin:, lmin:], Cl_masked[lmin:lmax + 1]))
doPlot = False #True
if doPlot:
plt.plot(thetaArray, cArray)
plt.xlabel('theta (degrees)')
plt.ylabel('C(theta)')
plt.title('covariance of simulated CMB')
plt.show()
if doTime:
print 'time elapsed: ', int(
(time.time() - startTime) / 60.), ' minutes'
avgEnsembleFull = np.average(covEnsembleFull, axis=0)
stdEnsembleFull = np.std(covEnsembleFull, axis=0)
# do I need a better way to describe confidence interval?
avgEnsembleCut = np.average(covEnsembleCut, axis=0)
stdEnsembleCut = np.std(covEnsembleCut, axis=0)
#Clsim_full_avg = Clsim_full_sum / nSims
##############################################################################
# plot/print results
doPlot = True
if doPlot:
print 'plotting correlation functions... '
# first the whole sky statistics
plt.plot(thetaArray,
avgEnsembleFull,
label='sim. ensemble average (no mask)')
plt.fill_between(thetaArray,
avgEnsembleFull + stdEnsembleFull,
avgEnsembleFull - stdEnsembleFull,
alpha=0.25,
label='simulation 1sigma envelope')
#plt.plot(thetaArray2,C_SMICA,label='SMICA R2 (inpainted,anafast)')
plt.plot(thetaArray2sp, C_SMICAsp, label='SMICA R2 (inpainted,spice)')
plt.xlabel('theta (degrees)')
plt.ylabel('C(theta)')
plt.title('whole sky covariance of ' + str(nSims) +
' simulated CMBs, lmax=' + str(lmax))
plt.ylim([-500, 1000])
plt.plot([0, 180], [0, 0]) #horizontal line
plt.legend()
plt.show()
# now the cut sky
plt.plot(thetaArray,
avgEnsembleCut,
label='sim. ensemble average (masked)')
plt.fill_between(thetaArray,
avgEnsembleCut + stdEnsembleCut,
avgEnsembleCut - stdEnsembleCut,
alpha=0.25,
label='simulation 1sigma envelope')
#plt.plot(thetaArray2,C_SMICAmasked,label='SMICA R2 (masked ,anafast)')
plt.plot(thetaArray2sp,
C_SMICAmaskedsp,
label='SMICA R2 (masked ,spice)')
plt.xlabel('theta (degrees)')
plt.ylabel('C(theta)')
plt.title('cut sky covariance of ' + str(nSims) +
' simulated CMBs, lmax=' + str(lmax))
plt.ylim([-500, 1000])
plt.plot([0, 180], [0, 0]) #horizontal line
plt.legend()
plt.show()
print 'plotting S_{1/2} distributions... '
myBins = np.logspace(2, 7, 100)
plt.axvline(x=S_SMICAnomasksp,
color='b',
linewidth=3,
label='SMICA inpainted')
plt.axvline(x=S_SMICAmaskedsp,
color='g',
linewidth=3,
label='SMICA masked')
plt.hist(sEnsembleFull, bins=myBins, histtype='step', label='full sky')
plt.hist(sEnsembleCut, bins=myBins, histtype='step', label='cut sky')
plt.gca().set_xscale("log")
plt.legend()
plt.xlabel('S_{1/2} (microK^4)')
plt.ylabel('Counts')
plt.title('S_{1/2} of ' + str(nSims) + ' simulated CMBs')
plt.show()
# S_{1/2} output
print ''
print 'using CIC method: '
#print 'S_{1/2}(anafast): SMICA, no mask: ',S_SMICAnomask,', masked: ',S_SMICAmasked
print 'S_{1/2}(spice): SMICA, no mask: ', S_SMICAnomasksp, ', masked: ', S_SMICAmaskedsp
print ''
#print 'using CCdx method: '
#print 'S_{1/2}(anafast): SMICA, no mask: ',SSnm2,', masked: ',SSmd2
#print 'S_{1/2}(spice): SMICA, no mask: ',SSnm2sp,', masked: ',SSmd2sp
#print ''
##############################################################################
# step 3
print 'step 3: profit'