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fisherTools.py
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fisherTools.py
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import os
from numpy import *
import numpy
import scipy
import scipy.linalg
import cambWrapTools
import classWrapTools
# utilities for dictionaries
def onedDict(names1):
output = {}
for a in names1:
output[a] = {}
return output
def twodDict(names1, names2):
output = {}
for a in names1:
output[a] = {}
for b in names2:
output[a][b] = {}
return output
def threedDict(names1, names2, names3):
output = {}
for a in names1:
output[a] = {}
for b in names2:
output[a][b] = {}
for c in names3:
output[a][b][c] = {}
return output
def fourdDict(names1, names2, names3, names4):
output = {}
for a in names1:
output[a] = {}
for b in names2:
output[a][b] = {}
for c in names3:
output[a][b][c] = {}
for d in names4:
output[a][b][c][d] = {}
return output
def fivedDict(names1, names2, names3, names4, names5):
output = {}
for a in names1:
output[a] = {}
for b in names2:
output[a][b] = {}
for c in names3:
output[a][b][c] = {}
for d in names4:
output[a][b][c][d] = {}
for e in names5:
output[a][b][c][d][e] = {}
return output
# utilities for calculating Fisher forecasts
def noiseSpectra(l, noiseLevelT, useSqrt2 = True, beamArcmin = 1.4, beamFile = None, noiseLevelP = None):
#make a full set of noise spectra.
if beamFile == None:
beam_sigma_radians = (beamArcmin * numpy.pi / (180. * 60.)) / numpy.sqrt(8. * numpy.log(2) )
beamPower = numpy.exp(l * (l+1) * beam_sigma_radians**2)
print('** noiseSpectra: using analytic beam')
else:
beamVals = numpy.loadtxt(beamFile)
beamValsOnL = (scipy.interpolate.interp1d(beamVals[:,0], beamVals[:,1], bounds_error = False))(l)
beamPower = 1/(beamValsOnL**2)
print('** noiseSpectra: using beam from file')
noise_ster = (numpy.pi / (180. * 60))**2 * noiseLevelT**2
nl = len(l)
cl_TT = numpy.empty(nl)
cl_TT.fill(noise_ster)
cl_TT *= beamPower
cl_EE = numpy.empty(nl)
if useSqrt2:
cl_EE.fill(noise_ster * 2.)
else:
noise_sterP = (numpy.pi / (180. * 60))**2 * noiseLevelP**2
cl_EE.fill(noise_sterP)
cl_EE *= beamPower
cl_BB = numpy.empty(nl)
if useSqrt2:
cl_BB.fill(noise_ster * 2.)
else:
noise_sterP = (numpy.pi / (180. * 60))**2 * noiseLevelP**2
cl_BB.fill(noise_sterP)
cl_BB *= beamPower
cl_TE = numpy.empty(nl)
cl_TE.fill(0.)
output = {'l' : l,\
'cl_TT' : cl_TT,\
'cl_EE' : cl_EE,\
'cl_TE' : cl_TE,\
'cl_BB' : cl_BB,
'dl_TT' : cl_TT * l * (l + 1) / 2 / numpy.pi,\
'dl_EE' : cl_EE * l * (l + 1) / 2 / numpy.pi,\
'dl_TE' : cl_TE * l * (l + 1) / 2 / numpy.pi,\
'dl_BB' : cl_BB * l * (l + 1) / 2 / numpy.pi
}
return output
def getPlanckInvVarNoise(ells, includePol = True):
#numbers are taken from "Planck_pol.pdf" from https://cosmo.uchicago.edu/CMB-S4workshops/index.php/File:Planck_pol.pdf
freqs = ["30", "44", "70", "100", "143", "217", "353"]
nFreqs = len(freqs)
fwhmsArcmin = [33., 23., 14., 10., 7., 5., 5.]
tempNoisesUKarcmin = [145., 149., 137., 65., 43., 66., 200]
polNoisesUKarcmin = [numpy.inf, numpy.inf, 450., 103., 81., 134., 406.]
cmbNoiseSpectra = onedl(nFreqs)
#get noise curve for each frequency
for f, freq in enumerate(freqs):
cmbNoiseSpectra[f] = noiseSpectra(ells, \
noiseLevelT = tempNoisesUKarcmin[f], \
noiseLevelP = polNoisesUKarcmin[f], \
beamArcmin = fwhmsArcmin[f], \
useSqrt2 = False)
#now get the result via inverse-variance sum
polCombs = list((cmbNoiseSpectra[0]).keys())
overallResult = onedDict(polCombs)
for pc, polComb in enumerate(polCombs):
runningTotal = numpy.zeros(len(ells))
for f, freq in enumerate(freqs):
runningTotal += 1/cmbNoiseSpectra[f][polComb]
overallResult[polComb] = 1/runningTotal
#the ells got messed up as part of the process ... fix this.
overallResult['l'] = ells
if not includePol:
polCombsPolarization = ['cl_EE', 'cl_TE', 'cl_BB', 'dl_EE', 'dl_TE', 'dl_BB' ]
for polComb in polCombsPolarization:
overallResult[polComb] = numpy.inf * numpy.ones(len(ells))
return overallResult
def onedl(rows):
return [None] * rows
def getPowerDerivWithParams(cosmoFid, stepSizes, polCombs, cmbNoiseSpectraK, deflectionNoisesK,
spectrumTypes = ['unlensed', 'lensed', 'delensed', 'lensing'],
lmax = 5000,
fileNameBase = 'testing', paramsToDifferentiate = None,
accuracy = 2.,
useClass = False,
doLensedWithCAMB = False,
classExecDir = os.path.dirname(os.path.abspath(__file__)) + '/../../CLASS_delens/',
classDataDir = os.path.dirname(os.path.abspath(__file__)) + '/../../CLASS_delens/',
extraParams = dict()):
if paramsToDifferentiate == None:
paramsToDifferentiate = list(cosmoFid.keys())
nParams = len(paramsToDifferentiate)
oneSidedParams = ['DM_Pann']
if 'mnu' in cosmoFid.keys():
if cosmoFid['mnu'] < stepSizes['mnu']:
oneSidedParams.append('mnu')
oneSidedParamsIso = ['c_ad_cdi', 'c_ad_bi', 'c_ad_nid', 'c_ad_niv', \
'c_bi_cdi', 'c_bi_nid', 'c_bi_niv', \
'c_cdi_nid', 'c_cdi_niv', \
'c_nid_niv'] #could be + or - 1
powersPlus = dict()
powersMinus = dict()
for cosmo in paramsToDifferentiate:
print(('getting deriv w.r.t. %s' %cosmo))
cosmoPlus = cosmoFid.copy() #copy all params including those not being perturbed.
cosmoMinus = cosmoFid.copy()
cosmoPlus[cosmo] = cosmoPlus[cosmo] + stepSizes[cosmo]
cosmoMinus[cosmo] = cosmoMinus[cosmo] - stepSizes[cosmo]
if useClass is True:
powersPlus[cosmo], junk = classWrapTools.class_generate_data(cosmoPlus,
rootName = fileNameBase,
cmbNoise = cmbNoiseSpectraK,
deflectionNoise = deflectionNoisesK,
classExecDir = classExecDir,
classDataDir = classDataDir,
lmax = lmax,
extraParams = extraParams)
else:
powersPlus[cosmo], junk = classWrapTools.camb_class_generate_data(cosmoPlus,
rootName = fileNameBase,
cmbNoise = cmbNoiseSpectraK,
deflectionNoise = deflectionNoisesK,
classExecDir = classExecDir,
classDataDir = classDataDir,
lmax = lmax,
extraParams = extraParams,
accuracy = accuracy,
doLensedWithCAMB = doLensedWithCAMB)
#### For one-sided derivatives, use fiducial parameters for PowersMinus
if cosmo in oneSidedParams:
cosmoMinus = cosmoFid.copy()
#### isocurvature cross-correlation
if cosmo in oneSidedParamsIso:
if cosmoFid[cosmo] == 1.:
cosmoPlus = cosmoFid.copy()
elif cosmoFid[cosmo] == -1.:
cosmoMinus = cosmoFid.copy()
if useClass is True:
powersMinus[cosmo], junk = classWrapTools.class_generate_data(cosmoMinus,
rootName = fileNameBase,
cmbNoise = cmbNoiseSpectraK,
deflectionNoise = deflectionNoisesK,
classExecDir = classExecDir,
classDataDir = classDataDir,
lmax = lmax,
extraParams = extraParams)
else:
powersMinus[cosmo], junk = classWrapTools.camb_class_generate_data(cosmoMinus,
rootName = fileNameBase,
cmbNoise = cmbNoiseSpectraK,
deflectionNoise = deflectionNoisesK,
classExecDir = classExecDir,
classDataDir = classDataDir,
lmax = lmax,
extraParams = extraParams,
accuracy = accuracy,
doLensedWithCAMB = doLensedWithCAMB)
#PARAM DERIVATIVES
polCombsTemp = polCombs.copy()
if 'cl_dd' in polCombs:
polCombsTemp.remove('cl_dd')
paramDerivs = threedDict(paramsToDifferentiate, spectrumTypes, polCombsTemp)
for cosmo in paramsToDifferentiate:
#### Use this for one-sided derivatives (PowersMinus is PowersFid in this case)
if cosmo in oneSidedParams:
denom = stepSizes[cosmo]
else:
#### Other parameters use two-sided derivatives
denom = 2 * stepSizes[cosmo]
for pc, polComb in enumerate(polCombs):
if polComb == 'cl_dd':
if 'lensing' in spectrumTypes:
paramDerivs[cosmo]['lensing'] = dict()
paramDerivs[cosmo]['lensing']['cl_dd'] = \
(powersPlus[cosmo]['lensing']['cl_dd'] - powersMinus[cosmo]['lensing']['cl_dd']) / denom
else:
print('lensing must be in spectrum types to calculate cl_dd derivatives.')
else:
if 'unlensed' in spectrumTypes:
paramDerivs[cosmo]['unlensed'][polComb] = \
(powersPlus[cosmo]['unlensed'][polComb] - powersMinus[cosmo]['unlensed'][polComb]) / denom
if 'lensed' in spectrumTypes:
paramDerivs[cosmo]['lensed'][polComb] = \
(powersPlus[cosmo]['lensed'][polComb] - powersMinus[cosmo]['lensed'][polComb]) / denom
if 'delensed' in spectrumTypes:
paramDerivs[cosmo]['delensed'][polComb] = \
(powersPlus[cosmo]['delensed'][polComb] - powersMinus[cosmo]['delensed'][polComb]) / denom
return paramDerivs
def getParamDerivsBAOandH0(cosmoFid, stepSizes, redshifts, paramsToDifferentiate = None):
externalData = ['BAO', 'H0']
BAOPlus = dict()
BAOMinus = dict()
H0Plus = dict()
H0Minus = dict()
if paramsToDifferentiate == None:
paramsToDifferentiate = list(cosmoFid.keys())
nParams = len(paramsToDifferentiate)
oneSidedParams = ['DM_Pann']
if 'mnu' in cosmoFid.keys():
if cosmoFid['mnu'] < stepSizes['mnu']:
oneSidedParams.append('mnu')
for cosmo in paramsToDifferentiate:
print(('getting deriv w.r.t. %s' %cosmo))
cosmoPlus = cosmoFid.copy() #copy all params including those not being perturbed.
cosmoMinus = cosmoFid.copy()
cosmoPlus[cosmo] = cosmoPlus[cosmo] + stepSizes[cosmo]
cosmoMinus[cosmo] = cosmoMinus[cosmo] - stepSizes[cosmo]
#### For one-sided derivatives, use fiducial parameters for PowersMinus
if cosmo in oneSidedParams:
cosmoMinus = cosmoFid.copy()
BAOPlus[cosmo] = cambWrapTools.getBAOParams(cosmoPlus, redshifts)
BAOMinus[cosmo] = cambWrapTools.getBAOParams(cosmoMinus, redshifts)
H0Plus[cosmo] = cambWrapTools.get_H0_from_theta(cosmoPlus)
H0Minus[cosmo] = cambWrapTools.get_H0_from_theta(cosmoMinus)
#PARAM DERIVATIVES
paramDerivs = twodDict(paramsToDifferentiate, externalData)
for cosmo in paramsToDifferentiate:
#### Use this for one-sided derivatives (PowersMinus is PowersFid in this case)
if cosmo in oneSidedParams:
denom = stepSizes[cosmo]
else:
#### Other parameters use two-sided derivatives
denom = 2 * stepSizes[cosmo]
paramDerivs[cosmo]['BAO'] = (BAOPlus[cosmo][:,0] - BAOMinus[cosmo][:,0]) / denom
paramDerivs[cosmo]['H0'] = (H0Plus[cosmo] - H0Minus[cosmo]) / denom
return paramDerivs
def getBAODerivWithParams(cosmoFid, stepSizes, redshifts,
fileNameBase = 'testing',
paramsToDifferentiate = None,
classExecDir = os.path.dirname(os.path.abspath(__file__)) + '/../../CLASS_delens/',
classDataDir = os.path.dirname(os.path.abspath(__file__)) + '/../../CLASS_delens/',
extraParams = dict()):
if paramsToDifferentiate == None:
paramsToDifferentiate = list(cosmoFid.keys())
nParams = len(paramsToDifferentiate)
oneSidedParams = ['DM_Pann']
if 'mnu' in cosmoFid.keys():
if cosmoFid['mnu'] < stepSizes['mnu']:
oneSidedParams.append('mnu')
oneSidedParamsIso = ['c_ad_cdi', 'c_ad_bi', 'c_ad_nid', 'c_ad_niv', \
'c_bi_cdi', 'c_bi_nid', 'c_bi_niv', \
'c_cdi_nid', 'c_cdi_niv', \
'c_nid_niv'] #could be + or - 1
BAOPlus = dict()
BAOMinus = dict()
for cosmo in paramsToDifferentiate:
#print(('getting deriv w.r.t. %s' %cosmo))
cosmoPlus = cosmoFid.copy() #copy all params including those not being perturbed.
cosmoMinus = cosmoFid.copy()
cosmoPlus[cosmo] = cosmoPlus[cosmo] + stepSizes[cosmo]
cosmoMinus[cosmo] = cosmoMinus[cosmo] - stepSizes[cosmo]
#### For one-sided derivatives, use fiducial parameters for PowersMinus
if cosmo in oneSidedParams:
cosmoMinus = cosmoFid.copy()
#### isocurvature cross-correlation
if cosmo in oneSidedParamsIso:
if cosmoFid[cosmo] == 1.:
cosmoPlus = cosmoFid.copy()
elif cosmoFid[cosmo] == -1.:
cosmoMinus = cosmoFid.copy()
BAOPlus[cosmo] = classWrapTools.getBAOParams(cosmo = cosmoPlus,
redshifts = redshifts,
rootName = fileNameBase,
classExecDir = classExecDir,
classDataDir = classDataDir,
extraParams = extraParams
)
BAOMinus[cosmo] = classWrapTools.getBAOParams(cosmo = cosmoMinus,
redshifts = redshifts,
rootName = fileNameBase,
classExecDir = classExecDir,
classDataDir = classDataDir,
extraParams = extraParams
)
#PARAM DERIVATIVES
paramDerivs = onedDict(paramsToDifferentiate)
for cosmo in paramsToDifferentiate:
#### Use this for one-sided derivatives (PowersMinus is PowersFid in this case)
if cosmo in oneSidedParams or cosmo in oneSidedParamsIso:
denom = stepSizes[cosmo]
else:
#### Other parameters use two-sided derivatives
denom = 2 * stepSizes[cosmo]
paramDerivs[cosmo] = BAOPlus[cosmo] - BAOMinus[cosmo]
return paramDerivs
def getSecondDerivsBAOandH0(cosmoFid, stepSizes, redshifts, paramsToDifferentiate = None):
externalData = ['BAO', 'H0']
derivsPlus = dict()
derivsMinus = dict()
if paramsToDifferentiate == None:
paramsToDifferentiate = list(cosmoFid.keys())
nParams = len(paramsToDifferentiate)
oneSidedParams = ['DM_Pann']
if 'mnu' in cosmoFid.keys():
if cosmoFid['mnu'] < stepSizes['mnu']:
oneSidedParams.append('mnu')
for cosmo in paramsToDifferentiate:
print('getting second deriv w.r.t. %s' %cosmo)
cosmoPlus = cosmoFid.copy() #copy all params including those not being perturbed.
cosmoMinus = cosmoFid.copy()
cosmoPlus[cosmo] = cosmoPlus[cosmo] + stepSizes[cosmo]
cosmoMinus[cosmo] = cosmoMinus[cosmo] - stepSizes[cosmo]
derivsPlus[cosmo] = getParamDerivsBAOandH0(cosmoPlus, stepSizes, redshifts, paramsToDifferentiate)
#### For one-sided derivatives, use fiducial parameters for PowersMinus
if cosmo in oneSidedParams:
cosmoMinus = cosmoFid.copy()
derivsMinus[cosmo] = getParamDerivsBAOandH0(cosmoMinus, stepSizes, redshifts, paramsToDifferentiate)
#PARAM DERIVATIVES
secondDerivs = threedDict(paramsToDifferentiate, paramsToDifferentiate, externalData)
for cosmo1 in paramsToDifferentiate:
#### Use this for one-sided derivatives (derivsMinus is derivsFid in this case)
if cosmo1 in oneSidedParams:
denom = stepSizes[cosmo1]
else:
#### Other parameters use two-sided derivatives
denom = 2 * stepSizes[cosmo1]
for cosmo2 in paramsToDifferentiate:
for ed, exData in enumerate(externalData):
secondDerivs[cosmo1][cosmo2][exData] = \
(derivsPlus[cosmo1][cosmo2][exData] - derivsMinus[cosmo1][cosmo2][exData]) / denom
return secondDerivs
def getGaussianCov(powersFid, cmbNoiseSpectra, deflectionNoises, \
polCombsToUse = ['cl_TT', 'cl_TE', 'cl_EE', 'cl_dd'], \
spectrumTypes = ['unlensed', 'lensed', 'delensed'], \
lmax = 3000):
nPolCombsToUse = len(polCombsToUse)
ell = powersFid['unlensed']['l']
oneOver2ellPlusOne = 1. / (2. * ell[:lmax-2] + 1.)
nElls = len(oneOver2ellPlusOne)
covs = dict()
for st, spectrumType in enumerate(spectrumTypes):
covs[spectrumType] = numpy.zeros((nPolCombsToUse, nPolCombsToUse, nElls))
#on-diagonals for TT and EE
for polComb1 in ['cl_TT', 'cl_EE', 'cl_BB']:
if polComb1 in polCombsToUse:
pc1 = polCombsToUse.index(polComb1)
covs[spectrumType][pc1, pc1, :] = \
2. * oneOver2ellPlusOne \
* ((powersFid[spectrumType][polComb1][:lmax-2] \
+ cmbNoiseSpectra[polComb1][:lmax-2])**2)
#on-diagonal for cl_TE
if ('cl_TE' in polCombsToUse):
pcTE = polCombsToUse.index('cl_TE')
covs[spectrumType][pcTE, pcTE, :] = \
1. * oneOver2ellPlusOne \
* (powersFid[spectrumType]['cl_TE'][:lmax-2]**2 + \
+ ((powersFid[spectrumType]['cl_TT'][:lmax-2] \
+ cmbNoiseSpectra['cl_TT'][:lmax-2]) \
* ((powersFid[spectrumType]['cl_EE'][:lmax-2] \
+ cmbNoiseSpectra['cl_EE'][:lmax-2]))))
#cross for TT and EE
if ('cl_TT' in polCombsToUse and 'cl_EE' in polCombsToUse):
pcEE = polCombsToUse.index('cl_EE')
pcTT = polCombsToUse.index('cl_TT')
covs[spectrumType][pcTT, pcEE, :] = \
2. * oneOver2ellPlusOne \
* (powersFid[spectrumType]['cl_TE'][:lmax-2]**2) #no noise on this one
covs[spectrumType][pcEE, pcTT, :] = \
covs[spectrumType][pcTT, pcEE, :]
#cross for TE and {TT, EE}
if ('cl_TE' in polCombsToUse):# and 'cl_TT' in polCombsToUse):
pcTE = polCombsToUse.index('cl_TE')
for polComb1 in ['cl_TT', 'cl_EE']:
if polComb1 in polCombsToUse:
pc1 = polCombsToUse.index(polComb1)
covs[spectrumType][pcTE, pc1, :] = \
2. * oneOver2ellPlusOne \
* powersFid[spectrumType]['cl_TE'][:lmax-2] \
* (powersFid[spectrumType][polComb1][:lmax-2] \
+ cmbNoiseSpectra[polComb1][:lmax-2])
covs[spectrumType][pc1, pcTE, :] = \
covs[spectrumType][pcTE, pc1, :]
#on-diagonals for DD
if ('cl_dd' in polCombsToUse):
pcDD = polCombsToUse.index('cl_dd')
covs[spectrumType][pcDD, pcDD, :] = \
2. * oneOver2ellPlusOne \
* ((powersFid['lensing']['cl_dd'][:lmax-2] + \
deflectionNoises[:lmax-2])**2)
return covs
def getDiagonalCovariances(polCombsToUse, powersFidES, cmbNoiseSpectraE = None, deflectionNoisesES = None, lmax = None):
#powersFid already indexed by type
if lmax == None:
raise ValueError("auto lmax not coded up yet")
ell = numpy.arange(2,lmax)
nPolCombsToUse = len(polCombsToUse)
oneOver2ellPlusOne = 1. / (2. * ell[:lmax-2] + 1.)
nElls = len(oneOver2ellPlusOne)
covs = zeros((nPolCombsToUse, nPolCombsToUse, nElls))
invCovs = zeros((nPolCombsToUse, nPolCombsToUse, nElls))
#on-diagonals for TT and EE
for polComb1 in ['cl_TT', 'cl_EE', 'cl_BB']:
if polComb1 in polCombsToUse:
pc1 = polCombsToUse.index(polComb1)
covs[pc1, pc1, :] = \
2. * oneOver2ellPlusOne \
* ((powersFidES[polComb1][:lmax-2] \
+ cmbNoiseSpectraE[polComb1][:lmax-2])**2)
#on-diagonal for cl_TE
if ('cl_TE' in polCombsToUse):
pcTE = polCombsToUse.index('cl_TE')
covs[pcTE, pcTE, :] = \
1. * oneOver2ellPlusOne \
* (powersFidES['cl_TE'][:lmax-2]**2 + \
+ ((powersFidES['cl_TT'][:lmax-2] \
+ cmbNoiseSpectraE['cl_TT'][:lmax-2]) \
* ((powersFidES['cl_EE'][:lmax-2] \
+ cmbNoiseSpectraE['cl_EE'][:lmax-2]))))
#cross for TT and EE
if ('cl_TT' in polCombsToUse and 'cl_EE' in polCombsToUse):
pcEE = polCombsToUse.index('cl_EE')
pcTT = polCombsToUse.index('cl_TT')
covs[pcTT, pcEE, :] = \
2. * oneOver2ellPlusOne \
* (powersFidES['cl_TE'][:lmax-2]**2) #no noise on this one
covs[pcEE, pcTT, :] = \
covs[pcTT, pcEE, :]
#cross for TE and {TT, EE}
if ('cl_TE' in polCombsToUse):# and 'cl_TT' in polCombsToUse):
pcTE = polCombsToUse.index('cl_TE')
for polComb1 in ['cl_TT', 'cl_EE']:
if polComb1 in polCombsToUse:
pc1 = polCombsToUse.index(polComb1)
covs[pcTE, pc1, :] = \
2. * oneOver2ellPlusOne \
* powersFidES['cl_TE'][:lmax-2] \
* (powersFidES[polComb1][:lmax-2] \
+ cmbNoiseSpectraE[polComb1][:lmax-2])
covs[pc1, pcTE, :] = \
covs[pcTE, pc1, :]
#on-diagonals for DD
if ('cl_dd' in polCombsToUse):
pcDD = polCombsToUse.index('cl_dd')
covs[pcDD, pcDD, :] = \
2. * oneOver2ellPlusOne \
* ((powersFidES[exp]['lensing']['cl_dd'][:lmax-2] + \
deflectionNoises[exp][exp][pcReconst][mcReconst][:lmax-2])**2)
for l in range(nElls):
try:
invCovs[:, :, l] = linalg.inv(covs[:, :, l])
except:
print("warning, cov inversion problem " , ell[l])
invCovs[:, :, l] = full((nPolCombsToUse, nPolCombsToUse), nan)
return covs , invCovs
def getNonGaussianCov(powersFid, \
cmbNoiseSpectra, \
deflectionNoiseSpectra, \
dCldCLd, \
dCldCLu = None, \
lmax = 3000, \
polCombsToUse = ['cl_TT', 'cl_TE', 'cl_EE', 'cl_dd'], \
spectrumType = 'delensed',\
rescaleToCorrelation = False,\
rescaleToNoiseless = False):
gaussianCov = getGaussianCov(powersFid = powersFid, \
cmbNoiseSpectra = cmbNoiseSpectra, \
deflectionNoises = deflectionNoiseSpectra, \
polCombsToUse = polCombsToUse, \
spectrumTypes = [spectrumType], \
lmax = lmax+1)
cov = twodDict(polCombsToUse, polCombsToUse)
for pc1, polComb1 in enumerate(polCombsToUse):
for pc2, polComb2 in enumerate(polCombsToUse):
if pc2 <= pc1:
cov[polComb1][polComb2] = numpy.diag(gaussianCov[spectrumType][pc1, pc2])
dCldCLd['cl_dd'] = numpy.eye(lmax+1)
ell = powersFid['unlensed']['l'][:lmax-1]
oneOver2ellPlusOne = 1. / (2. * ell[:lmax-1] + 1.)
deflCov = 2*oneOver2ellPlusOne * (powersFid['lensing']['cl_dd'][:lmax-1])**2
if dCldCLu is not None:
zeroNoiseSpectra = onedDict(polCombsToUse)
for polComb in polCombsToUse:
zeroNoiseSpectra[polComb] = numpy.zeros(lmax)
zeroDeflectionNoise = numpy.zeros(lmax)
noiselessCov = getGaussianCov(powersFid = powersFid, \
cmbNoiseSpectra = zeroNoiseSpectra, \
deflectionNoises = zeroDeflectionNoise, \
polCombsToUse = polCombsToUse, \
spectrumTypes = ['unlensed'], \
lmax = lmax+1)
for pc1, polComb1 in enumerate(polCombsToUse):
for pc2, polComb2 in enumerate(polCombsToUse):
if pc2 <= pc1:
print('Computing covaraince for ', polComb1, ' and ', polComb2)
# old - troubleshooting
# cov[polComb1][polComb2] += numpy.tensordot(dCldCLd[polComb1][2:lmax+1,2:lmax+1], \
# numpy.tensordot(numpy.diag(deflCov), dCldCLd[polComb2][2:lmax+1,2:lmax+1], axes = (1,1)), axes = (1,0))
if polComb1 == 'cl_dd' and polComb2 == 'cl_dd':
## Avoid double counting on-diagonal covariance for deflection power
cov[polComb1][polComb2] += 0.
else:
cov[polComb1][polComb2] += numpy.tensordot(dCldCLd[polComb1][2:lmax+1,2:lmax+1], \
numpy.tensordot(numpy.diag(deflCov), dCldCLd[polComb2][2:lmax+1,2:lmax+1], axes = (1,1)), axes = (1,0))
if dCldCLu is not None:
for pc3, polComb3 in enumerate(polCombsToUse):
for pc4, polComb4 in enumerate(polCombsToUse):
if (polComb1 + '_' + polComb3 in dCldCLu.keys()
and polComb2 + '_' + polComb4 in dCldCLu.keys()):
print('Adding covaraince from d' + polComb1 + '/d' + polComb3 + ' and d' + polComb2 + '/d' + polComb4)
tempCov = \
numpy.tensordot(dCldCLu[polComb1 + '_' + polComb3][2:lmax+1,2:lmax+1], \
numpy.tensordot(numpy.diag(noiselessCov['unlensed'][pc3, pc4]), \
dCldCLu[polComb2 + '_' + polComb4][2:lmax+1,2:lmax+1], \
axes = (1,1)), axes = (1,0))
## Need to subtract off on-diagonal piece to avoid doubling it
numpy.fill_diagonal(tempCov, 0.)
cov[polComb1][polComb2] += tempCov
if rescaleToCorrelation:
if rescaleToNoiseless:
zeroNoiseSpectra2 = onedDict(polCombsToUse)
for polComb in polCombsToUse:
zeroNoiseSpectra2[polComb] = numpy.zeros(lmax)
zeroDeflectionNoise2 = numpy.zeros(lmax)
noiselessCov2 = getGaussianCov(powersFid = powersFid, \
cmbNoiseSpectra = zeroNoiseSpectra2, \
deflectionNoises = zeroDeflectionNoise2, \
polCombsToUse = polCombsToUse, \
spectrumTypes = [spectrumType], \
lmax = lmax+1)
for pc1, polComb1 in enumerate(polCombsToUse):
for pc2, polComb2 in enumerate(polCombsToUse):
if pc2 <= pc1:
if rescaleToNoiseless:
denom = numpy.sqrt(numpy.einsum('i,j->ij', noiselessCov2[spectrumType][pc1,pc1,:], noiselessCov2[spectrumType][pc2,pc2,:]))
else:
denom = numpy.sqrt(numpy.einsum('i,j->ij', gaussianCov[spectrumType][pc1,pc1,:], gaussianCov[spectrumType][pc2,pc2,:]))
cov[polComb1][polComb2] = cov[polComb1][polComb2] / denom
matrix = list()
for pc1, polComb1 in enumerate(polCombsToUse):
row = list()
for pc2, polComb2 in enumerate(polCombsToUse):
if pc2 > pc1:
row.append(cov[polComb2][polComb1].T)
else:
row.append(cov[polComb1][polComb2])
matrix.append(row)
covMatrix = numpy.block(matrix)
return covMatrix
def getNonGaussianCMBFisher(invCovDotParamDerivs, paramDerivStack, cosmoParams):
nParams = len(cosmoParams)
fisher = numpy.zeros((nParams,nParams))
for cp1, cosmo1 in enumerate(cosmoParams):
for cp2, cosmo2 in enumerate(cosmoParams):
fisher[cp1, cp2] = sum(paramDerivStack[cosmo1] * invCovDotParamDerivs[cosmo2])
return fisher
def fixParametersInFisher(fisher, cosmoParams, paramsToFix, returnFixedParamList = False):
cosmoParamsTemp = cosmoParams[:]
fixed_fisher = fisher.copy()
for fp, fixedParam in enumerate(paramsToFix):
fixed_fisher = numpy.delete(numpy.delete(fixed_fisher, cosmoParamsTemp.index(fixedParam), axis = 0), cosmoParamsTemp.index(fixedParam), axis = 1)
cosmoParamsTemp.remove(fixedParam)
if returnFixedParamList:
return fixed_fisher, cosmoParamsTemp
else:
return fixed_fisher
def getGaussianCMBFisher(powersFid, paramDerivs, cmbNoiseSpectra, deflectionNoises, cosmoParams,\
spectrumTypes = ['unlensed', 'lensed', 'delensed'], \
polCombsToUse = ['cl_TT', 'cl_TE', 'cl_EE', 'cl_dd'], \
ellsToUse = None, \
lmax = None):
ellsToUse, lmax = createEllsToUseDict(ellsToUse = ellsToUse, \
lmax = lmax, \
polCombsToUse = polCombsToUse)
covs = getGaussianCov(powersFid = powersFid, \
cmbNoiseSpectra = cmbNoiseSpectra, \
deflectionNoises = deflectionNoises, \
polCombsToUse = polCombsToUse, \
lmax = lmax+1)
## Copy data structure of covs to invcovs (values will be overwritten)
invCovs = covs.copy()
ell = powersFid[list(powersFid.keys())[0]]['l'][:lmax-1]
nElls = len(ell)
nPolCombsToUse = len(polCombsToUse)
nPars = len(cosmoParams)
fisherContribs = threedDict(spectrumTypes, cosmoParams, cosmoParams)
paramDerivArray = twodDict(cosmoParams, spectrumTypes)
paramDerivToUse = twodDict(cosmoParams, spectrumTypes)
fisher = dict()
for spectrumType in spectrumTypes:
fisher[spectrumType] = numpy.zeros((nPars, nPars))
for l in range(nElls):
try:
invCovs[spectrumType][:, :, l] = linalg.inv(covs[spectrumType][:, :, l])
except:
print("warning, cov inversion problem " , spectrumType, ell[l])
invCovs[spectrumType][:, :, l] = numpy.full((nPolCombsToUse, nPolCombsToUse), numpy.nan)
for cp1, cosmo1 in enumerate(cosmoParams):
paramDerivArray[cosmo1][spectrumType] = numpy.zeros((nPolCombsToUse, nElls))
paramDerivToUse[cosmo1][spectrumType] = numpy.zeros((nPolCombsToUse, nElls))
for pc, polComb in enumerate(polCombsToUse):
if polComb == 'cl_dd':
#deflection as a special case; use same data regardless of spectrumType
if 'cl_dd' in polCombsToUse:
pcDD = polCombsToUse.index('cl_dd')
paramDerivArray[cosmo1][spectrumType][pcDD, :] = \
paramDerivs[cosmo1]['lensing']['cl_dd'][:lmax-1]
else:
paramDerivArray[cosmo1][spectrumType][pc, :] = \
paramDerivs[cosmo1][spectrumType][polComb][:lmax-1]
paramDerivToUse[cosmo1][spectrumType][pc, ellsToUse[polComb][0]-2 : ellsToUse[polComb][1]-1] = 1.
paramDerivArray[cosmo1][spectrumType][pc, :] = \
paramDerivArray[cosmo1][spectrumType][pc, :] * paramDerivToUse[cosmo1][spectrumType][pc, :]
for cp1, cosmo1 in enumerate(cosmoParams):
for cp2, cosmo2 in enumerate(cosmoParams):
fisherContribs[spectrumType][cosmo1][cosmo2] = \
numpy.einsum('ik,ijk,jk->k', \
paramDerivArray[cosmo1][spectrumType], invCovs[spectrumType], paramDerivArray[cosmo2][spectrumType])
fisher[spectrumType][cp1, cp2] = sum(fisherContribs[spectrumType][cosmo1][cosmo2])
return fisher
def getBAOFisher(paramDerivs, rs_dV_errors, cosmoParams):
nPars = len(cosmoParams)
fisherBAO = numpy.zeros((nPars,nPars))
for cp1, cosmo1 in enumerate(cosmoParams):
for cp2, cosmo2 in enumerate(cosmoParams):
fisherBAO[cp1,cp2] = sum(paramDerivs[cosmo1] * paramDerivs[cosmo2]/(rs_dV_errors * rs_dV_errors))
return fisherBAO
def choleskyInvCovDotParamDerivsNG(powersFid, \
cmbNoiseSpectra, \
deflectionNoiseSpectra, \
dCldCLd,
paramDerivs, \
cosmoParams, \
dCldCLu = None, \
ellsToUse = None, \
lmax = None, \
polCombsToUse = ['cl_TT', 'cl_TE', 'cl_EE', 'cl_dd'], \
spectrumType = 'delensed'):
ellsToUse, lmax = createEllsToUseDict(ellsToUse = ellsToUse, \
lmax = lmax, \
polCombsToUse = polCombsToUse)
if 'lmaxCov' in list(ellsToUse.keys()) and ellsToUse['lmaxCov'] > lmax:
lmax = ellsToUse['lmaxCov']
covMatrix = getNonGaussianCov(powersFid = powersFid, \
cmbNoiseSpectra = cmbNoiseSpectra, \
deflectionNoiseSpectra = deflectionNoiseSpectra, \
dCldCLd = dCldCLd, \
dCldCLu = dCldCLu, \
lmax = lmax, \
polCombsToUse = polCombsToUse, \
spectrumType = spectrumType)
try:
covMatrix = scipy.linalg.cho_factor(covMatrix, overwrite_a = True)
except:
print('Warning Cholesky decomposition failed')
covMatrix = scipy.linalg.cho_factor(numpy.eye(len(polCombsToUse)*(lmax-1)))
paramDerivStack = onedDict(cosmoParams)
invCovDotParamDerivs = onedDict(cosmoParams)
for cosmo in cosmoParams:
paramDerivStack[cosmo] = numpy.empty(0)
for pc, polComb in enumerate(polCombsToUse):
paramDerivTemp = numpy.zeros(lmax-1)
paramDerivTemp[ellsToUse[polComb][0]-2 : ellsToUse[polComb][1]-1] = 1.
if polComb == 'cl_dd':
paramDerivStack[cosmo] = numpy.append(paramDerivStack[cosmo], paramDerivTemp * paramDerivs[cosmo]['lensing'][polComb][:lmax-1])
else:
paramDerivStack[cosmo] = numpy.append(paramDerivStack[cosmo], paramDerivTemp * paramDerivs[cosmo][spectrumType][polComb][:lmax-1])
try:
invCovDotParamDerivs[cosmo] = scipy.linalg.cho_solve(covMatrix, paramDerivStack[cosmo])
except:
print('Warning inverse covariance problem with ' + cosmo + ' ' + spectrumType)
invCovDotParamDerivs[cosmo] = full((lmax-2), nan)
return invCovDotParamDerivs, paramDerivStack
def getBiasVectorGaussian(powersFid, paramDerivs, cmbNoiseSpectra, deflectionNoises, cosmoParams, sysSpectrum,\
spectrumTypes = ['unlensed', 'lensed', 'delensed'], \
polCombsToUse = ['cl_TT', 'cl_TE', 'cl_EE', 'cl_dd'], \
lmax = 5000):
covs = getGaussianCov(powersFid = powersFid, \
cmbNoiseSpectra = cmbNoiseSpectra, \
deflectionNoises = deflectionNoises, \
polCombsToUse = polCombsToUse, \
lmax = lmax+1)
## Copy data structure of covs to invcovs (values will be overwritten)
invCovs = covs.copy()
ell = powersFid[list(powersFid.keys())[0]]['l'][:lmax-1]
nElls = len(ell)
nPolCombsToUse = len(polCombsToUse)
nPars = len(cosmoParams)
biasVectorContribs = twodDict(spectrumTypes, cosmoParams)
paramDerivArray = twodDict(cosmoParams, spectrumTypes)
biasVector = dict()
sysSpectrumArray = dict()
for spectrumType in spectrumTypes:
biasVector[spectrumType] = numpy.zeros(nPars)
sysSpectrumArray[spectrumType] = numpy.zeros((nPolCombsToUse, nElls))
for l in range(nElls):
try:
invCovs[spectrumType][:, :, l] = linalg.inv(covs[spectrumType][:, :, l])
except:
print ("warning, cov inversion problem " , spectrumType, ell[l])
invCovs[spectrumType][:, :, l] = numpy.full((nPolCombsToUse, nPolCombsToUse), numpy.nan)
for cp1, cosmo1 in enumerate(cosmoParams):
paramDerivArray[cosmo1][spectrumType] = numpy.zeros((nPolCombsToUse, nElls))
for pc, polComb in enumerate(polCombsToUse):
if polComb == 'cl_dd':
#deflection as a special case; use same data regardless of spectrumType
if 'cl_dd' in polCombsToUse:
pcDD = polCombsToUse.index('cl_dd')
paramDerivArray[cosmo1][spectrumType][pcDD, :] = \
paramDerivs[cosmo1]['lensing']['cl_dd'][:lmax-1]
sysSpectrumArray[spectrumType][pcDD, :] = \
sysSpectrum['lensing']['cl_dd'][:lmax-1]
else:
paramDerivArray[cosmo1][spectrumType][pc, :] = \
paramDerivs[cosmo1][spectrumType][polComb][:lmax-1]
sysSpectrumArray[spectrumType][pc, :] = \
sysSpectrum[spectrumType][polComb][:lmax-1]
for cp1, cosmo1 in enumerate(cosmoParams):
biasVectorContribs[spectrumType][cosmo1] = \
numpy.einsum('ik,ijk,jk->k', \
sysSpectrumArray[spectrumType], invCovs[spectrumType], paramDerivArray[cosmo1][spectrumType])
biasVector[spectrumType][cp1] = sum(biasVectorContribs[spectrumType][cosmo1])
return biasVector
def getBiasVectorNonGaussian(invCovDotParamDerivs, cosmoParams, sysSpectrum, polCombsToUse = ['cl_TT', 'cl_TE', 'cl_EE', 'cl_dd'], \
lmax=5000, spectrumType = ['delensed']):
sysSpectrumStack = numpy.empty(0)
for pc, polComb in enumerate(polCombsToUse):
if polComb == 'cl_dd':
sysSpectrumStack = numpy.append(sysSpectrumStack, sysSpectrum['lensing'][polComb][:lmax-1])
else:
sysSpectrumStack = numpy.append(sysSpectrumStack, sysSpectrum[spectrumType][polComb][:lmax-1])
nParams = len(cosmoParams)
biasVector = numpy.zeros(nParams)
for cp1, cosmo1 in enumerate(cosmoParams):
biasVector[cp1] = sum(sysSpectrumStack * invCovDotParamDerivs[cosmo1])
return biasVector
def getSecondPowerDerivWithParams(cosmoFid, stepSizes, polCombs, cmbNoiseSpectraK, deflectionNoisesK,
spectrumTypes = ['unlensed', 'lensed', 'delensed', 'lensing'],
lmax = 5000,
fileNameBase = 'testing', paramsToDifferentiate = None,
accuracy = 2.,
useClass = False,
doLensedWithCAMB = False,