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lens.py
460 lines (377 loc) · 17.7 KB
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lens.py
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# quicklens/qest/lens.py
# --
# this module contains quadratic estimators for the phi and psi potentials
# which give the CMB lensing deflection
# d(n) = \grad \phi(n) + \curl \psi(n).
# they use weight functions W for combinations of temperature (T) and
# polarization (E,B) from Hu et. al. http://arxiv.org/abs/astro-ph/0111606
import numpy as np
import qest
class phi_TT(qest.qest):
""" temperature-temperature (TT) lensing potential gradient-mode estimator. """
def __init__(self, cltt):
""" initialize the TT lensing potential gradient-mode estimator.
* cltt = lensed TT power spectrum.
"""
self.cltt = cltt
self.lmax = len(cltt)-1
self.ntrm = 4
self.wl = { i : {} for i in xrange(0, self.ntrm) }
self.sl = { i : {} for i in xrange(0, self.ntrm) }
self.wl[0][0] = self.wc_ml; self.sl[0][0] = +1
self.wl[0][1] = self.wo_d2; self.sl[0][1] = +0
self.wl[0][2] = self.wo_ml; self.sl[0][2] = +1
self.wl[1][0] = self.wc_ml; self.sl[1][0] = -1
self.wl[1][1] = self.wo_d2; self.sl[1][1] = +0
self.wl[1][2] = self.wo_ml; self.sl[1][2] = -1
self.wl[2][0] = self.wo_d2; self.sl[2][0] = +0
self.wl[2][1] = self.wc_ml; self.sl[2][1] = +1
self.wl[2][2] = self.wo_ml; self.sl[2][2] = +1
self.wl[3][0] = self.wo_d2; self.sl[3][0] = +0
self.wl[3][1] = self.wc_ml; self.sl[3][1] = -1
self.wl[3][2] = self.wo_ml; self.sl[3][2] = -1
def wo_d2(self, l, lx=None, ly=None):
return -0.5
def wo_ml(self, l, lx=None, ly=None):
return np.sqrt(l*(l+1.))
def wc_ml(self, l, lx=None, ly=None):
return np.interp( l, np.arange(0, len(self.cltt)), self.cltt, right=0 ) * np.sqrt(l*(l+1.))
class phi_TT_s0(qest.qest):
""" version of the temperature-temperature (TT) lensing potential gradient-mode estimator with spin-0 weights.
equivalent to phi_TT, but with different implementation of the weights.
this class is meant to represent more closely the usual temperatre x (gradient temperature)
description of the TT lensing estimator. """
def __init__(self, cltt):
""" initialize the spin-0 TT lensing estimator.
* cltt = lensed TT power spectrum.
"""
self.cltt = cltt
self.lmax = len(cltt)-1
self.ntrm = 4
self.wl = { i : {} for i in xrange(0, self.ntrm) }
self.sl = { i : [0,0,0] for i in xrange(0,self.ntrm) }
self.wl[0][0] = self.wc_lx
self.wl[0][1] = self.wo_m1
self.wl[0][2] = self.wo_lx
self.wl[1][0] = self.wc_ly
self.wl[1][1] = self.wo_m1
self.wl[1][2] = self.wo_ly
self.wl[2][0] = self.wo_m1
self.wl[2][1] = self.wc_lx
self.wl[2][2] = self.wo_lx
self.wl[3][0] = self.wo_m1
self.wl[3][1] = self.wc_ly
self.wl[3][2] = self.wo_ly
def wo_m1(self, l, lx, ly):
return 1.0
def wo_lx(self, l, lx, ly):
return lx
def wc_lx(self, l, lx, ly):
return np.interp( l, np.arange(0, len(self.cltt)), self.cltt, right=0 ) * lx
def wo_ly(self, l, lx, ly):
return ly
def wc_ly(self, l, lx, ly):
return np.interp( l, np.arange(0, len(self.cltt)), self.cltt, right=0 ) * ly
class phi_TE(qest.qest):
""" TE lensing potential gradient-mode estimator. """
def __init__(self, clte):
""" initialize the TE lensing potential gradient-mode estimator.
* clte = lensed TE power spectrum.
"""
self.clte = clte
self.lmax = len(clte)-1
self.ntrm = 6
self.wl = { i : {} for i in xrange(0, self.ntrm) }
self.sl = { i : {} for i in xrange(0, self.ntrm) }
# t de
self.wl[0][0] = self.wc_m3; self.sl[0][0] = +3
self.wl[0][1] = self.wo_d4; self.sl[0][1] = -2
self.wl[0][2] = self.wo_m1; self.sl[0][2] = +1
self.wl[1][0] = self.wc_m3; self.sl[1][0] = -3
self.wl[1][1] = self.wo_d4; self.sl[1][1] = +2
self.wl[1][2] = self.wo_m1; self.sl[1][2] = -1
self.wl[2][0] = self.wc_m2; self.sl[2][0] = -1
self.wl[2][1] = self.wo_d4; self.sl[2][1] = +2
self.wl[2][2] = self.wo_m1; self.sl[2][2] = +1
self.wl[3][0] = self.wc_m2; self.sl[3][0] = +1
self.wl[3][1] = self.wo_d4; self.sl[3][1] = -2
self.wl[3][2] = self.wo_m1; self.sl[3][2] = -1
# dt e
self.wl[4][0] = self.wo_d2; self.sl[4][0] = +0
self.wl[4][1] = self.wc_m1; self.sl[4][1] = +1
self.wl[4][2] = self.wo_m1; self.sl[4][2] = +1
self.wl[5][0] = self.wo_d2; self.sl[5][0] = +0
self.wl[5][1] = self.wc_m1; self.sl[5][1] = -1
self.wl[5][2] = self.wo_m1; self.sl[5][2] = -1
def wo_d2(self, l, lx=None, ly=None):
return -0.50
def wo_d4(self, l, lx=None, ly=None):
return -0.25
def wo_m1(self, l, lx=None, ly=None):
return np.sqrt(l*(l+1.))
def wc_m1(self, l, lx=None, ly=None):
return np.interp( l, np.arange(0, len(self.clte)), self.clte, right=0 ) * np.sqrt( l*(l+1.) )
def wc_m2(self, l, lx=None, ly=None):
return np.interp( l, np.arange(0, len(self.clte)), self.clte, right=0 ) * np.nan_to_num( np.sqrt( (l+2.)*(l-1.) ) )
def wc_m3(self, l, lx=None, ly=None):
return np.interp( l, np.arange(0, len(self.clte)), self.clte, right=0 ) * np.nan_to_num( np.sqrt( (l+3.)*(l-2.) ) )
class phi_TB(qest.qest):
""" TB lensing potential gradient-mode estimator. """
def __init__(self, clte):
""" initialize the TB lensing potential gradient-mode estimator.
* clte = lensed TE power spectrum.
"""
self.clte = clte
self.lmax = len(clte)-1
self.ntrm = 4
self.wl = { i : {} for i in xrange(0, self.ntrm) }
self.sl = { i : {} for i in xrange(0, self.ntrm) }
# t de
self.wl[0][0] = self.wc_m3; self.sl[0][0] = +3
self.wl[0][1] = self.wo_di; self.sl[0][1] = -2
self.wl[0][2] = self.wo_m1; self.sl[0][2] = +1
self.wl[1][0] = self.wc_m3; self.sl[1][0] = -3
self.wl[1][1] = self.wo_mi; self.sl[1][1] = +2
self.wl[1][2] = self.wo_m1; self.sl[1][2] = -1
self.wl[2][0] = self.wc_m2; self.sl[2][0] = -1
self.wl[2][1] = self.wo_mi; self.sl[2][1] = +2
self.wl[2][2] = self.wo_m1; self.sl[2][2] = +1
self.wl[3][0] = self.wc_m2; self.sl[3][0] = +1
self.wl[3][1] = self.wo_di; self.sl[3][1] = -2
self.wl[3][2] = self.wo_m1; self.sl[3][2] = -1
def wo_di(self, l, lx=None, ly=None):
return +0.25j
def wo_mi(self, l, lx=None, ly=None):
return -0.25j
def wo_m1(self, l, lx=None, ly=None):
return np.sqrt(l*(l+1.))
def wc_m2(self, l, lx=None, ly=None):
return np.interp( l, np.arange(0, len(self.clte)), self.clte, right=0 ) * np.nan_to_num( np.sqrt( (l+2.)*(l-1.) ) )
def wc_m3(self, l, lx=None, ly=None):
return np.interp( l, np.arange(0, len(self.clte)), self.clte, right=0 ) * np.nan_to_num( np.sqrt( (l+3.)*(l-2.) ) )
class phi_EE(qest.qest):
""" EE lensing potential gradient-mode estimator. """
def __init__(self, clee):
""" initialize the EE lensing potential gradient-mode estimator.
* clee = lensed EE power spectrum.
"""
self.clee = clee
self.lmax = len(clee)-1
self.ntrm = 8
self.wl = { i : {} for i in xrange(0, self.ntrm) }
self.sl = { i : {} for i in xrange(0, self.ntrm) }
# first term.
self.wl[0][0] = self.wo_d4; self.sl[0][0] = -2
self.wl[0][1] = self.wc_m3; self.sl[0][1] = +3
self.wl[0][2] = self.wo_m1; self.sl[0][2] = +1
self.wl[1][0] = self.wo_d4; self.sl[1][0] = +2
self.wl[1][1] = self.wc_m3; self.sl[1][1] = -3
self.wl[1][2] = self.wo_m1; self.sl[1][2] = -1
self.wl[2][0] = self.wc_m3; self.sl[2][0] = +3
self.wl[2][1] = self.wo_d4; self.sl[2][1] = -2
self.wl[2][2] = self.wo_m1; self.sl[2][2] = +1
self.wl[3][0] = self.wc_m3; self.sl[3][0] = -3
self.wl[3][1] = self.wo_d4; self.sl[3][1] = +2
self.wl[3][2] = self.wo_m1; self.sl[3][2] = -1
# second term.
self.wl[4][0] = self.wo_d4; self.sl[4][0] = +2
self.wl[4][1] = self.wc_m2; self.sl[4][1] = -1
self.wl[4][2] = self.wo_m1; self.sl[4][2] = +1
self.wl[5][0] = self.wo_d4; self.sl[5][0] = -2
self.wl[5][1] = self.wc_m2; self.sl[5][1] = +1
self.wl[5][2] = self.wo_m1; self.sl[5][2] = -1
self.wl[6][0] = self.wc_m2; self.sl[6][0] = -1
self.wl[6][1] = self.wo_d4; self.sl[6][1] = +2
self.wl[6][2] = self.wo_m1; self.sl[6][2] = +1
self.wl[7][0] = self.wc_m2; self.sl[7][0] = +1
self.wl[7][1] = self.wo_d4; self.sl[7][1] = -2
self.wl[7][2] = self.wo_m1; self.sl[7][2] = -1
def wo_d4(self, l, lx=None, ly=None):
return -0.25
def wo_m1(self, l, lx=None, ly=None):
return np.sqrt(l*(l+1.))
def wc_m2(self, l, lx=None, ly=None):
return np.interp( l, np.arange(0, len(self.clee)), self.clee, right=0 ) * np.nan_to_num( np.sqrt( (l+2.)*(l-1.) ) )
def wc_m3(self, l, lx=None, ly=None):
return np.interp( l, np.arange(0, len(self.clee)), self.clee, right=0 ) * np.nan_to_num( np.sqrt( (l+3.)*(l-2.) ) )
class phi_EB(qest.qest):
""" EB lensing potential gradient-mode estimator. """
def __init__(self, clee):
""" initialize the EB lensing potential gradient-mode estimator.
* clte = lensed TE power spectrum.
"""
self.clee = clee
self.lmax = len(clee)-1
self.ntrm = 4
self.wl = { i : {} for i in xrange(0, self.ntrm) }
self.sl = { i : {} for i in xrange(0, self.ntrm) }
# t de
self.wl[0][0] = self.wc_m3; self.sl[0][0] = +3
self.wl[0][1] = self.wo_di; self.sl[0][1] = -2
self.wl[0][2] = self.wo_m1; self.sl[0][2] = +1
self.wl[1][0] = self.wc_m3; self.sl[1][0] = -3
self.wl[1][1] = self.wo_mi; self.sl[1][1] = +2
self.wl[1][2] = self.wo_m1; self.sl[1][2] = -1
self.wl[2][0] = self.wc_m2; self.sl[2][0] = -1
self.wl[2][1] = self.wo_mi; self.sl[2][1] = +2
self.wl[2][2] = self.wo_m1; self.sl[2][2] = +1
self.wl[3][0] = self.wc_m2; self.sl[3][0] = +1
self.wl[3][1] = self.wo_di; self.sl[3][1] = -2
self.wl[3][2] = self.wo_m1; self.sl[3][2] = -1
def wo_di(self, l, lx=None, ly=None):
return +0.25j
def wo_mi(self, l, lx=None, ly=None):
return -0.25j
def wo_m1(self, l, lx=None, ly=None):
return np.sqrt( l*(l+1.) )
def wc_m2(self, l, lx=None, ly=None):
return np.interp( l, np.arange(0, len(self.clee)), self.clee, right=0 ) * np.nan_to_num( np.sqrt( (l+2.)*(l-1.) ) )
def wc_m3(self, l, lx=None, ly=None):
return np.interp( l, np.arange(0, len(self.clee)), self.clee, right=0 ) * np.nan_to_num( np.sqrt( (l+3.)*(l-2.) ) )
class phi_ET(phi_TE):
""" ET lensing potential gradient-mode estimator. equivalent to phi_TE, but with E in first index position. """
def __init__(self, clte):
""" initialize the ET lensing potential gradient-mode estimator.
* clte = lensed TE power spectrum.
"""
super(phi_ET, self).__init__(clte)
for i in xrange(0,self.ntrm):
twl = self.wl[i][0]
tsl = self.sl[i][0]
self.wl[i][0] = self.wl[i][1]
self.sl[i][0] = self.sl[i][1]
self.wl[i][1] = twl
self.sl[i][1] = tsl
class phi_BT(phi_TB):
""" BT lensing potential gradient-mode estimator. equivalent to phi_TB, but with B in the first index position. """
def __init__(self, clte):
""" initialize the BT lensing potential gradient-mode estimator.
* clte = lensed TE power spectrum.
"""
super(phi_BT, self).__init__(clte)
for i in xrange(0,self.ntrm):
twl = self.wl[i][0]
tsl = self.sl[i][0]
self.wl[i][0] = self.wl[i][1]
self.sl[i][0] = self.sl[i][1]
self.wl[i][1] = twl
self.sl[i][1] = tsl
class phi_BE(phi_EB):
""" BE lensing potential gradient-mode estimator. equivalent to phi_EB, but with B in first index position. """
def __init__(self, clee):
""" initialize the BE lensing potential gradient-mode estimator.
* clee = lensed EE power spectrum.
"""
super(phi_BE, self).__init__(clee)
for i in xrange(0,self.ntrm):
twl = self.wl[i][0]
tsl = self.sl[i][0]
self.wl[i][0] = self.wl[i][1]
self.sl[i][0] = self.sl[i][1]
self.wl[i][1] = twl
self.sl[i][1] = tsl
class psi_TT(qest.qest):
""" temperature-temperature (TT) lensing potential curl-mode estimator. """
def __init__(self, cltt):
""" initialize the TT lensing potential curl-mode estimator.
* cltt = lensed TT power spectrum.
"""
self.cltt = cltt
self.lmax = len(cltt)-1
self.ntrm = 4
self.wl = { i : {} for i in xrange(0, self.ntrm) }
self.sl = { i : {} for i in xrange(0, self.ntrm) }
self.wl[0][0] = self.wc_m1; self.sl[0][0] = +1
self.wl[0][1] = self.wo_d2; self.sl[0][1] = +0
self.wl[0][2] = self.wo_m1; self.sl[0][2] = +1
self.wl[1][0] = self.wc_m1; self.sl[1][0] = -1
self.wl[1][1] = self.wo_n2; self.sl[1][1] = +0
self.wl[1][2] = self.wo_m1; self.sl[1][2] = -1
self.wl[2][0] = self.wo_d2; self.sl[2][0] = +0
self.wl[2][1] = self.wc_m1; self.sl[2][1] = +1
self.wl[2][2] = self.wo_m1; self.sl[2][2] = +1
self.wl[3][0] = self.wo_n2; self.sl[3][0] = +0
self.wl[3][1] = self.wc_m1; self.sl[3][1] = -1
self.wl[3][2] = self.wo_m1; self.sl[3][2] = -1
def wo_d2(self, l, lx=None, ly=None):
return -0.5j
def wo_n2(self, l, lx=None, ly=None):
return +0.5j
def wo_m1(self, l, lx=None, ly=None):
return np.sqrt(l*(l+1.))
def wc_m1(self, l, lx=None, ly=None):
return np.interp( l, np.arange(0, len(self.cltt)), self.cltt, right=0 ) * np.sqrt(l*(l+1.))
class blen_EP(qest.qest):
""" E-mode-phi (EP) estimator for the lensed B-mode. """
def __init__(self, clee, clpp):
""" initialize the EP lensing B-mode estimator.
* clee = lensed E-mode power spectrum.
* clpp = gradient-mode lensing potential power spectrum.
"""
self.clee = clee
self.clpp = clpp
assert(len(clee) == len(clpp))
self.lmax = len(clee)-1
self.ntrm = 4
self.wl = { i : {} for i in xrange(0, self.ntrm) }
self.sl = { i : {} for i in xrange(0, self.ntrm) }
# t de
self.wl[0][0] = self.wc_m3; self.sl[0][0] = +3
self.wl[0][1] = self.wp_m1; self.sl[0][1] = -1
self.wl[0][2] = self.wo_di; self.sl[0][2] = +2
self.wl[1][0] = self.wc_m3; self.sl[1][0] = -3
self.wl[1][1] = self.wp_m1; self.sl[1][1] = +1
self.wl[1][2] = self.wo_mi; self.sl[1][2] = -2
self.wl[2][0] = self.wc_m2; self.sl[2][0] = -1
self.wl[2][1] = self.wp_m1; self.sl[2][1] = -1
self.wl[2][2] = self.wo_mi; self.sl[2][2] = -2
self.wl[3][0] = self.wc_m2; self.sl[3][0] = +1
self.wl[3][1] = self.wp_m1; self.sl[3][1] = +1
self.wl[3][2] = self.wo_di; self.sl[3][2] = +2
def wo_di(self, l, lx=None, ly=None):
return -0.25j
def wo_mi(self, l, lx=None, ly=None):
return +0.25j
def wc_m2(self, l, lx=None, ly=None):
return np.interp( l, np.arange(0, len(self.clee)), self.clee, right=0 ) * np.nan_to_num( np.sqrt( (l+2.)*(l-1.) ) )
def wc_m3(self, l, lx=None, ly=None):
return np.interp( l, np.arange(0, len(self.clee)), self.clee, right=0 ) * np.nan_to_num( np.sqrt( (l+3.)*(l-2.) ) )
def wp_m1(self, l, lx=None, ly=None):
return np.interp( l, np.arange(0, len(self.clpp)), self.clpp, right=0 ) * np.sqrt( l*(l+1.) )
class blen_EX(qest.qest):
""" E-mode-psi (EX) estimator for the lensed B-mode. """
def __init__(self, clee, clpp):
""" initialize the EP lensing B-mode estimator.
* clee = lensed E-mode power spectrum.
* clpp = curl-mode lensing potential power spectrum.
"""
self.clee = clee
self.clpp = clpp
assert(len(clee) == len(clpp))
self.lmax = len(clee)-1
self.ntrm = 4
self.wl = { i : {} for i in xrange(0, self.ntrm) }
self.sl = { i : {} for i in xrange(0, self.ntrm) }
# t de
self.wl[0][0] = self.wc_m3; self.sl[0][0] = +3
self.wl[0][1] = self.wp_m1; self.sl[0][1] = -1
self.wl[0][2] = self.wo_di; self.sl[0][2] = +2
self.wl[1][0] = self.wc_m3; self.sl[1][0] = -3
self.wl[1][1] = self.wp_m1; self.sl[1][1] = +1
self.wl[1][2] = self.wo_di; self.sl[1][2] = -2
self.wl[2][0] = self.wc_m2; self.sl[2][0] = -1
self.wl[2][1] = self.wp_m1; self.sl[2][1] = -1
self.wl[2][2] = self.wo_mi; self.sl[2][2] = -2
self.wl[3][0] = self.wc_m2; self.sl[3][0] = +1
self.wl[3][1] = self.wp_m1; self.sl[3][1] = +1
self.wl[3][2] = self.wo_mi; self.sl[3][2] = +2
def wo_di(self, l, lx=None, ly=None):
return -0.25j
def wo_mi(self, l, lx=None, ly=None):
return +0.25j
def wc_m2(self, l, lx=None, ly=None):
return np.interp( l, np.arange(0, len(self.clee)), self.clee, right=0 ) * np.nan_to_num( np.sqrt( (l+2.)*(l-1.) ) )
def wc_m3(self, l, lx=None, ly=None):
return np.interp( l, np.arange(0, len(self.clee)), self.clee, right=0 ) * np.nan_to_num( np.sqrt( (l+3.)*(l-2.) ) )
def wp_m1(self, l, lx=None, ly=None):
return np.interp( l, np.arange(0, len(self.clpp)), self.clpp, right=0 ) * np.sqrt( l*(l+1.) )