`basic` – Some basic tools¶

`delens` – analytic calculation for delensing¶

basic.delens.lintemplate(lmax, elmin, elmax, klmin, klmax, CE, Cm, WE, Wm, gtype='p')¶

Estimate of lensing template B-mode power spectrum (Wiener filters as inputs)

Args:

lmax (int):	Maximum multipole of output spectrum
elmin (int):	Minimum multipole of E
elmax (int):	Maximum multipole of E
klmin (int):	Minimum multipole of lensing mass
klmax (int):	Maximum multipole of lensing mass
CE[l] (double):	Power spectrum of E-mode, with bounds (0:dlmax)
Cp[l] (double):	Power spectrum of lensing pontential, with bounds (0:dlmax)
WE[l] (double):	Wiener filter of E-mode, with bounds (0:dlmax)
Wp[l] (double):	Wiener filter of lensing potential, with bountd (0:dlmax)

Args(optional):

gtype (str):	specify type of the input Cp, p (default) or k.

Returns:

CB[l] (double):	Lensing B-mode power spectrum, with bounds (0:lmax)

Usage:

CB = basic.delens.lintemplate(lmax,elmin,elmax,klmin,klmax,CE,Cm,WE,Wm,gtype):

basic.delens.lensingbb(lmax, dlmin, dlmax, CE, Cp)¶

Lensing B-mode power spectrum as a convolution of ClEE and Clpp

Args:

lmax (int): Maximum multipole of output spectrum

dlmin (int): Minimum multipole of E and lensing for delensing

dlmax (int): Maximum multipole of E and lensing for delensing

CE[l] (double): Power spectrum of E-mode, with bounds (0:dlmax)

Cp[l] (double): Power spectrum of lensing pontential, with bounds (0:dlmax)

Returns:

CB[l] (double): Lensing B-mode power spectrum, with bounds (0:lmax)

Usage:

CB = basic.delens.lensingbb(lmax,dlmin,dlmax,CE,Cp):

basic.delens.delensbias_dom(lmax, dlmin, dlmax, CE, CB, Cp, NP1, NP2, Ag)¶

Dominant term of the delensing bias in the B-mode internal delensing

Args:

NP1[l] (double):
lmax (int):	Maximum multipole of output spectrum
dlmin (int):	Minimum multipole of E and lensing for delensing
dlmax (int):	Maximum multipole of E and lensing for delensing
CE[l] (double):	Power spectrum of E-mode, with bounds (0:dlmax)
CB[l] (double):	Power spectrum of B-mode, with bounds (0:dlmax)
Cp[l] (double):	Power spectrum of lensing pontential, with bounds (0:dlmax)
	Pol. noise spectrum for lensing reconstruction, with bounds (0:dlmax)
NP2[l] (double):
	Pol. noise spectrum for B-mode to be delensed, with bounds (0:dlmax)
Ag[l] (double):	Lensing reconstruction noise, with bounds (0:dlmax)

Returns:

DB[l] (double):	Lensing B-mode power spectrum, with bounds (0:lmax)

Usage:

DB = basic.delens.delensbias_dom(lmax,dlmin,dlmax,CE,CB,Cp,NP1,NP2,Ag):

`bispec` – analytic calculation of bispectrum¶

basic.bispec.cl_flat(cpmodel, z, dz, zs, lmax, k, pk0, zn=0, kn=0, pktype='T12', cltype='kk', dNdz=None, wdel=None)¶

Compute flat-sky lensing powerspectrum analytically

Args:

dz[zn] (double):
cpmodel (str):	cosmological parameter model (model0, modelw, or modelp)
z[zn] (double):	redshift points for the z-integral
	interval of z
zs[2] (double):	two source redshifts
lmin/lmax (int):
	minimum/maximum multipoles of the bispectrum
k[kn] (double):	k for the matter power spectrum in unit of [h/Mpc]
pk0[kn] (double):
	the linear matter power spectrum at z=0 in unit of [Mpc^3/h^3]

Args(optional):

dNdz[zn] (double):
pktype (str):	fitting formula for the matter power spectrum (Lin, S02 or T12)
cltype (str):	kk, gk, or gg
	redshift distribution of galaxy, only used when cltype includes g
wdel[zn,l] (double):
	modified chi-kernel function for z-cleaning at l=0 to lmax

Returns:

cl[l] (double):	power spectrum from LSS contributions at [lmin,lmax]

Usage:

cl = basic.bispec.cl_flat(cpmodel,z,dz,zs,lmax,k,pk0,zn,kn,pktype,cltype,dNdz,wdel):

basic.bispec.bispeclens(shap, cpmodel, model, z, dz, zs, lmin, lmax, k, pk0, zn=0, kn=0, lan=0.0, kan=0.0, pktype='T12', ltype='', btype='kkk', dNdz=None, wdel=None)¶

Compute lensing bispectrum analytically

Args:

dz[zn] (double):
shap (str):	shape of the bispectrum (equi, fold, sque, or isos)
cpmodel (str):	cosmological parameter model (model0, modelw, or modelp)
model (str):	fitting formula of the matter bispectrum (LN=linear, SC=SC03, GM=Gil-Marin+12, 3B=3-shape-bispectrum, or RT=Takahashi+19)
z[zn] (double):	redshift points for the z-integral
	interval of z
zs[3] (double):	source redshifts
lmin/lmax (int):
	minimum/maximum multipoles of the bispectrum
k[kn] (double):	k for the matter power spectrum in unit of [h/Mpc]
pk0[kn] (double):
	the linear matter power spectrum at z=0 in unit of [Mpc^3/h^3]

Args(optional):

lan, kan (double):
	parameters for the modified gravity extension, default to lan=kan=1 (GR)
pktype (str):	fitting formula for the matter power spectrum (Lin=Linear, S02=Smith et al. 2002 or T12=Takahashi et al. 2012), default to T12
ltype (str):	fullsky correction (full) or not
btype (str):	bispectrum type, i.e., kkk (lens-lens-lens), gkk (density-lens-lens), ggk (density-density-lens), or ggg (density-density-density)
dNdz[zn] (double):
	redshift distribution of galaxy, only used when btype includes g
wdel[zn,l] (double):
	modified chi-kernel function by z-cleaning at l=0 to lmax

Returns:

bl0[l] (double):
	lensing bispectrum from LSS contributions at [lmin,lmax]
bl1[l] (double):
	lensing bispectrum from post-Born contributions at [lmin,lmax]

Usage:

bl0,bl1 = basic.bispec.bispeclens(shap,cpmodel,model,z,dz,zs,lmin,lmax,k,pk0,lan,kan,zn,kn,pktype,ltype,btype,dNdz,wdel):

basic.bispec.bispeclens_bin(shap, cpmodel, model, z, dz, zs, lmin, lmax, bn, k, pk0, zn=0, kn=0, lan=0.0, kan=0.0, pktype='T12', btype='kkk', dNdz=None, wdel=None)¶

Compute binned lensing bispectrum analytically

Args:

dz[zn] (double):
shap (str):	shape of the bispectrum (equi, fold, sque, or isos)
cpmodel (str):	cosmological parameter model (model0, modelw, or modelp)
model (str):	fitting formula of the matter bispectrum (LN=linear, SC=SC03, GM=Gil-Marin+12, 3B=3-shape-bispectrum, or RT=Takahashi+19)
z[zn] (double):	redshift points for the z-integral
	interval of z
zs[3] (double):	source redshifts
lmin/lmax (int):
	minimum/maximum multipoles of the bispectrum
bn (int):	number of multipole bins
k[kn] (double):	k for the matter power spectrum in unit of [h/Mpc]
pk0[kn] (double):
	the linear matter power spectrum at z=0 in unit of [Mpc^3/h^3]

Args(optional):

lan, kan (double):
	parameters for the modified gravity extension, default to lan=kan=1 (GR)
pktype (str):	fitting formula for the matter power spectrum (Lin, S02 or T12)
btype (str):	bispectrum type, i.e., kkk (lens-lens-lens), gkk (density-lens-lens), ggk (density-density-lens), or ggg (density-density-density)
dNdz[zn] (double):
	redshift distribution of galaxy, only used when btype includes g
wdel[zn,l] (double):
	modified chi-kernel function by z-cleaning at l=0 to lmax

Returns:

bc[bn] (double):
	multipole bin centers
bl0[bn] (double):
	binned lensing bispectrum from LSS contributions
bl1[bn] (double):
	binned lensing bispectrum from post-Born contributions

Usage:

bc,bl0,bl1 = basic.bispec.bispeclens_bin(shap,cpmodel,model,z,dz,zn,zs,lmin,lmax,bn,k,pk0,kn,lan,kan,pktype,btype,dNdz,wdel):

basic.bispec.bispeclens_snr(cpmodel, model, z, dz, zs, lmin, lmax, cl, k, pk0, zn=0, kn=0, pktype='T12', btype='kkk', dNdz=None, wdel=None, cgg=None, ro=100)¶

Compute SNR of lensing bispectrum analytically

Args:

dz[zn] (double):
cpmodel (str):	cosmological parameter model (model0, modelw, or modelp)
model (str):	fitting formula of the matter bispectrum (LN=linear, SC=SC03, GM=Gil-Marin+12, 3B=3-shape-bispectrum, or RT=Takahashi+19)
z[zn] (double):	redshift points for the z-integral
	interval of z
zs[3] (double):	source redshifts
lmin/lmax (int):
	minimum/maximum multipoles of the bispectrum
cl[l] (int):	observed angular power spectrum at 0<=l<=lmax
k[kn] (double):	k for the matter power spectrum in unit of [h/Mpc]
pk0[kn] (double):
	the linear matter power spectrum at z=0 in unit of [Mpc^3/h^3]

Args(optional):

dNdz[zn] (double):
pktype (str):	fitting formula for the matter power spectrum (Lin, S02 or T12)
btype (str):	bispectrum type, i.e., kkk (lens-lens-lens), gkk (density-lens-lens), ggk (density-density-lens), or ggg (density-density-density)
	redshift distribution of galaxy, only used when btype includes g
wdel[zn,l] (double):
	modified chi-kernel function by z-cleaning at l=0 to lmax
cgg[l] (double):
	observed galaxy spectrum
ro (int):	output progress for every “ro” multipoles (ro=100, default)

Returns:

snr[2] (double):
	total SNR amd LSS-only SNR

Usage:

snr = basic.bispec.bispeclens_snr(cpmodel,model,z,dz,zn,zs,lmin,lmax,cl,k,pk0,kn,pktype,btype,dNdz,cgg,ro,wdel):

basic.bispec.bispeclens_gauss_bin(shap, bn, lmin, lmax, cl)¶

Compute binned bispectrum analytically for the quadratic gaussian model

Args:

lmin/lmax (int):
shap (str):	shape of the bispectrum (equi, fold, sque, or isos)
bn (int):	number of multipole bins
	minimum/maximum multipoles of the bispectrum
cl[l] (double):	the power spectrum at [0:lmax+1]

Returns:

bc[bn] (double):
	multipole bin centers
bl[bn] (double):
	binned bispectrum

Usage:

bc,bl = basic.bispec.bispeclens_gauss_bin(shap,bn,lmin,lmax,cl):

basic.bispec.zpoints(zmin, zmax, zn, zspace=1)¶

Precomputing interpolation points for z

Args:

zmin/zmax (double):
	minimum/maximum redshifts
zn (int):	number of redshifts

Args(optional):

zspace (int):	type of spacing

Returns:

dz[zn] (double):
z[zn] (double):	redshifts
	redshift intervals

Usage:

z,dz = basic.bispec.zpoints(zmin,zmax,zn,zspace):

basic.bispec.skewspeclens(cpmodel, model, zmin, zmax, zn, zs, ols, lmin, lmax, k, pk0, pktype='T12', pb=True, theta=0.0, Om=0.3, H0=70.0, w0=-1.0, wa=0.0, mnu=0.06, ns=0.965, bn=0, kn=0, verbose=True, wdel=None)¶

Compute skew spectrum using a matter bispectrum fitting formula

Args:

cpmodel (str): cosmological parameter model (model0, modelw, modelp, or input)

model (str): fitting formula of the matter bispectrum (LN=linear, SC=SC03, GM=Gil-Marin+12, 3B=3-shape-bispectrum, or RT=Takahashi+19)

zmin/zmax (double):

minimum/maximum z for z-integral

zn (int): number of redshifts for the z-integral

zs[2] (double): source redshifts where zs[2] is used for the squared map

lmin/lmax (int):

minimum/maximum multipoles of alms included in the skew spectrum

ols[bn] (int): output multipoles to be computed for skew spectrum

k[kn] (double): k for the matter power spectrum [h/Mpc]

pk0 (double): the linear matter power spectrum at z=0 [Mpc^3/h^3]

Args(optional):

pktype (str): fitting formula for the matter power spectrum (Lin, S02 or T12)

theta (double): kappa map resolution in arcmin

pb (bool): with post-Born correction or not (default=True)

verbose (bool): output messages

wdel[zn,l] (double):

modified chi-kernel function by z-cleaning at l=0 to lmax

Returns:

skew (double): skew-spectrum

Usage:

skew = basic.bispec.skewspeclens(cpmodel,model,zmin,zmax,zn,zs,bn,ols,lmin,lmax,k,pk0,kn,theta,pktype,pb,Om,H0,w0,wa,mnu,ns,verbose,wdel):

`galaxy` – tools for galaxy z distribution¶

basic.galaxy.dndz_sf(z, a, b, zm=0, z0=0, zn=None)¶

A model of galaxy z distribution

Args:

z[zn] (double): redshifts at which dNdz is returned

a, b (double): shape parameters of Schechter-like galaxy distribution

Args(optional):

zm (double): mean redshift, default to 0

z0 (double): a parameter relevant to zm, default to 0. Either zm or z0 has to be specified.

Returns:

dndz[zn] (double):

galaxy z distribution

Usage:

dndz = basic.galaxy.dndz_sf(zn,z,a,b,zm,z0):

basic.galaxy.photoz_error(z, zi, zn=None, sigma=0.03, zbias=0.0)¶

Photo-z error on z distribution which is multiplied to original galaxy z distribution. See Eq.(13) of arXiv:1103.1118 for details.

Args:

z[zn] (double): redshifts at which photoz error function is returned

zi[2] (double): z-bin edges

sigma (double): a parameter of photo-z error which is given by, sigma x (1+z)

zbias (double): photo-z mean bias

Returns:

pz[zn] (double):

photoz error function

Usage:

pz = basic.galaxy.photoz_error(zn,z,zi,sigma,zbias):

basic.galaxy.zbin(zn, a, b, zm=0, z0=0, verbose=False)¶

Computing z-interval of z-bin so that number of galaxies at each z-bin is equal

Args:

zn (int): number of z-bins

a, b (double): shape parameters of Schechter-like galaxy distribution

Args(optional):

zm (double): mean redshift, default to 0

z0 (double): a parameter relevant to zm, default to 0. Either zm or z0 has to be specified.

verbose (bool): output messages (default to True)

Returns:

zb[zn+1] (double):

z-intervals

Usage:

zb = basic.galaxy.zbin(zn,a,b,zm,z0,verbose):

basic.galaxy.frac(zn, zb, a, b, zm, verbose=False, zbias=0.0, sigma=0.0)¶

Computing z-interval of z-bin so that number of galaxies at each z-bin is equal

Args:

zn (int): number of z-bins

a, b (double): shape parameters of Schechter-like galaxy distribution

zm (double): mean redshift

zb[zn+1] (double):

z-intervals

Args(optional):

verbose (bool): output messages (default to True)

zbias (double): constant bias to true photo-z

sigma (double): uncertaines of photo-z

Returns:

nfrac[zn] (double):

fraction of galaxy number at each bin, defined by int_zi^zi+1 dz N(z)/int dz N(z)

Usage:

nfrac = basic.galaxy.frac(zn,zb,a,b,zm,zbias,sigma,verbose):

`cosmofuncs` – tools for cosmology related functions¶

basic.cosmofuncs.hubble(z, H0=70.0, Ov=0.7, Om=0.3, w0=-1.0, wa=0.0, zn=0, divc=False)¶

Compute the expansion rate in unit of 1/Mpc, H/c, or in unit of km/s/Mpc, H.

Args:

z[zn] (double):	Redshifts at which H is computed

Args(optional):

w0, wa (double):
H0 (double):	The current value of hubble parameter in km/s/Mpc, default to 70 km/s/Mpc
Om (double):	The current value of Omega_matter, default to 0.3
Ov (double):	The current value of Omega_Dark-energy, default to 0.7
	The EoS of Dark Energy, default to w0=-1 and wa=0.
divc (bool):	Divide H by c or not, default to False.

Returns:

Hz[zn] (double):
	The expansion rate, H(z), divided by c or not.

Usage:

Hz = basic.cosmofuncs.hubble(z,H0,Om,Ov,w0,wa,zn,divc):

basic.cosmofuncs.dhubble_dz(z, H0=70.0, Ov=0.7, Om=0.3, w0=-1.0, wa=0.0, zn=0)¶

Usage:

dHdz = basic.cosmofuncs.dhubble_dz(z,H0,Om,Ov,w0,wa,zn):

basic.cosmofuncs.dist2z(rz, H0=70.0, Ov=0.7, Om=0.3, w0=-1.0, wa=0.0, zn=0)¶

Usage:

z = basic.cosmofuncs.dist2z(rz,H0,Om,Ov,w0,wa,zn):

basic.cosmofuncs.dist_comoving(z, H0=70.0, Ov=0.7, Om=0.3, w0=-1.0, wa=0.0, zn=0)¶

Usage:

rz = basic.cosmofuncs.dist_comoving(z,H0,Om,Ov,w0,wa,zn):

basic.cosmofuncs.dist_luminosity(z, H0=70.0, Ov=0.7, Om=0.3, w0=-1.0, wa=0.0, zn=0)¶

Usage:

DLz = basic.cosmofuncs.dist_luminosity(z,H0,Om,Ov,w0,wa,zn):

basic.cosmofuncs.growth_factor(z, normed=False, H0=70.0, Ov=0.7, Om=0.3, w0=-1.0, wa=0.0, zn=0)¶

Usage:

Dz = basic.cosmofuncs.growth_factor(z,H0,Om,Ov,w0,wa,zn,normed):

basic.cosmofuncs.growth_rate(z, H0=70.0, Ov=0.7, Om=0.3, w0=-1.0, wa=0.0, zn=0)¶

Usage:

fz = basic.cosmofuncs.growth_rate(z,H0,Om,Ov,w0,wa,zn):

basic.cosmofuncs.nz_gw(z, Cz, Hz, ntype='CH06', dotn0=1e-06, Tobs=3.0)¶

Distribution function of NS binary sources per redshift (dN/dz) at z

Args:

z (double):	redshift
Cz (double):	comoving distance
Hz (double):	expansion rate

Args(optional):

ntype (str):	type of dotn functional form, i.e, CH06 (default) or none.
dotn0 (double):	current merger-rate
Tobs (double):	total observation time

Returns:

nz (double):	distribution function at z

Usage:

nz = basic.cosmofuncs.nz_gw(z,Cz,Hz,ntype,dotn0,Tobs):

basic.cosmofuncs.drate_dz(z, ntype='CH06', zn=0)¶

Usage:

dndz = basic.cosmofuncs.drate_dz(z,zn,ntype):

`flat` – cross-check tools for flat-sky normalization¶

basic.flat.alxy(qest, qtype, lmax, rlmin, rlmax, fC, W1, W2, gln=100, lxcut=0, gle=1e-14)¶

Compute flat-sky quadratic estimator normalization CAUTION: This code interpolates the input Cl at the non-integer multipole by simply Cl(int(ell)) which leads to a small discrepancy in the normalization computed from the FFT-based method (which uses linear interpolation) and from this code. It is desireble to use the FFT-based normalization if you want to normalize the simulation results.

Args:

rlmax/rlmin (double):
qest (str):	estimator combination (TT, TE, TB, EE, EB, or BB)
qtype (str):	estimator type (lensing, patchytau)
lmax (double):	output maximum multipole
	input CMB multipole range for reconstruction
fC[rlmax] (double):
	power spectrum in the numerator

:W1/W2[rlmax] : inverse of the observed power spectrum

Args(optional):

gln (int):	number of the GL integration points
lxcut (int):	multipole cut in x-direction, \|l_x\| < lx
gle (double):	convergence parameter for the GL integration

Returns:

Ag/Ac[l] (double):
	normalization for even and odd estimator pairs

Usage:

Ag,Ac = basic.flat.alxy(qest,qtype,lmax,rlmin,rlmax,fC,W1,W2,gln,gle,lxcut):

basic.flat.alxy_asym(qest, qtype, lmax, rlmin, rlmax, fC, AA, BB, AB, gln=100, lxcut=0, gle=1e-14)¶

Usage:

Ag,Ac = basic.flat.alxy_asym(qest,qtype,lmax,rlmin,rlmax,fC,AA,BB,AB,gln,gle,lxcut):

basic.flat.bbxy(lmax, rlmin, rlmax, XX, YY, weight='lensing', gln=100, gle=1e-14)¶

Usage:

BB = basic.flat.bbxy(lmax,rlmin,rlmax,XX,YY,weight,gln,gle):

`wigner_funcs` – Wigner 3j symbols¶

basic.wigner_funcs.wigner_3j(l2, l3, m2, m3)¶

Compute wigner3j for all possible l1 where w3j = (j1,j2,j3/m1,m2,m3)

Args:

dz[zn] (double):
shap (str):	shape of the bispectrum (equi, fold, sque, or isos)
cpmodel (str):	cosmological parameter model (model0, modelw, or modelp)
model (str):	fitting formula of the matter bispectrum (LN=linear, SC=SC03, GM=Gil-Marin+12, 3B=3-shape-bispectrum, or RT=Takahashi+19)
z[zn] (double):	redshift points for the z-integral
zn (int):	number of redshifts for the z-integral
	interval of z
zs[3] (double):	source redshifts
lmin/lmax (int):
	minimum/maximum multipoles of the bispectrum
k[kn] (double):	k for the matter power spectrum
pk0 (double):	the linear matter power spectrum at z=0
kn (int):	size of k

Returns:

bl0[l] (double):
	lensing bispectrum from LSS contributions at [lmin,lmax]
bl1[l] (double):
	lensing bispectrum from post-Born contributions at [lmin,lmax]

Usage:

w3j = basic.wigner_funcs.wigner_3j(l2,l3,m2,m3):

basic – Some basic tools¶

delens – analytic calculation for delensing¶

bispec – analytic calculation of bispectrum¶

galaxy – tools for galaxy z distribution¶

cosmofuncs – tools for cosmology related functions¶

flat – cross-check tools for flat-sky normalization¶

wigner_funcs – Wigner 3j symbols¶

`basic` – Some basic tools¶

`delens` – analytic calculation for delensing¶

`bispec` – analytic calculation of bispectrum¶

`galaxy` – tools for galaxy z distribution¶

`cosmofuncs` – tools for cosmology related functions¶

`flat` – cross-check tools for flat-sky normalization¶

`wigner_funcs` – Wigner 3j symbols¶