basic – Some basic tools

delens – analytic calculation for delensing

cmblensplus.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/elmax (int):

Minimum/Maximum multipole of E-modes

klmin/klmax (int):

Minimum/Maximum multipole of lensing potential or kappa

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)

cmblensplus.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)

cmblensplus.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:

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)

NP1[l] (double):

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)

bispec – analytic calculation of bispectrum

cmblensplus.basic.bispec.cl_flat(cpmodel, z, dz, zs, lmax, k, pk0, pktype='T12', cltype='kk', dNdz=None, wdel=None)

Compute flat-sky lensing power spectrum analytically

Args:

cpmodel (str):

cosmological parameter model (model0, modelw, or modelp)

z[zn] (double):

redshift points for the z-integral

dz[zn] (double):

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):

pktype (str):

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

cltype (str):

kk, gk, or gg

dNdz[zn] (double):

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]

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

Compute lensing bispectrum analytically

Args:

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

dz[zn] (double):

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]

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

Compute binned lensing bispectrum analytically

Args:

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

dz[zn] (double):

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

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

Compute SNR of lensing bispectrum analytically

Args:

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

dz[zn] (double):

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):

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

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

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

Compute binned bispectrum analytically for the quadratic gaussian model

Args:

shap (str):

shape of the bispectrum (equi, fold, sque, or isos)

bn (int):

number of multipole bins

lmin/lmax (int):

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

cmblensplus.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. 0 for linear and 1 for gauss-legendre.

Returns:

z[zn] (double):

redshifts

dz[zn] (double):

redshift intervals

cmblensplus.basic.bispec.skewspeclens(cpmodel, model, z, dz, zs, ols, lmin, lmax, k, pk0, theta=0.0, pktype='T12', btype='kkk', pb=True, Om=0.3, H0=70.0, w0=-1.0, wa=0.0, mnu=0.06, ns=0.965, verbose=True, dNdz=None, wdel=None)

Compute skew spectrum using a matter bispectrum fitting formula (Xl1,Yl2,Yl3)

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)

z[zn] (double):

redshift points for the z-integral

dz[zn] (double):

interval of z

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)

btype (str):

bispectrum type, i.e., kkk (lens-lens^2), gkk (density-lens^2), kgg (lens-density^2), or ggg (density-density^2)

dNdz[zn] (double):

redshift distribution of galaxy, only used when btype includes g

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[3,2,l] (double):

skew-spectrum (S0, S1, S2) from LSS and PB contributions, separately

galaxy – tools for galaxy z distribution

cmblensplus.basic.galaxy.dndz_sf(z, a, b, zm=0, z0=0)

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

cmblensplus.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

cmblensplus.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

cmblensplus.basic.galaxy.frac(zn, zb, a, b, zm, zbias=0.0, sigma=0.0, 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

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)

cosmofuncs – tools for cosmology related functions

cmblensplus.basic.cosmofuncs.hubble(z, H0=70.0, Om=0.3, Ov=0.7, w0=-1.0, wa=0.0, 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):

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

w0, wa (double):

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.

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

Compute dH(z)/dz.

Args:

z[zn] (double):

Redshifts at which dH/dz is computed

Args(optional):

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

w0, wa (double):

The EoS of Dark Energy, default to w0=-1 and wa=0.

Returns:

dHdz[zn] (double):

The derivative of the expansion rate, dH(z)/dz.

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

Compute redshift as a function of comoving distance

Args:

rz[zn] (double):

Comoving distance [Mpc]

Args(optional):

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

w0, wa (double):

The EoS of Dark Energy, default to w0=-1 and wa=0.

Returns:

z[zn] (double):

Redshift

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

Compute comoving distance as a function of z

Args:

z[zn] (double):

Redshift

Args(optional):

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

w0, wa (double):

The EoS of Dark Energy, default to w0=-1 and wa=0.

Returns:

rz[zn] (double):

Comoving distance [Mpc]

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

Compute luminosity distance as a function of z

Args:

z[zn] (double):

Redshift

Args(optional):

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

w0, wa (double):

The EoS of Dark Energy, default to w0=-1 and wa=0.

Returns:

DLz[zn] (double):

Luminosity distance [Mpc]

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

Compute analytic linear growth factor D(z) as a function of z

Args:

z[zn] (double):

Redshift

Args(optional):

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

w0, wa (double):

The EoS of Dark Energy, default to w0=-1 and wa=0.

normed (bool):

If True, D(z=0)=1. Otherwise, the normalization is defined so that D(z)=a in the pure matter universe, Om(a)=1.

Returns:

Dz[zn] (double):

Growth factor

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

Compute linear growth rate f(z) = dlnD/dlna as a function of z

Args:

z[zn] (double):

Redshift

Args(optional):

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

w0, wa (double):

The EoS of Dark Energy, default to w0=-1 and wa=0.

Returns:

fz[zn] (double):

Growth rate

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

Distribution function of NS-NS merger events 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

cmblensplus.basic.cosmofuncs.drate_dz(z, ntype='CH06')

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

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

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:

qest (str):

estimator combination (TT, TE, TB, EE, EB, or BB)

qtype (str):

estimator type (lensing, patchytau)

lmax (double):

output maximum multipole

rlmax/rlmin (double):

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

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

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

wigner_funcs – Wigner 3j symbols

cmblensplus.basic.wigner_funcs.wigner_3j(l2, l3, m2, m3)

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

Args:

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

dz[zn] (double):

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]