curvedsky – Curvedsky analysis tools

rec_lens – quadratic lensing reconstruction

curvedsky.rec_lens.qtt(lmax, rlmin, rlmax, fC, Tlm1, Tlm2, nside_t=0, gtype='', verbose=False)

Reconstructing CMB lensing potential and its curl mode from the temperature quadratic estimator

Args:
lmax (int):Maximum multipole of output lensing potential alms
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
fC [l] (double):
 TT spectrum, with bounds (0:rlmax)
Tlm1 [l,m] (dcmplx):
 1st inverse-variance filtered temperature alm, with bounds (0:rlmax,0:rlmax)
Tlm2 [l,m] (dcmplx):
 2nd inverse-variance filtered temperature alm, with bounds (0:rlmax,0:rlmax)
Args(optional):
nside_t (int):Nside for the convolution calculation
gtype (str):Type of output, i.e., convergence (gtype=’k’) or lensing potential (gtype=’‘, default)
verbose (bool):Output messages, default to False
Returns:
glm [l,m] (dcmplx):
 CMB lensing potential alm, with bounds (0:lmax,0:lmax)
clm [l,m] (dcmplx):
 Curl mode (pseudo lensing potential) alm, with bounds (0:lmax,0:lmax)
Usage:
glm,clm = curvedsky.rec_lens.qtt(lmax,rlmin,rlmax,fC,Tlm1,Tlm2,nside_t,gtype,verbose):
 
curvedsky.rec_lens.qte(lmax, rlmin, rlmax, fC, Tlm, Elm, nside_t=0, gtype='', verbose=False)

Reconstructing CMB lensing potential and its curl mode from the TE quadratic estimator

Args:
lmax (int):Maximum multipole of output lensing potential alms
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
fC [l] (double):
 TE spectrum, with bounds (0:rlmax)
Tlm [l,m] (dcmplx):
 Inverse-variance filtered temperature alm, with bounds (0:rlmax,0:rlmax)
Elm [l,m] (dcmplx):
 Inverse-variance filtered E-mode alm, with bounds (0:rlmax,0:rlmax)
Args(optional):
nside_t (int):Nside for the convolution calculation
gtype (str):Type of output, i.e., convergence (gtype=’k’) or lensing potential (gtype=’‘, default)
verbose (bool):Output messages, default to False
Returns:
glm [l,m] (dcmplx):
 CMB lensing potential, with bounds (0:lmax,0:lmax)
clm [l,m] (dcmplx):
 Curl mode (pseudo lensing potential), with bounds (0:lmax,0:lmax)
Usage:
glm,clm = curvedsky.rec_lens.qte(lmax,rlmin,rlmax,fC,Tlm,Elm,nside_t,gtype,verbose):
 
curvedsky.rec_lens.qtb(lmax, rlmin, rlmax, fC, Tlm, Blm, nside_t=0, gtype='', verbose=False)

Reconstructing CMB lensing potential and its curl mode from the TB quadratic estimator

Args:
lmax (int):Maximum multipole of output lensing potential alms
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
fC [l] (double):
 TE spectrum, with bounds (0:rlmax)
Tlm [l,m] (dcmplx):
 Inverse-variance filtered temperature alm, with bounds (0:rlmax,0:rlmax)
Blm [l,m] (dcmplx):
 Inverse-variance filtered B-mode alm, with bounds (0:rlmax,0:rlmax)
Args(optional):
nside_t (int):Nside for the convolution calculation
gtype (str):Type of output, i.e., convergence (gtype=’k’) or lensing potential (gtype=’‘, default)
verbose (bool):Output messages, default to False
Returns:
glm [l,m] (dcmplx):
 CMB lensing potential, with bounds (0:lmax,0:lmax)
clm [l,m] (dcmplx):
 Curl mode (pseudo lensing potential), with bounds (0:lmax,0:lmax)
Usage:
glm,clm = curvedsky.rec_lens.qtb(lmax,rlmin,rlmax,fC,Tlm,Blm,nside_t,gtype,verbose):
 
curvedsky.rec_lens.qee(lmax, rlmin, rlmax, fC, Elm1, Elm2, nside_t=0, gtype='', verbose=False)

Reconstructing CMB lensing potential and its curl mode from the EE quadratic estimator

Args:
lmax (int):Maximum multipole of output lensing potential alms
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
fC [l] (double):
 EE spectrum, with bounds (0:rlmax)
Elm1 [l,m] (dcmplx):
 1st inverse-variance filtered E-mode alm, with bounds (0:rlmax,0:rlmax)
Elm2 [l,m] (dcmplx):
 2nd inverse-variance filtered E-mode alm, with bounds (0:rlmax,0:rlmax)
Args(optional):
nside_t (int):Nside for the convolution calculation
gtype (str):Type of output, i.e., convergence (gtype=’k’) or lensing potential (gtype=’‘, default)
verbose (bool):Output messages, default to False
Returns:
glm [l,m] (dcmplx):
 CMB lensing potential, with bounds (0:lmax,0:lmax)
clm [l,m] (dcmplx):
 Curl mode (pseudo lensing potential), with bounds (0:lmax,0:lmax)
Usage:
glm,clm = curvedsky.rec_lens.qee(lmax,rlmin,rlmax,fC,Elm1,Elm2,nside_t,gtype,verbose):
 
curvedsky.rec_lens.qeb(lmax, rlmin, rlmax, fC, Elm, Blm, nside_t=0, gtype='', verbose=False)

Reconstructing CMB lensing potential and its curl mode from the EB quadratic estimator

Args:
lmax (int):Maximum multipole of output lensing potential alms
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
fC [l] (double):
 EE spectrum, with bounds (0:rlmax)
Elm [l,m] (dcmplx):
 Inverse-variance filtered E-mode alm, with bounds (0:rlmax,0:rlmax)
Blm [l,m] (dcmplx):
 Inverse-variance filtered B-mode alm, with bounds (0:rlmax,0:rlmax)
Args(optional):
nside_t (int):Nside for the convolution calculation
gtype (str):Type of output, i.e., convergence (gtype=’k’) or lensing potential (gtype=’‘, default)
verbose (bool):Output messages, default to False
Returns:
glm [l,m] (dcmplx):
 CMB lensing potential, with bounds (0:lmax,0:lmax)
clm [l,m] (dcmplx):
 Curl mode (pseudo lensing potential), with bounds (0:lmax,0:lmax)
Usage:
glm,clm = curvedsky.rec_lens.qeb(lmax,rlmin,rlmax,fC,Elm,Blm,nside_t,gtype,verbose):
 
curvedsky.rec_lens.qbb(lmax, rlmin, rlmax, fC, Blm1, Blm2, nside_t=0, gtype='', verbose=False)

Reconstructing CMB lensing potential and its curl mode from the BB quadratic estimator

Args:
lmax (int):Maximum multipole of output lensing potential alms
rlmin/rlmax (int):
 Minimum/Maximum multipoles of CMB for reconstruction
fC [l] (double):
 BB spectrum, with bounds (0:rlmax)
Blm1 [l,m] (dcmplx):
 1st inverse-variance filtered B-mode alm, with bounds (0:rlmax,0:rlmax)
Blm2 [l,m] (dcmplx):
 2nd inverse-variance filtered B-mode alm, with bounds (0:rlmax,0:rlmax)
Args(optional):
nside_t (int):Nside for the convolution calculation
gtype (str):Type of output, i.e., convergence (gtype=’k’) or lensing potential (gtype=’‘, default)
verbose (bool):Output messages, default to False
Returns:
glm [l,m] (dcmplx):
 CMB lensing potential, with bounds (0:lmax,0:lmax)
clm [l,m] (dcmplx):
 Curl mode (pseudo lensing potential), with bounds (0:lmax,0:lmax)
Usage:
glm,clm = curvedsky.rec_lens.qbb(lmax,rlmin,rlmax,fC,Blm1,Blm2,nside_t,gtype,verbose):
 

rec_rot – quadratic rotation reconstruction

curvedsky.rec_rot.qeb(lmax, rlmin, rlmax, fCE, Elm, Blm, nside_t=0, verbose=False)

Reconstructing pol rotation angle from the EB quadratic estimator

Args:
lmax (int):Maximum multipole of output lensing potential alms
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
fCE [l] (double):
 EE spectrum, with bounds (0:rlmax)
Elm [l,m] (dcmplx):
 Inverse-variance filtered E-mode alm, with bounds (0:rlmax,0:rlmax)
Blm [l,m] (dcmplx):
 Inverse-variance filtered B-mode alm, with bounds (0:rlmax,0:rlmax)
Args(optional):
nside_t (int):Nside for the convolution calculation
verbose (bool):Output messages, default to False
Returns:
alm [l,m] (dcmplx):
 Rotation angle alm, with bounds (0:lmax,0:lmax)
Usage:
alm = curvedsky.rec_rot.qeb(lmax,rlmin,rlmax,fCE,Elm,Blm,nside_t,verbose):
 

rec_tau – quadratic tau reconstruction

curvedsky.rec_tau.qtt(lmax, rlmin, rlmax, fC, Tlm1, Tlm2, nside_t=0, verbose=False)

Reconstructing inhomogeneous tau from the temperature quadratic estimator

Args:
lmax (int):Maximum multipole of output tau alms
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
fC [l] (double):
 TT spectrum, with bounds (1:rlmax)
Tlm1 [l,m] (dcmplx):
 1st inverse-variance filtered temperature alm, with bounds (0:rlmax,0:rlmax)
Tlm2 [l,m] (dcmplx):
 2nd inverse-variance filtered temperature alm, with bounds (0:rlmax,0:rlmax)
Args(optional):
nside_t (int):Nside for the convolution calculation
verbose (bool):Output messages, default to False
Returns:
alm [l,m] (dcmplx):
 Amplitude modulation alm, with bounds (0:lmax,0:lmax)
Usage:
alm = curvedsky.rec_tau.qtt(lmax,rlmin,rlmax,fC,Tlm1,Tlm2,nside_t,verbose):
 
curvedsky.rec_tau.qeb(lmax, rlmin, rlmax, fCE, Elm, Blm, nside_t=0, verbose=False)

Reconstructing amplitude modulation from the EB quadratic estimator

Args:
lmax (int):Maximum multipole of output lensing potential alms
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
fCE [l] (double):
 EE spectrum, with bounds (0:rlmax)
Elm [l,m] (dcmplx):
 Inverse-variance filtered E-mode alm, with bounds (0:rlmax,0:rlmax)
Blm [l,m] (dcmplx):
 Inverse-variance filtered B-mode alm, with bounds (0:rlmax,0:rlmax)
Args(optional):
nside_t (int):Nside for the convolution calculation
verbose (bool):Output messages, default to False
Returns:
alm [l,m] (dcmplx):
 Amplitude modulation alm, with bounds (0:lmax,0:lmax)
Usage:
alm = curvedsky.rec_tau.qeb(lmax,rlmin,rlmax,fCE,Elm,Blm,nside_t,verbose):
 

rec_src – quadratic point-soruce reconstruction

curvedsky.rec_src.qtt(lmax, rlmin, rlmax, Tlm1, Tlm2, nside_t=0, verbose=False)

Reconstructing point sources from the temperature quadratic estimator

Args:
lmax (int):Maximum multipole of output point-source alms
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
Tlm1 [l,m] (dcmplx):
 1st inverse-variance filtered temperature alm, with bounds (0:rlmax,0:rlmax)
Tlm2 [l,m] (dcmplx):
 2nd inverse-variance filtered temperature alm, with bounds (0:rlmax,0:rlmax)
Args(optional):
nside_t (int):Nside for the convolution calculation
verbose (bool):Output messages, default to False
Returns:
slm [l,m] (dcmplx):
 Point-source alm, with bounds (0:lmax,0:lmax)
Usage:
slm = curvedsky.rec_src.qtt(lmax,rlmin,rlmax,Tlm1,Tlm2,nside_t,verbose):
 

norm_quad – normalization of quadratic estimator reconstruction

curvedsky.norm_quad.qtt(est, lmax, rlmin, rlmax, TT, OCT, lfac='')

Normalization of reconstructed fields from the temperature quadratic estimator

Args:
lmax (int):Maximum multipole of output normalization spectrum
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
TT [l] (double):
 Theory TT spectrum, with bounds (0:rlmax)
OCT [l] (double):
 Observed TT spectrum, with bounds (0:rlmax)
Args(optional):
lfac (str):Multiplying square of L(L+1)/2, i.e., convergence (lfac=’k’) or lensing potential (lfac=’‘, default)
Returns:
Al [2,l] (double):
 Normalizations (1 is dummy except lens = 0 and curl = 1), with bounds (0:lmax)
Usage:
Al = curvedsky.norm_quad.qtt(est,lmax,rlmin,rlmax,TT,OCT,lfac):
 
curvedsky.norm_quad.qte(est, lmax, rlmin, rlmax, TE, OCT, OCE, lfac='')

Normalization of reconstructed fields from the TE quadratic estimator

Args:
lmax (int):Maximum multipole of output normalization spectrum
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
TE [l] (double):
 Theory TE spectrum, with bounds (0:rlmax)
OCT [l] (double):
 Observed TT spectrum, with bounds (0:rlmax)
OCE [l] (double):
 Observed EE spectrum, with bounds (0:rlmax)
Args(optional):
lfac (str):Multiplying square of L(L+1)/2, i.e., convergence (lfac=’k’) or lensing potential (lfac=’‘, default)
Returns:
Al [2,l] (double):
 Normalizations (1 is dummy except lens = 0 and curl = 1), with bounds (0:lmax)
Usage:
Al = curvedsky.norm_quad.qte(est,lmax,rlmin,rlmax,TE,OCT,OCE,lfac):
 
curvedsky.norm_quad.qtb(est, lmax, rlmin, rlmax, TE, OCT, OCB, lfac='')

Normalization of reconstructed fields from the TB quadratic estimator

Args:
lmax (int):Maximum multipole of output normalization spectrum
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
TE [l] (double):
 Theory TE spectrum, with bounds (0:rlmax)
OCT [l] (double):
 Observed TT spectrum, with bounds (0:rlmax)
OCB [l] (double):
 Observed BB spectrum, with bounds (0:rlmax)
Args(optional):
lfac (str):Multiplying square of L(L+1)/2, i.e., convergence (lfac=’k’) or lensing potential (lfac=’‘, default)
Returns:
Al [2,l] (double):
 Normalizations (1 is dummy except lens = 0 and curl = 1), with bounds (0:lmax)
Usage:
Al = curvedsky.norm_quad.qtb(est,lmax,rlmin,rlmax,TE,OCT,OCB,lfac):
 
curvedsky.norm_quad.qee(est, lmax, rlmin, rlmax, EE, OCE, lfac='')

Normalization of reconstructed amplitude modulation from the EE quadratic estimator

Args:
lmax (int):Maximum multipole of output normalization spectrum
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
EE [l] (double):
 Theory EE spectrum, with bounds (0:rlmax)
OCE [l] (double):
 Observed EE spectrum, with bounds (0:rlmax)
Args(optional):
lfac (str):Multiplying square of L(L+1)/2, i.e., convergence (lfac=’k’) or lensing potential (lfac=’‘, default)
Returns:
Al [2,l] (double):
 Normalization, with bounds (0:lmax)
Usage:
Al = curvedsky.norm_quad.qee(est,lmax,rlmin,rlmax,EE,OCE,lfac):
 
curvedsky.norm_quad.qeb(est, lmax, rlmin, rlmax, EE, OCE, OCB, lfac='', BB=0)

Normalization of reconstructed fields from the EB quadratic estimator

Args:
lmax (int):Maximum multipole of output normalization spectrum
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
EE [l] (double):
 Theory EE spectrum, with bounds (0:rlmax)
OCE [l] (double):
 Observed EE spectrum, with bounds (0:rlmax)
OCB [l] (double):
 Observed BB spectrum, with bounds (0:rlmax)
Args(optionals):
BB [l] (double):
 Theory BB spectrum, with bounds (0:rlmax)
lfac (str):Multiplying square of L(L+1)/2, i.e., convergence (lfac=’k’) or lensing potential (lfac=’‘, default)
Returns:
Al [2,l] (double):
 Normalization, with bounds (0:lmax)
Usage:
Al = curvedsky.norm_quad.qeb(est,lmax,rlmin,rlmax,EE,OCE,OCB,BB,lfac):
 
curvedsky.norm_quad.qbb(est, lmax, rlmin, rlmax, BB, OCB, lfac='')

Normalization of reconstructed amplitude modulation from the BB quadratic estimator

Args:
lmax (int):Maximum multipole of output normalization spectrum
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
BB [l] (double):
 Theory BB spectrum, with bounds (0:rlmax)
OCB [l] (double):
 Observed BB spectrum, with bounds (0:rlmax)
Args(optional):
lfac (str):Multiplying square of L(L+1)/2, i.e., convergence (lfac=’k’) or lensing potential (lfac=’‘, default)
Returns:
Al [2,l] (double):
 Normalization, with bounds (0:lmax)
Usage:
Al = curvedsky.norm_quad.qbb(est,lmax,rlmin,rlmax,BB,OCB,lfac):
 
curvedsky.norm_quad.qttte(est, lmax, rlmin, rlmax, fCTT, fCTE, OCT, OCE, OCTE, lfac='')

Correlation between unnormalized TT and TE quadratic estimators

Args:
lmax (int):Maximum multipole of output normalization spectrum
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
fCTT [l] (double):
 Theory TT spectrum, with bounds (0:rlmax)
fCTE [l] (double):
 Theory TE spectrum, with bounds (0:rlmax)
OCT [l] (double):
 Observed TT spectrum, with bounds (0:rlmax)
OCE [l] (double):
 Observed EE spectrum, with bounds (0:rlmax)
OCTE [l] (double):
 Observed TE spectrum, with bounds (0:rlmax)
Args(optional):
lfac (str):Multiplying square of L(L+1)/2, i.e., convergence (lfac=’k’) or lensing potential (lfac=’‘, default)
Returns:
Ig [l] (double):
 Correlation between lensing potential estimators, with bounds (0:lmax)
Ic [l] (double):
 Correlation between curl mode estimators, with bounds (0:lmax)
Usage:
Ig,Ic = curvedsky.norm_quad.qttte(est,lmax,rlmin,rlmax,fCTT,fCTE,OCT,OCE,OCTE,lfac):
 
curvedsky.norm_quad.qttee(est, lmax, rlmin, rlmax, fCTT, fCEE, OCT, OCE, OCTE, lfac='')

Correlation between unnormalized TT and EE quadratic estimators

Args:
lmax (int):Maximum multipole of output normalization spectrum
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
fCTT [l] (double):
 Theory TT spectrum, with bounds (0:rlmax)
fCEE [l] (double):
 Theory EE spectrum, with bounds (0:rlmax)
OCT [l] (double):
 Observed TT spectrum, with bounds (0:rlmax)
OCE [l] (double):
 Observed EE spectrum, with bounds (0:rlmax)
OCTE [l] (double):
 Observed TE spectrum, with bounds (0:rlmax)
Args(optional):
lfac (str):Multiplying square of L(L+1)/2, i.e., convergence (lfac=’k’) or lensing potential (lfac=’‘, default)
Returns:
Ig [l] (double):
 Correlation between lensing potential estimators, with bounds (0:lmax)
Ic [l] (double):
 Correlation between curl mode estimators, with bounds (0:lmax)
Usage:
Ig,Ic = curvedsky.norm_quad.qttee(est,lmax,rlmin,rlmax,fCTT,fCEE,OCT,OCE,OCTE,lfac):
 
curvedsky.norm_quad.qteee(est, lmax, rlmin, rlmax, fCEE, fCTE, OCT, OCE, OCTE, lfac='')

Correlation between unnormalized TE and EE quadratic estimators

Args:
lmax (int):Maximum multipole of output normalization spectrum
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
fCEE [l] (double):
 Theory EE spectrum, with bounds (0:rlmax)
fCTE [l] (double):
 Theory TE spectrum, with bounds (0:rlmax)
OCT [l] (double):
 Observed TT spectrum, with bounds (0:rlmax)
OCE [l] (double):
 Observed EE spectrum, with bounds (0:rlmax)
OCTE [l] (double):
 Observed TE spectrum, with bounds (0:rlmax)
Args(optional):
lfac (str):Multiplying square of L(L+1)/2, i.e., convergence (lfac=’k’) or lensing potential (lfac=’‘, default)
Returns:
Ig [l] (double):
 Correlation between lensing potential estimators, with bounds (0:lmax)
Ic [l] (double):
 Correlation between curl mode estimators, with bounds (0:lmax)
Usage:
Ig,Ic = curvedsky.norm_quad.qteee(est,lmax,rlmin,rlmax,fCEE,fCTE,OCT,OCE,OCTE,lfac):
 
curvedsky.norm_quad.qtbeb(est, lmax, rlmin, rlmax, fCEE, fCBB, fCTE, OCT, OCE, OCB, OCTE, lfac='')

Correlation between unnormalized TB and EB quadratic estimators

Args:
lmax (int):Maximum multipole of output normalization spectrum
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
fCEE [l] (double):
 Theory EE spectrum, with bounds (0:rlmax)
fCBB [l] (double):
 Theory BB spectrum, with bounds (0:rlmax)
OCT [l] (double):
 Observed TT spectrum, with bounds (0:rlmax)
OCE [l] (double):
 Observed EE spectrum, with bounds (0:rlmax)
OCB [l] (double):
 Observed BB spectrum, with bounds (0:rlmax)
OCTE [l] (double):
 Observed TE spectrum, with bounds (0:rlmax)
Args(optional):
lfac (str):Multiplying square of L(L+1)/2, i.e., convergence (lfac=’k’) or lensing potential (lfac=’‘, default)
Returns:
Ig [l] (double):
 Correlation between lensing potential estimators, with bounds (0:lmax)
Ic [l] (double):
 Correlation between curl mode estimators, with bounds (0:lmax)
Usage:
Ig,Ic = curvedsky.norm_quad.qtbeb(est,lmax,rlmin,rlmax,fCEE,fCBB,fCTE,OCT,OCE,OCB,OCTE,lfac):
 
curvedsky.norm_quad.qmv(lmax, QDO, Al, Il)

Compute MV estimator normalization. Currently BB is ignored.

Args:
lmax (int):Maximum multipole of the output power spectra
QDO[6] (bool):Specifying which estimators to be combined for the minimum variance estimator, with size (6). The oder is TT, TE, EE, TB, EB and BB. Currently, BB is always False
Al [5,l] (double):
 Normalizations of each estimator (TT, TE, EE, TB, EB).
Il [4,l] (double):
 Correlation between different estimators (TTxTE, TTxEE, TExEE, TBxEB).
Returns:
MV [l] (double):
 Normalization of the MV estimator, with bounds (0:lmax)
Nl [6,l] (double):
 Weights for each estimator (TT, TE, EE, TB, EB, BB=0), with bounds (0:lmax)
Usage:
MV,Nl = curvedsky.norm_quad.qmv(lmax,QDO,Al,Il):
 
curvedsky.norm_quad.qall(est, QDO, lmax, rlmin, rlmax, fC, OC, lfac='')

Compute MV estimator normalization. Currently BB is ignored.

Args:
QDO[6] (bool):Specifying which estimators to be combined for the minimum variance estimator, with size (6). The oder is TT, TE, EE, TB, EB and BB.
lmax (int):Maximum multipole of the output power spectra
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
fC/OC [l] (double):
 Theory/Observed CMB angular power spectra (TT, EE, BB, TE), with bounds (0:rlmax)
Args(optional):
lfac (str):Multiplying square of L(L+1)/2, i.e., convergence (lfac=’k’) or lensing potential (lfac=’‘, default)
Returns:
Ag [6,l] (double):
 Normalization of the TT, TE, EE, TB, EB, and MV estimators for lensing potential, with bounds (6,0:lmax)
Ac [6,l] (double):
 Same as Ag but for curl mode
Nlg [6,l] (double):
 Weights for TT, TE, EE, TB, EB, and BB (=0) estimators for lensing potential, with bounds (6,0:lmax)
Nlc [6,l] (double):
 Same as Nlg but for curl mode
Usage:
Ag,Ac,Nlg,Nlc = curvedsky.norm_quad.qall(est,QDO,lmax,rlmin,rlmax,fC,OC,lfac):
 
curvedsky.norm_quad.qeb_iter(lmax, elmax, rlmin, rlmax, dlmin, dlmax, CE, OCE, OCB, Cpp, iter=1, conv=1e-05)

Normalization of reconstructed CMB lensing potential and its curl mode from the EB quadratic estimator

Args:
lmax (int):Maximum multipole of output normalization
elmax (int):Maximum multipole of input EE spectra, CE and OCE
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
dlmin/dlmax (int):
 Minimum/Maximum multipole of E mode and lensing potential for delensing
CE [l] (double):
 Theory EE angular power spectrum, with bounds (0:elmax)
OCE [l] (double):
 Observed EE spectrum, with bounds (0:elmax)
OCB [l] (double):
 Observed BB spectrum, with bounds (0:rlmax)
Cpp [l] (double):
 Theory lensing potential spectrum, with bounds (0:dlmax)
Args(optional):
iter (int):number of iteration, default to 1 (no iteration)
conv (double):a parameter for convergence the iteration, default to 0.00001
Returns:
Ag [l] (double):
 CMB lensing potential normalization, with bounds (0:lmax)
Ac [l] (double):
 Curl mode (pseudo lensing potential) normalization, with bounds (0:lmax)
Usage:
Ag,Ac = curvedsky.norm_quad.qeb_iter(lmax,elmax,rlmin,rlmax,dlmin,dlmax,CE,OCE,OCB,Cpp,iter,conv):
 
curvedsky.norm_quad.xtt(est, lmax, rlmin, rlmax, fC, OCT, lfac='')

Unnormalized response between lensing potential and amplitude modulation from the temperature quadratic estimator

Args:
lmax (int):Maximum multipole of output normalization spectrum
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
fC [l] (double):
 Theory TT spectrum, with bounds (0:rlmax)
OCT [l] (double):
 Observed TT spectrum, with bounds (0:rlmax)
Args(optional):
lfac (str):Multiplying square of L(L+1)/2, i.e., convergence (lfac=’k’) or lensing potential (lfac=’‘, default)
Returns:
Ag [l] (double):
 Cross normalization, with bounds (0:lmax)
Usage:
Ag = curvedsky.norm_quad.xtt(est,lmax,rlmin,rlmax,fC,OCT,lfac):
 
curvedsky.norm_quad.xeb(est, lmax, rlmin, rlmax, EE, EB, OCE, OCB, BB=None)

Response of reconstructed field to other in the EB quadratic estimator

Args:
lmax (int):Maximum multipole of output normalization spectrum
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
EE [l] (double):
 Theory EE spectrum, with bounds (0:rlmax)
EB [l] (double):
 Theory EB spectrum, with bounds (0:rlmax)
OCE [l] (double):
 Observed EE spectrum, with bounds (0:rlmax)
OCB [l] (double):
 Observed BB spectrum, with bounds (0:rlmax)
Args(optionals):
BB [l] (double):
 Theory BB spectrum, with bounds (0:rlmax)
Returns:
Aa [l] (double):
 Pol. rot. angle normalization, with bounds (0:lmax)
Usage:
Aa = curvedsky.norm_quad.xeb(est,lmax,rlmin,rlmax,EE,EB,OCE,OCB,BB):
 

norm_imag – normalization of imaginary quadratic estimator reconstruction

curvedsky.norm_imag.qte(est, lmax, rlmin, rlmax, TB, OCT, OCE, lfac='')

Normalization of reconstructed imaginary CMB lensing potential and its curl mode from the TE quadratic estimator

Args:
lmax (int):Maximum multipole of output normalization spectrum
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
TB [l] (double):
 Theory TB spectrum, with bounds (0:rlmax)
OCT [l] (double):
 Observed TT spectrum, with bounds (0:rlmax)
OCE [l] (double):
 Observed EE spectrum, with bounds (0:rlmax)
Args(optional):
lfac (str):Type of output, i.e., convergence (lfac=’k’) or lensing potential (lfac=’‘, default)
Returns:
Al [2,l] (double):
 Normalization, with bounds (0:lmax)
Usage:
Al = curvedsky.norm_imag.qte(est,lmax,rlmin,rlmax,TB,OCT,OCE,lfac):
 
curvedsky.norm_imag.qtb(est, lmax, rlmin, rlmax, TB, OCT, OCB, lfac='')

Normalization of reconstructed imaginary CMB lensing potential and its curl mode from the TB quadratic estimator

Args:
lmax (int):Maximum multipole of output normalization spectrum
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
TB [l] (double):
 Theory TE spectrum, with bounds (0:rlmax)
OCT [l] (double):
 Observed TT spectrum, with bounds (0:rlmax)
OCB [l] (double):
 Observed BB spectrum, with bounds (0:rlmax)
Args(optional):
lfac (str):Type of output, i.e., convergence (lfac=’k’) or lensing potential (lfac=’‘, default)
Returns:
Al [2,l] (double):
 Normalization, with bounds (0:lmax)
Usage:
Al = curvedsky.norm_imag.qtb(est,lmax,rlmin,rlmax,TB,OCT,OCB,lfac):
 
curvedsky.norm_imag.qee(est, lmax, rlmin, rlmax, fC, OCE, lfac='')

Normalization of reconstructed imaginary CMB lensing potential and its curl mode from the E-mode quadratic estimator

Args:
lmax (int):Maximum multipole of output normalization spectrum
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
fC [l] (double):
 Theory EE spectrum, with bounds (0:rlmax)
OCE [l] (double):
 Observed EE spectrum, with bounds (0:rlmax)
Args(optional):
lfac (str):Type of output, i.e., convergence (lfac=’k’) or lensing potential (lfac=’‘, default)
Returns:
Al [2,l] (double):
 Normalization, with bounds (0:lmax)
Usage:
Al = curvedsky.norm_imag.qee(est,lmax,rlmin,rlmax,fC,OCE,lfac):
 
curvedsky.norm_imag.qeb(est, lmax, rlmin, rlmax, fC, OCE, OCB, lfac='')

Normalization of reconstructed imaginary CMB lensing potential and its curl mode from the EB quadratic estimator

Args:
lmax (int):Maximum multipole of output normalization spectrum
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
fC [l] (double):
 Theory EB spectrum, with bounds (0:rlmax)
OCE [l] (double):
 Observed EE spectrum, with bounds (0:rlmax)
OCB [l] (double):
 Observed BB spectrum, with bounds (0:rlmax)
Args(optional):
lfac (str):Type of output, i.e., convergence (lfac=’k’) or lensing potential (lfac=’‘, default)
Returns:
Al [2,l] (double):
 Normalization, with bounds (0:lmax)
Usage:
Al = curvedsky.norm_imag.qeb(est,lmax,rlmin,rlmax,fC,OCE,OCB,lfac):
 
curvedsky.norm_imag.qbb(est, lmax, rlmin, rlmax, fC, OCB, lfac='')

Normalization of reconstructed imaginary CMB lensing potential and its curl mode from the B-mode quadratic estimator

Args:
lmax (int):Maximum multipole of output normalization spectrum
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
fC [l] (double):
 Theory BB spectrum, with bounds (0:rlmax)
OCB [l] (double):
 Observed BB spectrum, with bounds (0:rlmax)
Args(optional):
lfac (str):Type of output, i.e., convergence (lfac=’k’) or lensing potential (lfac=’‘, default)
Returns:
Al [2,l] (double):
 Normalization, with bounds (0:lmax)
Usage:
Al = curvedsky.norm_imag.qbb(est,lmax,rlmin,rlmax,fC,OCB,lfac):
 
curvedsky.norm_imag.qbb_asym(est, lmax, rlmin, rlmax, fC, OCB1, OCB2, lfac='')

Normalization of reconstructed imaginary CMB lensing potential and its curl mode from the B-mode quadratic estimator

Args:
lmax (int):Maximum multipole of output normalization spectrum
rlmin/rlmax (int):
 Minimum/Maximum multipole of CMB for reconstruction
fC [l] (double):
 Theory BB spectrum, with bounds (0:rlmax)
OCB1/2 [l] (double):
 Observed BB spectrum for experiment 1 and 2, with bounds (0:rlmax)
Args(optional):
lfac (str):Type of output, i.e., convergence (lfac=’k’) or lensing potential (lfac=’‘, default)
Returns:
Al [2,l] (double):
 Normalization, with bounds (0:lmax)
Usage:
Al = curvedsky.norm_imag.qbb_asym(est,lmax,rlmin,rlmax,fC,OCB1,OCB2,lfac):
 

delens – delensing for simulation

curvedsky.delens.lensingb(lmax, elmin, elmax, plmin, plmax, wElm, wplm, nside_t=0, gtype='p')

Computing lensing B mode as a convolution of wiener-filtered E-mode and lensing potential

Args:
lmax (int):Maximum multipole of output lensing B-mode alm
elmin (int):Minimum multipole of wiener-filtered E-mode alm
elmax (int):Maximum multipole of wiener-filtered E-mode alm
plmin (int):Minimum multipole of wiener-filtered lensing potential alm
plmax (int):Maximum multipole of wiener-filtered lensing potential alm
wElm [l,m] (dcmplx):
 Wiener-filtered E-mode alm, with bounds (0:elmax,0:elmax)
wplm [l,m] (dcmplx):
 Wiener-filtered lensing potential (or kappa) alm, with bounds (0:plmax,0:plmax)
Args(optional):
nside_t (int):Nside for the convolution calculation
gtype (str):Type of input wplm (‘p’=phi or ‘k’=kappa), default to ‘p’ (phi).
Returns:
lBlm [l,m] (dcmplx):
 Lensing B-mode alm, with bounds (0:lmax,0:lmax)
Usage:
lBlm = curvedsky.delens.lensingb(lmax,elmin,elmax,plmin,plmax,wElm,wplm,nside_t,gtype):
 
curvedsky.delens.shiftvec(nside, lmax, plm, nremap)

Return the anti deflection vector, beta, at the Healpix pixel for the delensing where

beta(n) + alphaiw(n+beta(n)) = 0

and alphaw is the filtered lensing deflection vector (see arXiv:1701.01712).

Args:
nside (int):Nside of output shift vector
lmax (int):Maximum multipole of the input plm
plm [l,m] (dcmplx):
 Wiener-filtered lensing potential alm, with bounds (0:lmax,0:lmax)
Args(optional):
nremap (int):Number of iteration for computing the shift vector
Returns:
beta [pix,2] (double):
 2D shift vector, with bounds (0:npix-1,1:2)
Usage:
beta = curvedsky.delens.shiftvec(nside,lmax,plm,nremap):
 
curvedsky.delens.phi2grad(nside, lmax, plm)

Return the deflection vector, grad, at the Healpix pixel

Args:
nside (int):Nside of output deflection vector
lmax (int):Maximum multipole of the input plm/clm
plm [l,m] (dcmplx):
 Lensing potential alm, with bounds (0:lmax,0:lmax)
Returns:
grad [pix,2] (double):
 2D deflection vector, with bounds (0:npix-1,1:2)
Usage:
grad = curvedsky.delens.phi2grad(nside,lmax,plm):
 
curvedsky.delens.remap_tp(nside, lmax, beta, alm_in)

Remapping CMB temperaure and polarization with a given shift vector based on a simple implementation of LensPix This function returs X(n+beta) where n is the original direction and beta is the shift vector The output is given by alms where alm[0,l,m] is temperature, alm[1,l,m] is E mode, and alm[2,l,m] is B mode.

Args:
nside (int):Nside of input shift vector
lmax (int):Maximum multipole of the input plm
beta [pix,2] (double):
 2D shift vector, with bounds (0:npix-1,1:2)
alm_in [TEB,l,m] (dcmplx):
 Input T/E/B alms to be remapped, with bounds (1:3,0:lmax,0:lmax).
Returns:
alm_re [TEB,l,m] (dcmplx):
 Remapped T/E/B alms, with bounds (1:3,0:lmax,0:lmax).
Usage:
alm_re = curvedsky.delens.remap_tp(nside,lmax,beta,alm_in):
 
curvedsky.delens.remap_tp_map(nside, lmax, beta, alm_in)

Remapping CMB temperaure and polarization with a given shift vector based on a simple implementation of LensPix This function returs X(n+beta) where n is the original direction and beta is the shift vector The output is given by alms where alm[0,l,m] is temperature, alm[1,l,m] is E mode, and alm[2,l,m] is B mode.

Args:
nside (int):Nside of input shift vector
lmax (int):Maximum multipole of the input plm
beta [pix,2] (double):
 2D shift vector, with bounds (0:npix-1,1:2)
alm_in [TEB,l,m] (dcmplx):
 Input T/E/B alms to be remapped, with bounds (1:3,0:lmax,0:lmax).
Returns:
map_re [pix,TQU] (double):
 Remapped T/Q/U alms, with bounds (0:lmax,0:lmax,1:3).
Usage:
map_re = curvedsky.delens.remap_tp_map(nside,lmax,beta,alm_in):
 

bispec – binned reduced bispectrum

curvedsky.bispec.make_quad_gauss(lmax, alm)

Return a non-Gaussian alm. The corresponding non-Gaussian field is defined as

delta^NL(n) = delta^L(n) + delta^L(n)**2

where delta^L(n) is a gaussian field obtained from the input alm.

Args:
lmax (int):Maximum multipole of alm
alm [l,m] (dcmplx):
 Input harmonic coefficients, with bounds (0:lmax,0:lmax).
Returns:
qlm [l,m] (dcmplx):
 Output harmonic coefficients of the non-Gaussian fields, with bounds (0:lmax,0:lmax).
Usage:
qlm = curvedsky.bispec.make_quad_gauss(lmax,alm):
 
curvedsky.bispec.bispec_norm(bn, bp, bstype='equi', bst=2, sL=[0, 0])

Return normalization of the binned reduced bispectrum for a given multipole bin

Args:
bn (int):Number of multipole bins
bp [edge] (double):
 Bin edges, with bounds (bn+1)
Args(optional):
bstype (str):Configuration of the bispectrum, default to equilateral
bst (int):A parameter, bst=nside/lmax, which controls the accuracy of the calculation, default to 2. More accurate for a larger value.
sL[2] (int):The fixed bin for the squeezed configuration, b[sL,eL,eL], default to the lowest multipole bin
Returns:
norm [bin] (double):
 Normalization of the binned reduced bispectrum at each bin, with bounds (bn)
Usage:
norm = curvedsky.bispec.bispec_norm(bn,bp,bstype,bst,sL):
 
curvedsky.bispec.bispec_bin(bn, bp, lmax, alm, bst=2, bstype='equi', sL=[0, 0])

Return the unnormalized binned reduced bispectrum for a given multipole bin

Args:
bn (int):Number of multipole bins
bp [edge] (double):
 Bin edges, with bounds (bn+1)
lmax (int):Maximum multipole of the input alm
alm [l,m] (dcmplx):
 Input harmonic coefficients, with bounds (0:lmax,0:lmax)
Args(optional):
bstype (str):Configuration of the bispectrum, default to equilateral
bst (int):A parameter, bst=nside/lmax, which controls the accuracy of the calculation, default to 2. More accurate for a larger value.
sL[2] (int):The fixed bin for the squeezed configuration, b[sL,eL,eL], default to the lowest multipole bin
Returns:
bis [bin] (double):
 The unnormalized binned reduced bispectrum at each bin, with bounds (bn)
Usage:
bis = curvedsky.bispec.bispec_bin(bn,bp,lmax,alm,bstype,bst,sL):
 
curvedsky.bispec.xbispec_bin(bn, bp, lmax, n, alm, bst=2, bstype='equi', sL=[0, 0])

Return the unnormalized binned reduced cross-bispectrum for a given multipole bin

Args:
bn (int):Number of multipole bins
bp [edge] (double):
 Bin edges, with bounds (bn+1)
lmax (int):Maximum multipole of the input alm
n (int):Number of alms
alm [n,l,m] (dcmplx):
 Input harmonic coefficients, with bounds (0:n-1,0:lmax,0:lmax)
Args(optional):
bstype (str):Configuration of the bispectrum, default to equilateral
bst (int):A parameter, bst=nside/lmax, which controls the accuracy of the calculation, default to 2. More accurate for a larger value.
sL[2] (int):The fixed bin for the squeezed configuration, b[sL,eL,eL], default to the lowest multipole bin
Returns:
bis [bin] (double):
 The unnormalized binned reduced bispectrum at each bin, with bounds (bn)
Usage:
bis = curvedsky.bispec.xbispec_bin(bn,bp,lmax,n,alm,bstype,bst,sL):
 

cninv – Filtering Anisotropies

curvedsky.cninv.cnfilter_freq(n, mn, nside, lmax, cl, bl, iNcov, maps, chn=1, lmaxs=[0], nsides=[0], itns=[1], eps=[1e-06], filter='W', verbose=False, ro=50, stat='', inl=None)

Combining multiple frequency CMB maps optimally. The filtering would work if the noise variance is not significantly varied with scale (multipole). Please make sure that your input maps are beam-convolved. This code deconvolves the beam during filtering and the output are the filtered alms after the beam-deconvolution.

Args:
n (int):Number of maps, i.e., temperature only (n=1), polarization only (n=2) or both (n=3)
mn (int):Number of frequencies
nside (int):Nside of input map
lmax (int):Maximum multipole of the input cl
cl[n,l] (double):
 Theory signal power spectrum, with bounds (0:n-1,0:lmax)
bl[mn,l] (double):
 Beam spectrum, with bounds (0:mn-1,0:lmax)
iNcov[n,mn,pix] (double):
 Inverse of the noise variance at each pixel, with bounds (0:n-1,0:mn-1,0:npix-1)
maps[n,mn,pix] (double):
 Beam-convolved T, Q, U maps, with bouds (0:n-1,0:mn-1,0:npix-1)
Args(optional):
chn (int):Number of grids for preconsitioner (chn=1 for diagonal preconditioner, default)
lmaxs[chain] (int):
 Maximum multipole(s) at each preconditioning and lmaxs[0] is the input maximum multipole of cl
nsides[chain] (int):
 Nside(s) of preconditoner and nsides[0] should be consistent with the input map’s nside.
eps[chain] (double):
 Parameter to finish the iteration (i.e. terminate if the residul fraction becomes smaller than eps). Default to 1e-6.
itns[chain] (int):
 Number of interations.
filter (str):C-inverse (‘’) or Wiener filter (W), default to the Wiener filter.
inl[n,mn,l] (double):
 Inverse noise spectrum (0 for white noise case, default).
verbose (bool):Output messages, default to False
ro (int):the residual fraction is output for every ro iteration (e.g. ro=2 means 1 output per 2 iterations). Default to 50. Useful for convergence speed.
stat (str):Realtime status filename which contains the residual fraction, default to no output file
Returns:
xlm[n,l,m] (dcmplx):
 C-inverse / Wiener filtered multipoles, with bounds (0:n-1,0:lmax,0:lmax)
Usage:
xlm = curvedsky.cninv.cnfilter_freq(n,mn,nside,lmax,cl,bl,iNcov,maps,chn,lmaxs,nsides,itns,eps,filter,inl,verbose,ro,stat):
 
curvedsky.cninv.cnfilter_kappa(n, nside, lmax, cov, iNcov, maps, chn=1, lmaxs=[0], nsides=[0], itns=[1], eps=[1e-06], verbose=False, ro=50, stat='', inl=None)

Computing the inverse-variance weighted multipole, (C+N)^-1 x kappa, for multiple mass-tracers of kappa maps.

Args:
n (int):Number of input kappa maps to be combined
nside (int):Nside of input maps
lmax (int):Maximum multipole of the input cl
cov[n,n,l] (double):
 Signal covariance matrix for each multipole, with bounds (0:n-1,0:n-1,0:lmax)
iNcov[n,pix] (double):
 Inverse of the noise variance at each pixel, with bounds (0:n-1,0:npix-1)
maps[n,pix] (double):
 Input kappa maps, with bouds (0:n-1,0:npix-1)
Args(optional):
chn (int):Number of grids for preconsitioner (chn=1 for diagonal preconditioner, default)
lmaxs[chain] (int):
 Maximum multipole(s) at each preconditioning and lmaxs[0] is the input maximum multipole of cl
nsides[chain] (int):
 Nside(s) of preconditoner and nsides[0] should be consistent with the input map’s nside.
eps[chain] (double):
 Parameter to finish the iteration (i.e. terminate if the residul fraction becomes smaller than eps). Default to 1e-6.
itns[chain] (int):
 Number of interations.
inl[n,l] (double):
 Inverse noise spectrum for each mass map (0 for white noise case, default).
verbose (bool):Output messages, default to False
ro (int):the residual fraction is output for every ro iteration (e.g. ro=2 means 1 output per 2 iterations). Default to 50. Useful for convergence speed.
stat (str):Realtime status filename which contains the residual fraction, default to no output file
Returns:
xlm[n,l,m] (dcmplx):
 Wiener filtered multipoles, with bounds (n,0:lmax,0:lmax)
Usage:
xlm = curvedsky.cninv.cnfilter_kappa(n,nside,lmax,cov,iNcov,maps,chn,lmaxs,nsides,itns,eps,inl,verbose,ro,stat):
 
curvedsky.cninv.cnfilter_freq_nside(n, mn0, mn1, nside0, nside1, lmax, cl, bl0, bl1, iNcov0, iNcov1, maps0, maps1, chn=1, lmaxs=[0], nsides0=[0], nsides1=[0], itns=[1], eps=[1e-06], filter='W', verbose=False, reducmn=0, ro=50, stat='', inl=None)

Same as cnfilter_freq but for the maps with two different Nsides. Please make sure that your input maps are beam-convolved. This code deconvolves the beam during filtering and the output are the filtered alms after the beam-deconvolution.

Args:
n (int):Number of maps, i.e., temperature only (n=1), polarization only (n=2) or both (n=3)
mn0/1 (int):Number of frequencies
nside0/1 (int):Nsides of input maps
lmax (int):Maximum multipole of the input cl
cl[n,l] (double):
 Theory signal power spectrum, with bounds (0:n-1,0:lmax)
bl0/1[mn,l] (double):
 Beam function, with bounds (0:n-1,0:lmax)
iNcov0/1[n,mn,pix] (double):
 Inverse of the noise variance at each pixel, with bounds (0:n-1,0:npix-1)
maps0/1[n,mn,pix] (double):
 Beam-convolved T, Q, U maps, with bouds (0:n-1,0:npix-1)
Args(optional):
chn (int):Number of grids for preconsitioner (chn=1 for diagonal preconditioner, default)
lmaxs[chain] (int):
 Maximum multipole(s) at each preconditioning and lmaxs[0] is the input maximum multipole of cl
nsides0/1[chain] (int):
 Nside(s) of preconditoner and nsides[0] should be consistent with the input map’s nside.
eps[chain] (double):
 Parameter to finish the iteration (i.e. terminate if the residul fraction becomes smaller than eps). Default to 1e-6.
itns[chain] (int):
 Number of interations.
filter (str):C-inverse (‘’) or Wiener filter (W), default to the Wiener filter.
inl[n,mn,l] (double):
 Inverse noise spectrum, 0 for white noise case.
verbose (bool):Output messages, default to False
ro (int):the residual fraction is output for every ro iteration (e.g. ro=2 means 1 output per 2 iterations). Default to 50. Useful for convergence speed.
stat (str):Realtime status filename which contains the residual fraction, default to no output file
reducmn (int):Reducing number of maps per chain (1,2) or not (0, default). If 1, the maps are combined for the same nside inside the multigrid chain. If 2, in addition to the procedure of 1, the each nside maprs are further combined into a single map inside the second chain (chain>=3).
Returns:
xlm[n,l,m] (dcmplx):
 

C-inverse or Wiener filtered multipoles, with bounds (0:n-1,0:lmax,0:lmax)

mgc%cv(1,mi)%nij = iNcov0(:,mi,:)maps0(:,mi,:) mgc%cv(1,mi)%nij = iNcov1(:,mi-mn0,:)maps1(:,mi-mn0,:)
Usage:
xlm = curvedsky.cninv.cnfilter_freq_nside(n,mn0,mn1,nside0,nside1,lmax,cl,bl0,bl1,iNcov0,iNcov1,maps0,maps1,chn,lmaxs,nsides0,nsides1,itns,eps,filter,inl,verbose,reducmn,ro,stat):
 

utils – other tools

curvedsky.utils.gauss1alm(lmax, Cl)

Generating alm as a random Gaussian field whose power spectrum is cl. The output alm is given by a 2D array.

Args:
lmax (int):Maximum multipole of the output alm
Cl [l] (double):
 Angular power spectrum, with bounds (0:lmax)
Returns:
alm [l,m] (dcmplx):
 Random Gaussian alm, with bounds (0:lmax,0:lmax)
Usage:
alm = curvedsky.utils.gauss1alm(lmax,Cl):
 
curvedsky.utils.gauss2alm(lmax, cl1, cl2, xl)

Generating two alms as random Gaussian fields whose power spectra are cl1, cl2 and the cross spectrum is xl.

Args:
lmax (int):Maximum multipole of the output alm
cl1 [l] (double):
 Angular power spectrum of the 1st alm, with bounds (0:lmax)
cl2 [l] (double):
 Angular power spectrum of the 2nd alm, with bounds (0:lmax)
xl [l] (double):
 Cross-power spectrum between alm1 and alm2, with bounds (0:lmax)
Returns:
alm [2,l,m] (dcmplx):
 Random Gaussian alms, with bounds (2,0:lmax,0:lmax)
Usage:
alm = curvedsky.utils.gauss2alm(lmax,cl1,cl2,xl):
 
curvedsky.utils.gauss2alm_const(lmax, cl1, cl2, xl, flm)

Generating two alms as random Gaussian fields whose power spectra are cl1, cl2 and the cross spectrum is xl.

Args:
lmax (int):Maximum multipole of the output alm
cl1 [l] (double):
 Angular power spectrum of the 1st alm, with bounds (0:lmax)
cl2 [l] (double):
 Angular power spectrum of the 2nd alm, with bounds (0:lmax)
xl [l] (double):
 Cross-power spectrum between alm1 and alm2, with bounds (0:lmax)
flm [l,m] (dcmplx):
 Constrained realiation of alms whose power is cl1
Returns:
alm [2,l,m] (dcmplx):
 Random Gaussian alms, with bounds (2,0:lmax,0:lmax)
Usage:
alm = curvedsky.utils.gauss2alm_const(lmax,cl1,cl2,xl,flm):
 
curvedsky.utils.gaussTEB(lmax, TT, EE, BB, TE)

Generating T/E/B alms as random Gaussian fields whose power spectra are TT, EE, BB and the cross spectrum is TE.

Args:
lmax (int):Maximum multipole of the output alms
TT [l] (double):
 Angular power spectrum of temperature, with bounds (0:lmax)
EE [l] (double):
 Angular power spectrum of E mode, with bounds (0:lmax)
BB [l] (double):
 Angular power spectrum of B mode, with bounds (0:lmax)
TE [l] (double):
 TE cross-power spectrum, with bounds (0:lmax)
Returns:
alm [3,l,m] (dcmplx):
 Random Gaussian T/E/B alms, with bounds (3,0:lmax,0:lmax)
Usage:
alm = curvedsky.utils.gaussTEB(lmax,TT,EE,BB,TE):
 
curvedsky.utils.gaussalm(cl, n=None, lmax=None, ilm=None)

Generating alms as random Gaussian fields whose covariance is given by cl[i,j].

Args:
cl [i,j,l] (double):
 Covariance between the gaussian fields, with bounds (n,n,0:lmax)
Args:
ilm [l,m] (dcmplx):
 Input alm for the cl[0,0] element (default to None). The other alms are generated to be correlated with ilm.
Returns:
alm [i,l,m] (dcmplx):
 Random Gaussian alms, with bounds (n,0:lmax,0:lmax)
Usage:
alm = curvedsky.utils.gaussalm(n,lmax,cl,ilm):
 
curvedsky.utils.cov_diag_tri(n, cl)
Usage:
A = curvedsky.utils.cov_diag_tri(n,cl):
 
curvedsky.utils.get_baseline(npix, nside_subpatch, QU)

Calculate baseline of each subpatch. The subpatches have the same size. Written by Ryo Nagata.

Args:
npix (int):pixel number of the full map
nside_subpatch (int):
 Nside of sub patch
QU [pix,2] (double):
 Q/U maps, with bounds (0:npix-1,2)
Returns:
blmap [pix,2] (double):
 baseline maps, with bounds (0:npix-1,2)
Usage:
blmap = curvedsky.utils.get_baseline(npix,nside_subpatch,QU):
 
curvedsky.utils.get_winmap(nside_large, nside_small, ipix_pix, apod)

Return apodization window for subpatch. Written by Ryo Nagata.

Args:
nside_large (int):
 Nside of sub patch
nside_small (int):
 full Nside
ipix_pix (int):pixel index of full map
apod (double):apodization length
Returns:
wind_out (double):
 aporization window at ipix_pix
Usage:
win_out = curvedsky.utils.get_winmap(nside_large,nside_small,ipix_pix,apod):
 
curvedsky.utils.get_apod_window(s, a)

A sine apodization window

Args:
s (double):Distance from the center of the window
a (double):Apodization length, nothing (a=1) to all (a=0)
Returns:
w (double):Aporization window
Usage:
w = curvedsky.utils.get_apod_window(s,a):
 
curvedsky.utils.eb_separate(nside, lmax, W, Q, U)

E/B mode seperation based on the chi-field estimator. See e.g. Sec.III.2 of arXiv:1305.7441 for numerical implimentation.

Args:
npix (int):Pixel number of the desired map
lmax (int):Maximum multipole used for the harmonic transform internally
W[pix] (double):
 Window function satisfying zero 1st and 2nd derivatives at the boundary, with bounds (0:npix-1)
Q/U[pix] (double):
 Input Q/U map already multiplied by W, with bounds (0:npix-1)
Returns:
Elm/Blm[l,m] (dcmplx):
 Seperated E/B modes, with bounds (0:lmax,0:lmax)
Usage:
Elm,Blm = curvedsky.utils.eb_separate(nside,lmax,W,Q,U):
 
curvedsky.utils.alm2cl(lmax, alm1, alm2=None)

From alm to angular power spectrum

Args:
lmax (int):Maximum multipole of the input alm
alm1 [l,m] (dcmplx):
 1st harmonic coefficient, with bounds (0:lmax,0:lmax)
Args(optional):
alm2 [l,m] (dcmplx):
 2nd harmonic coefficient, with bounds (0:lmax,0:lmax), default to alm1
Returns:
cl [l] (double):
 Auto or cross angular power spectrum, with bounds (0:lmax)
Usage:
cl = curvedsky.utils.alm2cl(lmax,alm1,alm2):
 
curvedsky.utils.alm2bcl(bn, lmax, alm1, spc='', alm2=None)

From alm to angular power spectrum with multipole binning

Args:
bn (int):Number of multipole bins
lmax (int):maximum multipole of the input alm
alm1 [l,m] (dcmplx):
 1st harmonic coefficient, with bounds (0:lmax,0:lmax)
Args(optional):
alm2 [l,m] (dcmplx):
 2nd harmonic coefficient, with bounds (0:lmax,0:lmax), default to alm1
spc (str):Specify bin spacing, ‘’ = linear (default), ‘log’ = log spacing, ‘log10’ = log10 spacing, ‘p2’ = power of 2 spacing, ‘p3’ = power of 3 spacing
Returns:
cb [bin] (double):
 Auto or cross angular power spectrum with multipole binning, with bounds (0:bn-1)
Usage:
cb = curvedsky.utils.alm2bcl(bn,lmax,alm1,alm2,spc):
 
curvedsky.utils.alm2rho(lmax, alm1, alm2)

Compute correlation coefficients between two alms

Args:
lmax (int):Maximum multipole of the input alm
alm1 [l,m] (dcmplx):
 1st harmonic coefficient, with bounds (0:lmax,0:lmax)
alm2 [l,m] (dcmplx):
 2nd harmonic coefficient, with bounds (0:lmax,0:lmax)
Returns:
rho [l] (double):
 Auto or cross angular power spectrum, with bounds (0:lmax)
Usage:
rho = curvedsky.utils.alm2rho(lmax,alm1,alm2):
 
curvedsky.utils.alm2cov(alm, n=0, lmax=0)

Compute correlation coefficients between two alms

Args:
lmax (int):Maximum multipole of the input alms
alm [n,l,m] (dcmplx):
 1st harmonic coefficient, with bounds (0:lmax,0:lmax)
Returns:
cov [n,n,l] (double):
 Auto and cross angular power spectra between alm[i] and alm[j]
Usage:
cov = curvedsky.utils.alm2cov(n,lmax,alm):
 
curvedsky.utils.apodize(nside, rmask, ascale, order=1, holeminsize=0)

Compute apodized window function. Partially use Healpix’s process_mask code.

Args:
nside (int):Nside of the input map
rmask[pix] (double):
 Input window function, with bounds (0:pix-1). Pixels at rmask=0 is considered as masked pixels.
ascale (double):
 Apodization length [deg] from the closest masked pixel
Args(optional):
order (int):Pixel order, 1 for RING (default), otherwize NESTED
holeminsize (double):
 Minimum hole size [arcmin] (i.e., holes within this size is filled), default to 0
Returns:
amask[pix] (double):
 Apodization window, with bounds (0:npix-1), using the same ordering as input
Usage:
amask = curvedsky.utils.apodize(nside,rmask,ascale,order,holeminsize):
 
curvedsky.utils.almxfl(lmax, mmax, alm, cl)

Calculate xlm[l,m] = alm[l,m] x cl[l]

Args:
lmax (int):Maximum multipole of the input alm
mmax (int):Maximum m of the input alm
alm [l,m] (dcmplx):
 Harmonic coefficient to be transformed to a map, with bounds (0:lmax,0:lmax)
cl [l] (double):
 1D spectrum to be multiplied to alm, with bounds (0:lmax)
Returns:
xlm [l,m] (dcmplx):
 Modified alm, with bounds (0:lmax,0:lmax)
Usage:
xlm = curvedsky.utils.almxfl(lmax,mmax,alm,cl):
 
curvedsky.utils.hp_alm2map(nside, lmax, mmax, alm)

Ylm transform of the map to alm with the healpix (l,m) order

Args:
nside (int):Nside of the input map
lmax (int):Maximum multipole of the input alm
mmax (int):Maximum m of the input alm
alm [l,m] (dcmplx):
 Harmonic coefficient to be transformed to a map, with bounds (0:lmax,0:mmax)
Returns:
map [pix] (double):
 Transformed map, with bounds (0:npix-1)
Usage:
map = curvedsky.utils.hp_alm2map(nside,lmax,mmax,alm):
 
curvedsky.utils.hp_alm2map_spin(nside, lmax, mmax, spin, elm, blm)

Ylm transform of the map to alm with the healpix (l,m) order

Args:
nside (int):Nside of the input map
lmax (int):Maximum multipole of the input alm
mmax (int):Maximum m of the input alm
spin (int):Spin of the transform
elm [l,m] (dcmplx):
 Spin-s E-like harmonic coefficient to be transformed to a map, with bounds (0:lmax,0:mmax)
blm [l,m] (dcmplx):
 Spin-s B-like harmonic coefficient to be transformed to a map, with bounds (0:lmax,0:mmax)
Returns:
map0 [pix] (double):
 Real part of the transformed map (Q-like map), with bounds (0:npix-1)
map1 [pix] (double):
 Imaginary part of the transformed map (U-like map), with bounds (0:npix-1)
Usage:
map0,map1 = curvedsky.utils.hp_alm2map_spin(nside,lmax,mmax,spin,elm,blm):
 
curvedsky.utils.hp_map2alm(nside, lmax, mmax, map)

Ylm transform of the map to alm with the healpix (l,m) order

Args:
nside (int):Nside of the input map
lmax (int):Maximum multipole of the input alm
mmax (int):Maximum m of the input alm
map [pix] (double):
 Input map, with bounds (0:npix-1)
Returns:
alm [l,m] (dcmplx):
 Harmonic coefficient obtained from the input map, with bounds (0:lmax,0:mmax)
Usage:
alm = curvedsky.utils.hp_map2alm(nside,lmax,mmax,map):
 
curvedsky.utils.hp_map2alm_spin(nside, lmax, mmax, spin, map0, map1)

Spin Ylm transform of the map ( = map0 + i map1 ) to alm with the healpix (l,m) order. For example, if map0=Q, map1=U and spin=2, the alm contains E-mode and B-mode.

Args:
nside (int):Nside of the input map
lmax (int):Maximum multipole of the input alm
mmax (int):Maximum m of the input alm
spin (int):Spin of the transform
map0 [pix] (double):
 Real part of the input map, with bounds (0:npix-1)
map1 [pix] (double):
 Imaginary part of the input map, with bounds (0:npix-1)
Returns:
alm [2,l,m] (dcmplx):
 Parity-eve/odd harmonic coefficients obtained from the input map, with bounds (2,0:lmax,0:mmax)
Usage:
alm = curvedsky.utils.hp_map2alm_spin(nside,lmax,mmax,spin,map0,map1):
 
curvedsky.utils.map_mul_lfunc(nside, imap, lmax, lfunc)

Convert map to alm, multiply a function to alm and convert back again to map

Args:
nside (int):Nside of input map
imap [pix] (double):
 Input map, with bounds (0:12*nside**2-1)
lmax (int):Maximum multipole of the input alm
lfunc [l] (double):
 1D spectrum to be multiplied to alm, with bounds (0:lmax)
Returns:
omap [pix] (double):
 Output map, with bounds (0:12*nside**2-1)
Usage:
omap = curvedsky.utils.map_mul_lfunc(nside,imap,lmax,lfunc):
 
curvedsky.utils.mulwin(alm, win, nside=0, lmax=0, mmax=0)

Multiply window to a map obtained from alm

Args:
alm [l,m] (dcmplx):
 Harmonic coefficient to be multiplied at window, with bounds (0:lmax,0:mmax)
win [pix] (double):
 Transformed map, with bounds (0:npix-1)
Returns:
wlm [l,m] (dcmplx):
 Harmonic coefficient of the window-multiplied map, with bounds (0:lmax,0:mmax)
Usage:
wlm = curvedsky.utils.mulwin(nside,lmax,mmax,alm,win):
 
curvedsky.utils.mulwin_spin(elm, blm, win, nside=0, lmax=0, mmax=0, spin=2)

Multiply window to a map obtained from alm

Args:
elm [l,m] (dcmplx):
 Spin-s E-like harmonic coefficient to be transformed to a map, with bounds (0:lmax,0:mmax)
blm [l,m] (dcmplx):
 Spin-s B-like harmonic coefficient to be transformed to a map, with bounds (0:lmax,0:mmax)
win [pix] (double):
 Transformed map, with bounds (0:npix-1)
Args (Optional):
spin (int):Spin of the transform, default to 2
Returns:
wlm [2,l,m] (dcmplx):
 Parity-eve/odd harmonic coefficients obtained from the window-multiplied map, with bounds (2,0:lmax,0:mmax)
Usage:
wlm = curvedsky.utils.mulwin_spin(nside,lmax,mmax,spin,elm,blm,win):
 
curvedsky.utils.lmpy2lmax(lmpy)
Usage:
lmax = curvedsky.utils.lmpy2lmax(lmpy):
 
curvedsky.utils.lm_healpy2healpix(almpy, lmax, lmpy=0)

Transform healpy alm to healpix alm

Args:
lmax (int):Maximum multipole of the input/output alm satisfying 2 x lmpy = (lmax+1) x (lmax+2)
almpy[index] (dcmplx):
 Healpy alm, with bounds (0:lmpy-1)
Returns:
almpix [l,m] (dcmplx):
 Healpix alm, with bounds (0:lmax,0:lmax)
Usage:
almpix = curvedsky.utils.lm_healpy2healpix(lmpy,almpy,lmax):
 
curvedsky.utils.cosin_healpix(nside)

Return cos(theta) as a function of the Healpix pixel index

Args:
nside (int):Nside of the desired map
Returns:
cosin[pix] (double):
 cosin(theta), with bounds (0:npix-1)
Usage:
cosin = curvedsky.utils.cosin_healpix(nside):
 
curvedsky.utils.load_defangle_takahashi(fname, npix, verbose=False)

Read theta and phi coordinates at source plane obtained by Takahashi et al. (2017)

Args:
fname (str):file name
npix (int):Number of pixels of theta and phi data
Args (optional):
verbose (bool):output messages, default to False
Returns:
theta[pix] (double):
 theta, with bounds (0:npix-1)
phi[pix] (double):
 phi, with bounds (0:npix-1)
Usage:
theta,phi = curvedsky.utils.load_defangle_takahashi(fname,npix,verbose):
 
curvedsky.utils.polcoord2angle(npix, theta, phi, verbose=False)

Converting theta and phi coordinates at source plane to deflection angle. The algorithm is provided by Takashi Hamana and Ryuichi Takahashi.

Args:
npix (int):Number of pixels of theta and phi data
theta[pix] (double):
 theta, with bounds (0:npix-1)
phi[pix] (double):
 phi, with bounds (0:npix-1)
Args (optional):
verbose (bool):output messages, default to False
Returns:
angle[pix,2] (double):
 deflection angle vector containing two components, with bounds (0:npix-1,1:2)
Usage:
angle = curvedsky.utils.polcoord2angle(npix,theta,phi,verbose):
 
curvedsky.utils.polcoord2angle_alm(nside, lmax, theta, phi, verbose=False)

Converting theta and phi coordinates at source plane to deflection angle.

Args:
npix (int):Number of pixels of theta and phi data
lmax (int):Maximum multipole of alms for gradient and curl modes
theta[pix] (double):
 theta, with bounds (0:npix-1)
phi[pix] (double):
 phi, with bounds (0:npix-1)
Args (optional):
verbose (bool):output messages, default to False
Returns:
glm[l,m] (dcmplx):
 gradient mode, with bounds (0:lmax,0:lmax)
clm[l,m] (dcmplx):
 curl mode, with bounds (0:lmax,0:lmax)
Usage:
glm,clm = curvedsky.utils.polcoord2angle_alm(nside,lmax,theta,phi,verbose):
 
curvedsky.utils.calc_mfs(bn, nu, lmax, walm, nside=0)

Compute 2D Minkowski functionals from a given alm

Args:
bn (int):Number of nu bins
nu [bin] (double):
 Nu bins, with bounds (bn)
lmax (int):Maximum multipole of the input walm
walm [l,m] (dcmplx):
 Alm with filtering, possibly divided by the map variance, with bounds (0:lmax,0:lmax)
Args(optional):
nside (int):Nside of the intermediate map, default to lmax
Returns:
V [bin,type] (double):
 The three Minkowski functionals, V0, V1 and V2, at each nu bin, with bounds (bn,0:2)
Usage:
V = curvedsky.utils.calc_mfs(bn,nu,lmax,walm,nside):
 
curvedsky.utils.mock_galaxy_takahashi(fname, zn, ngz, zi, a=2.0, b=1.0, zm=1.0, sz=0.0, zbias=0.0, b0=1.0, btype='sqrtz')

Compute galaxy overdensity map from dark matter density map of Takahashi et al. (2017). The galaxy z distribution is assumed to have the functional form given by Eq.(7) of https://arxiv.org/abs/1810.03346

Args:
fname (str):Filename of density map
zn (int):Number of tomographic bins
ngz[zn] (double):
 Total number of galaxies at each z-bin
zi[zn+1] (double):
 Redshift intervals of the tomographic bins
Args(optional):
a (double):galaxy distribution shape parameter
b (double):galaxy distribution shape parameter
zm (double):mean redshift of galaxy distribution
b0 (double):constant galaxy bias at z=0
Returns:
gmap [pix,zbin] (double):
 The galaxy number density map at each zbin
Usage:
gmap = curvedsky.utils.mock_galaxy_takahashi(fname,zn,ngz,zi,b0,btype,a,b,zm,sz,zbias):