`flatsky` – Flatsky analysis tools¶

`rec_lens` – quadratic lensing reconstruction¶

flatsky.rec_lens.qtt(nx, ny, D, rL, fC, T1, T2, gtype='')¶

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

Args:

fC[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	Temperature power spectrum on 2D grid, with bounds (nx,ny)
T1[lx,ly] (dcmplx):
	2D Fourier modes of 1st inverse-variance filtered temperature, with bounds (nx,ny)
T2[lx,ly] (dcmplx):
	2D Fourier modes of 2nd inverse-variance filtered temperature, with bounds (nx,ny)

Args(optional):

gtype (str):	Type of output, i.e., convergence (gtype=’k’) or lensing potential (gtype=’‘, default)

Returns:

glm[lx,ly] (dcmplx):
	2D Fourier modes of CMB lensing potential, with bounds (nx,ny)
clm[lx,ly] (dcmplx):
	2D Fourier modes of Curl mode (pseudo lensing potential), with bounds (nx,ny)

Usage:

glm,clm = flatsky.rec_lens.qtt(nx,ny,D,rL,fC,T1,T2,gtype):

flatsky.rec_lens.qte(nx, ny, D, rL, fC, T, E, gtype='')¶

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

Args:

fC[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	TE cross power spectrum on 2D grid, with bounds (nx,ny)
T[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered temperature, with bounds (nx,ny)
E[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered E-mode, with bounds (nx,ny)

Args(optional):

gtype (str):	Type of output, i.e., convergence (gtype=’k’) or lensing potential (gtype=’‘, default)

Returns:

glm[lx,ly] (dcmplx):
	2D Fourier modes of CMB lensing potential, with bounds (nx,ny)
clm[lx,ly] (dcmplx):
	2D Fourier modes of Curl mode (pseudo lensing potential), with bounds (nx,ny)

Usage:

glm,clm = flatsky.rec_lens.qte(nx,ny,D,rL,fC,T,E,gtype):

flatsky.rec_lens.qtb(nx, ny, D, rL, fC, T, B, gtype='')¶

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

Args:

fC[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	TE cross power spectrum on 2D grid, with bounds (nx,ny)
T[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered temperature, with bounds (nx,ny)
B[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered B-mode, with bounds (nx,ny)

Args(optional):

gtype (str):	Type of output, i.e., convergence (gtype=’k’) or lensing potential (gtype=’‘, default)

Returns:

glm[lx,ly] (dcmplx):
	2D Fourier modes of CMB lensing potential, with bounds (nx,ny)
clm[lx,ly] (dcmplx):
	2D Fourier modes of Curl mode (pseudo lensing potential), with bounds (nx,ny)

Usage:

glm,clm = flatsky.rec_lens.qtb(nx,ny,D,rL,fC,T,B,gtype):

flatsky.rec_lens.qee(nx, ny, D, rL, fC, E1, E2, gtype='')¶

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

Args:

fC[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	EE power spectrum on 2D grid, with bounds (nx,ny)
E1[lx,ly] (dcmplx):
	2D Fourier modes of 1st inverse-variance filtered E-mode, with bounds (nx,ny)
E2[lx,ly] (dcmplx):
	2D Fourier modes of 2nd inverse-variance filtered E-mode, with bounds (nx,ny)

Args(optional):

gtype (str):	Type of output, i.e., convergence (gtype=’k’) or lensing potential (gtype=’‘, default)

Returns:

glm[lx,ly] (dcmplx):
	2D Fourier modes of CMB lensing potential, with bounds (nx,ny)
clm[lx,ly] (dcmplx):
	2D Fourier modes of Curl mode (pseudo lensing potential), with bounds (nx,ny)

Usage:

glm,clm = flatsky.rec_lens.qee(nx,ny,D,rL,fC,E1,E2,gtype):

flatsky.rec_lens.qeb(nx, ny, D, rL, fC, E, B, gtype='')¶

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

Args:

fC[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	EE power spectrum on 2D grid, with bounds (nx,ny)
E[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered E-mode, with bounds (nx,ny)
B[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered B-mode, with bounds (nx,ny)

Args(optional):

gtype (str):	Type of output, i.e., convergence (gtype=’k’) or lensing potential (gtype=’‘, default)

Returns:

glm[lx,ly] (dcmplx):
	2D Fourier modes of CMB lensing potential, with bounds (nx,ny)
clm[lx,ly] (dcmplx):
	2D Fourier modes of Curl mode (pseudo lensing potential), with bounds (nx,ny)

Usage:

glm,clm = flatsky.rec_lens.qeb(nx,ny,D,rL,fC,E,B,gtype):

flatsky.rec_lens.qbb(nx, ny, D, rL, fC, B1, B2, gtype='')¶

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

Args:

fC[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	BB power spectrum on 2D grid, with bounds (nx,ny)
B1[lx,ly] (dcmplx):
	2D Fourier modes of 1st inverse-variance filtered B-mode, with bounds (nx,ny)
B2[lx,ly] (dcmplx):
	2D Fourier modes of 2nd inverse-variance filtered B-mode, with bounds (nx,ny)

Args(optional):

gtype (str):	Type of output, i.e., convergence (gtype=’k’) or lensing potential (gtype=’‘, default)

Returns:

glm[lx,ly] (dcmplx):
	2D Fourier modes of CMB lensing potential, with bounds (nx,ny)
clm[lx,ly] (dcmplx):
	2D Fourier modes of Curl mode (pseudo lensing potential), with bounds (nx,ny)

Usage:

glm,clm = flatsky.rec_lens.qbb(nx,ny,D,rL,fC,B1,B2,gtype):

`rec_rot` – quadratic pol. rot. reconstruction¶

flatsky.rec_rot.qte(nx, ny, D, rL, fC, T, E)¶

Reconstructing anisotropic pol. rot. angles from TE quadratic estimator

Args:

fC[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	TE cross power spectrum on 2D grid, with bounds (nx,ny)
T[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered temperature, with bounds (nx,ny)
E[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered E-mode, with bounds (nx,ny)

Returns:

alm[lx,ly] (dcmplx):
	2D Fourier modes of anisotropic pol. rot. angles, with bounds (nx,ny)

Usage:

alm = flatsky.rec_rot.qte(nx,ny,D,rL,fC,T,E):

flatsky.rec_rot.qtb(nx, ny, D, rL, fC, T, B)¶

Reconstructing anisotropic pol. rot. angles from TB quadratic estimator

Args:

fC[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	TE cross power spectrum on 2D grid, with bounds (nx,ny)
T[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered temperature, with bounds (nx,ny)
B[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered B-mode, with bounds (nx,ny)

Returns:

alm[lx,ly] (dcmplx):
	2D Fourier modes of anisotropic pol. rot. angles, with bounds (nx,ny)

Usage:

alm = flatsky.rec_rot.qtb(nx,ny,D,rL,fC,T,B):

flatsky.rec_rot.qee(nx, ny, D, rL, fC, E1, E2)¶

Reconstructing anisotropic pol. rot. angles from EE quadratic estimator

Args:

fC[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	EE power spectrum on 2D grid, with bounds (nx,ny)
E1[lx,ly] (dcmplx):
	2D Fourier modes of 1st inverse-variance filtered E-mode, with bounds (nx,ny)
E2[lx,ly] (dcmplx):
	2D Fourier modes of 2nd inverse-variance filtered E-mode, with bounds (nx,ny)

Returns:

alm[lx,ly] (dcmplx):
	2D Fourier modes of anisotropic pol. rot. angles, with bounds (nx,ny)

Usage:

alm = flatsky.rec_rot.qee(nx,ny,D,rL,fC,E1,E2):

flatsky.rec_rot.qeb(nx, ny, D, rL, EE, E, B, BB=0)¶

Reconstructing anisotropic pol. rot. angles from EB quadratic estimator

Args:

fC[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	EE power spectrum on 2D grid, with bounds (nx,ny)
E[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered E-mode, with bounds (nx,ny)
B[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered B-mode, with bounds (nx,ny)

Args(Optional):

BB[lx,ly] (double):
	Theory B-mode spectrum on 2D grid, with bounds (nx,ny), default to BB=0

Returns:

alm[lx,ly] (dcmplx):
	2D Fourier modes of anisotropic pol. rot. angles, with bounds (nx,ny)

Usage:

alm = flatsky.rec_rot.qeb(nx,ny,D,rL,EE,E,B,BB):

`rec_tau` – quadratic patchy tau reconstruction¶

flatsky.rec_tau.qtt(nx, ny, D, rL, fC, T1, T2)¶

Reconstructing patchy tau from the temperature quadratic estimator

Args:

fC[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	Temperature power spectrum on 2D grid, with bounds (nx,ny)
T1[lx,ly] (dcmplx):
	2D Fourier modes of 1st inverse-variance filtered temperature, with bounds (nx,ny)
T2[lx,ly] (dcmplx):
	2D Fourier modes of 2nd inverse-variance filtered temperature, with bounds (nx,ny)

Returns:

tlm[lx,ly] (dcmplx):
	2D Fourier modes of patchy tau, with bounds (nx,ny)

Usage:

tlm = flatsky.rec_tau.qtt(nx,ny,D,rL,fC,T1,T2):

flatsky.rec_tau.qte(nx, ny, D, rL, fC, T, E)¶

Reconstructing patchy tau from the suboptimal TE quadratic estimator

Args:

fC[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	TE cross power spectrum on 2D grid, with bounds (nx,ny)
T[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered temperature, with bounds (nx,ny)
E[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered E-mode, with bounds (nx,ny)

Returns:

tlm[lx,ly] (dcmplx):
	2D Fourier modes of patchy tau, with bounds (nx,ny)

Usage:

tlm = flatsky.rec_tau.qte(nx,ny,D,rL,fC,T,E):

flatsky.rec_tau.qtb(nx, ny, D, rL, fC, T, B)¶

Reconstructing patchy tau from the TB quadratic estimator

Args:

fC[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	TE cross power spectrum on 2D grid, with bounds (nx,ny)
T[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered temperature, with bounds (nx,ny)
B[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered B-mode, with bounds (nx,ny)

Returns:

tlm[lx,ly] (dcmplx):
	2D Fourier modes of patchy tau, with bounds (nx,ny)

Usage:

tlm = flatsky.rec_tau.qtb(nx,ny,D,rL,fC,T,B):

flatsky.rec_tau.qee(nx, ny, D, rL, fC, E1, E2)¶

Reconstructing patchy tau from the EE quadratic estimator

Args:

fC[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	EE power spectrum on 2D grid, with bounds (nx,ny)
E1[lx,ly] (dcmplx):
	2D Fourier modes of 1st inverse-variance filtered E-mode, with bounds (nx,ny)
E2[lx,ly] (dcmplx):
	2D Fourier modes of 2nd inverse-variance filtered E-mode, with bounds (nx,ny)

Returns:

tlm[lx,ly] (dcmplx):
	2D Fourier modes of patchy tau, with bounds (nx,ny)

Usage:

tlm = flatsky.rec_tau.qee(nx,ny,D,rL,fC,E1,E2):

flatsky.rec_tau.qeb(nx, ny, D, rL, fE, fB, E, B)¶

Reconstructing patchy tau from the EB quadratic estimator

Args:

fE[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	EE power spectrum on 2D grid, with bounds (nx,ny)
fB[lx,ly] (double):
	BB power spectrum on 2D grid, with bounds (nx,ny)
E[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered E-mode, with bounds (nx,ny)
B[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered B-mode, with bounds (nx,ny)

Returns:

tlm[lx,ly] (dcmplx):
	2D Fourier modes of patchy tau, with bounds (nx,ny)

Usage:

tlm = flatsky.rec_tau.qeb(nx,ny,D,rL,fE,fB,E,B):

`rec_src` – quadratic point-src reconstruction¶

flatsky.rec_src.qtt(nx, ny, D, rL, T1, T2)¶

Reconstructing point source fields from the temperature quadratic estimator

Args:

fC[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	Temperature power spectrum on 2D grid, with bounds (nx,ny)
T1[lx,ly] (dcmplx):
	2D Fourier modes of 1st inverse-variance filtered temperature, with bounds (nx,ny)
T2[lx,ly] (dcmplx):
	2D Fourier modes of 2nd inverse-variance filtered temperature, with bounds (nx,ny)

Returns:

slm[lx,ly] (dcmplx):
	2D Fourier modes of point source fields, with bounds (nx,ny)

Usage:

slm = flatsky.rec_src.qtt(nx,ny,D,rL,T1,T2):

flatsky.rec_src.qte(nx, ny, D, rL, T, E)¶

Reconstructing point source fields from the suboptimal TE quadratic estimator

Args:

fC[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	TE cross power spectrum on 2D grid, with bounds (nx,ny)
T[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered temperature, with bounds (nx,ny)
E[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered E-mode, with bounds (nx,ny)

Returns:

slm[lx,ly] (dcmplx):
	2D Fourier modes of point source fields, with bounds (nx,ny)

Usage:

slm = flatsky.rec_src.qte(nx,ny,D,rL,T,E):

flatsky.rec_src.qtb(nx, ny, D, rL, T, B)¶

Reconstructing point source fields from the TB quadratic estimator

Args:

fC[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	TE cross power spectrum on 2D grid, with bounds (nx,ny)
T[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered temperature, with bounds (nx,ny)
B[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered B-mode, with bounds (nx,ny)

Returns:

slm[lx,ly] (dcmplx):
	2D Fourier modes of point source fields, with bounds (nx,ny)

Usage:

slm = flatsky.rec_src.qtb(nx,ny,D,rL,T,B):

flatsky.rec_src.qee(nx, ny, D, rL, E1, E2)¶

Reconstructing point source fields from the EE quadratic estimator

Args:

fC[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	EE power spectrum on 2D grid, with bounds (nx,ny)
E1[lx,ly] (dcmplx):
	2D Fourier modes of 1st inverse-variance filtered E-mode, with bounds (nx,ny)
E2[lx,ly] (dcmplx):
	2D Fourier modes of 2nd inverse-variance filtered E-mode, with bounds (nx,ny)

Returns:

slm[lx,ly] (dcmplx):
	2D Fourier modes of point source fields, with bounds (nx,ny)

Usage:

slm = flatsky.rec_src.qee(nx,ny,D,rL,E1,E2):

flatsky.rec_src.qeb(nx, ny, D, rL, E, B)¶

Reconstructing point source fields from the EB quadratic estimator

Args:

fC[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	EE power spectrum on 2D grid, with bounds (nx,ny)
E[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered E-mode, with bounds (nx,ny)
B[lx,ly] (dcmplx):
	2D Fourier modes of inverse-variance filtered B-mode, with bounds (nx,ny)

Returns:

slm[lx,ly] (dcmplx):
	2D Fourier modes of point source fields, with bounds (nx,ny)

Usage:

slm = flatsky.rec_src.qeb(nx,ny,D,rL,E,B):

`norm_lens` – normalization of quadratic lensing reconstruction¶

flatsky.norm_lens.qtt(nx, ny, D, rL, OT, TT, eL)¶

Normalization of the temperature quadratic estimator for CMB lensing potential and its curl mode

Args:

OT[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	Inverse of Observed temperature power spectrum on 2D grid, with bounds (nx,ny)
TT[lx,ly] (double):
	Theory temperature power spectrum on 2D grid, with bounds (nx,ny)
eL[2] (int):	Minimum and maximum multipole of output normalization spectrum, with bounds (2)

Returns:

Ag[lx,ly] (dcmplx):
	Normalization of CMB lensing potential on 2D grid, with bounds (nx,ny)
Ac[lx,ly] (dcmplx):
	Normalization of Curl mode (pseudo lensing potential) on 2D grid, with bounds (nx,ny)

Usage:

Ag,Ac = flatsky.norm_lens.qtt(nx,ny,D,rL,OT,TT,eL):

flatsky.norm_lens.qte(nx, ny, D, rL, OT, OE, TE, eL)¶

Normalization of the TE quadratic estimator for CMB lensing potential and its curl mode

Args:

OT[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	Inverse of Observed temperature power spectrum on 2D grid, with bounds (nx,ny)
OE[lx,ly] (double):
	Inverse of Observed E-mode power spectrum on 2D grid, with bounds (nx,ny)
TE[lx,ly] (double):
	Theory TE cross spectrum on 2D grid, with bounds (nx,ny)
eL[2] (int):	Minimum and maximum multipole of output normalization spectrum, with bounds (2)

Returns:

Ag[lx,ly] (dcmplx):
	Normalization of CMB lensing potential on 2D grid, with bounds (nx,ny)
Ac[lx,ly] (dcmplx):
	Normalization of Curl mode (pseudo lensing potential) on 2D grid, with bounds (nx,ny)

Usage:

Ag,Ac = flatsky.norm_lens.qte(nx,ny,D,rL,OT,OE,TE,eL):

flatsky.norm_lens.qtb(nx, ny, D, OT, OB, TE, rL, eL)¶

Normalization of the TB quadratic estimator for CMB lensing potential and its curl mode

Args:

OT[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	Inverse of Observed temperature power spectrum on 2D grid, with bounds (nx,ny)
OB[lx,ly] (double):
	Inverse of Observed B-mode power spectrum on 2D grid, with bounds (nx,ny)
TE[lx,ly] (double):
	Theory TE cross spectrum on 2D grid, with bounds (nx,ny)
eL[2] (int):	Minimum and maximum multipole of output normalization spectrum, with bounds (2)

Returns:

Ag[lx,ly] (dcmplx):
	Normalization of CMB lensing potential on 2D grid, with bounds (nx,ny)
Ac[lx,ly] (dcmplx):
	Normalization of Curl mode (pseudo lensing potential) on 2D grid, with bounds (nx,ny)

Usage:

Ag,Ac = flatsky.norm_lens.qtb(nx,ny,D,OT,OB,TE,rL,eL):

flatsky.norm_lens.qee(nx, ny, D, OE, EE, rL, eL)¶

Normalization of the EE quadratic estimator for CMB lensing potential and its curl mode

Args:

OE[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	Inverse of Observed E-mode power spectrum on 2D grid, with bounds (nx,ny)
EE[lx,ly] (double):
	Theory E-mode spectrum on 2D grid, with bounds (nx,ny)
eL[2] (int):	Minimum and maximum multipole of output normalization spectrum, with bounds (2)

Returns:

Ag[lx,ly] (dcmplx):
	Normalization of CMB lensing potential on 2D grid, with bounds (nx,ny)
Ac[lx,ly] (dcmplx):
	Normalization of Curl mode (pseudo lensing potential) on 2D grid, with bounds (nx,ny)

Usage:

Ag,Ac = flatsky.norm_lens.qee(nx,ny,D,OE,EE,rL,eL):

flatsky.norm_lens.qeb(nx, ny, D, OE, OB, EE, rL, eL)¶

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

Args:

OE[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	Inverse of Observed E-mode power spectrum on 2D grid, with bounds (nx,ny)
OB[lx,ly] (double):
	Inverse of Observed B-mode power spectrum on 2D grid, with bounds (nx,ny)
EE[lx,ly] (double):
	Theory E-mode spectrum on 2D grid, with bounds (nx,ny)
eL[2] (int):	Minimum and maximum multipole of output normalization spectrum, with bounds (2)

Returns:

Ag[lx,ly] (dcmplx):
	Normalization of CMB lensing potential on 2D grid, with bounds (nx,ny)
Ac[lx,ly] (dcmplx):
	Normalization of Curl mode (pseudo lensing potential) on 2D grid, with bounds (nx,ny)

Usage:

Ag,Ac = flatsky.norm_lens.qeb(nx,ny,D,OE,OB,EE,rL,eL):

`norm_rot` – normalization of quadratic pol. rot. reconstruction¶

flatsky.norm_rot.qeb(nx, ny, D, rL, IE, IB, EE, eL, BB=0)¶

Normalization of the EB quadratic estimator for anisotropic pol. rot. angles

Args:

IE[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	Inverse of observed E-mode power spectrum on 2D grid, with bounds (nx,ny)
IB[lx,ly] (double):
	Inverse of observed B-mode power spectrum on 2D grid, with bounds (nx,ny)
EE[lx,ly] (double):
	Theory E-mode spectrum on 2D grid, with bounds (nx,ny)
eL[2] (int):	Minimum and maximum multipole of output normalization spectrum, with bounds (2)

Args(Optional):

BB[lx,ly] (double):
	Theory B-mode spectrum on 2D grid, with bounds (nx,ny), default to BB=0

Returns:

Aa[lx,ly] (dcmplx):
	Normalization of anisotropic pol. rot. angles on 2D grid, with bounds (nx,ny)

Usage:

Aa = flatsky.norm_rot.qeb(nx,ny,D,rL,IE,IB,EE,eL,BB):

`norm_tau` – normalization of quadratic patchy tay reconstruction¶

flatsky.norm_tau.qtt(nx, ny, D, rL, OT, TT, eL)¶

Normalization of the temperature quadratic estimator for patchy tau

Args:

OT[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	Inverse of Observed temperature power spectrum on 2D grid, with bounds (nx,ny)
TT[lx,ly] (double):
	Theory temperature power spectrum on 2D grid, with bounds (nx,ny)
eL[2] (int):	Minimum and maximum multipole of output normalization spectrum, with bounds (2)

Returns:

At[lx,ly] (dcmplx):
	Normalization of patchy tau on 2D grid, with bounds (nx,ny)

Usage:

At = flatsky.norm_tau.qtt(nx,ny,D,rL,OT,TT,eL):

flatsky.norm_tau.qeb(nx, ny, D, rL, IE, IB, EE, eL)¶

Normalization of the EB quadratic estimator for patchy tau

Args:

IE[lx,ly] (double):
nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
rL[2] (int):	Minimum and maximum multipole of CMB for reconstruction
	Inverse of observed E-mode power spectrum on 2D grid, with bounds (nx,ny)
IB[lx,ly] (double):
	Inverse of observed B-mode power spectrum on 2D grid, with bounds (nx,ny)
EE[lx,ly] (double):
	Theory E-mode spectrum on 2D grid, with bounds (nx,ny)
eL[2] (int):	Minimum and maximum multipole of output normalization spectrum, with bounds (2)

Returns:

At[lx,ly] (dcmplx):
	Normalization of patchy tau on 2D grid, with bounds (nx,ny)

Usage:

At = flatsky.norm_tau.qeb(nx,ny,D,rL,IE,IB,EE,eL):

`bispec` – bispectrum tools¶

flatsky.bispec.bispec_norm(nx, ny, D, bp, bn=1, dbin_max=-1)¶

Usage:

norm = flatsky.bispec.bispec_norm(nx,ny,D,bp,dbin_max,bn):

flatsky.bispec.bispec_bin(kmap, bp, bn=1, kn=1, nx=0, ny=0, dbin_max=-1)¶

Usage:

bispec = flatsky.bispec.bispec_bin(kn,bn,nx,ny,kmap,bp,dbin_max):

flatsky.bispec.binfilter(nx, ny, D, bp, bn=1)¶

The multipole bin binary-mask given on the 2D Fourier grids so that M = 1 inside the multipole bin and 0 otherwise

Args:

bp[bn+1] (double):
nx, ny (int):	Number of Lx and Ly grids
D[2] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
	Multipole bin edges

Returns:

bf[bn,nx,ny] (double):
	The multipole bin binary-mask for each multipol bin

Usage:

bf = flatsky.bispec.binfilter(nx,ny,D,bp,bn):

flatsky.bispec.bispec_norm_1d(nx, ny, D, bfs, bn=1)¶

Normalization of the 1D binned bispectrum estimator

Args:

bfs[3,bn,nx,ny] (double):
nx, ny (int):	Number of Lx and Ly grids
D[2] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
	Multipole bin mask on 2D grids obtained from the binfilter function

Returns:

bnorm[bn] (double):
	Normalization of 1D binned bispectrum at each multipole bin

Usage:

bnorm = flatsky.bispec.bispec_norm_1d(nx,ny,D,bfs,bn):

flatsky.bispec.bispec_bin_1d(nx, ny, D, bfs, bnorm, alm, bn=1)¶

1D binned bispectrum estimator

Args:

bfs[3,bn,nx,ny] (double):
nx, ny (int):	Number of Lx and Ly grids
D[2] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
	Multipole bin mask on 2D grids obtained from the binfilter function
bnorm[bn] (double):
	Normalization of 1D binned bispectrum at each multipole bin
alm[3,nx,ny] (dcmplx):
	Fourier modes for each leg

Returns:

bispec[bn] (double):
	1D binned bispectrum at each multipole bin

Usage:

bispec = flatsky.bispec.bispec_bin_1d(nx,ny,D,bfs,bnorm,alm,bn):

`utils` – other tools¶

flatsky.utils.map2alm(nx, ny, D, map)¶

DFT for 2D array.

Args:

map[x,y] (double):
nx, ny (int):	Number of x and y grids
D[2] (double):	Side length (x and y) of map
	Map on 2D grid with bounds (nx,ny)

Returns:

alm[x,y] (dcmplx):
	Fourier modes on 2D grid, with bounds (nx,ny)

Usage:

alm = flatsky.utils.map2alm(nx,ny,D,map):

flatsky.utils.alm2map(nx, ny, D, alm)¶

DFT for 2D array.

Args:

alm[x,y] (dcmplx):
nx, ny (int):	Number of Lx and Ly grids
D[2] (double):	Side length (x and y) of map
	Fourier modes on 2D grid to be transformed, with bounds (nx,ny)

Returns:

map[x,y] (double):
	Map on 2D grid, with bounds (nx,ny)

Usage:

map = flatsky.utils.alm2map(nx,ny,D,alm):

flatsky.utils.el2d(nx, ny, D)¶

Return absolute value of multipole in 2D grids

Args:

nx, ny (int):	number of Lx and Ly grids
D[xy] (double):	map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)

Returns:

els[nx,ny] (double):
	absolute value of Fourier mode, (Lx2+Ly2)**0.5, with bounds (nx,ny)

Usage:

els = flatsky.utils.el2d(nx,ny,D):

flatsky.utils.elarrays(nx, ny, D)¶

Return Lx, Ly, absolute value of multipole, and its inverse in 2D grids

Args:

nx, ny (int):	number of Lx and Ly grids
D[xy] (double):	map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)

Returns:

elx[nx,ny] (double):
	Lx, with bounds (nx,ny)
ely[nx,ny] (double):
	Ly, with bounds (nx,ny)
els[nx,ny] (double):
	absolute value of Fourier mode, (Lx2+Ly2)**0.5, with bounds (nx,ny)
eli[nx,ny] (double):
	inverse of els, with bounds (nx,ny)

Usage:

elx,ely,els,eli = flatsky.utils.elarrays(nx,ny,D):

flatsky.utils.elmask(nx, ny, D, lmin=0, lmax=1000, lxcut=0, lycut=0)¶

Return mask in 2D Fourier space. The lmask is unity at lmin<=|L|<=lmax, |Lx|>=lxcut, |Ly|>=lycut, and otherwize zero.

Args:

nx, ny (int):	number of Lx and Ly grids
D[xy] (double):	map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)

Args(optional):

lmin/lmax (int):
	Minimum/Maximum of multipoles
lxcut/lycut (int):
	Remove \|Lx\|<lxcut / \|Ly\|<lycut cut of multipoles

Returns:

lmask[nx,ny] (double):
	Mask, with bounds (nx,ny)

Usage:

lmask = flatsky.utils.elmask(nx,ny,D,lmin,lmax,lxcut,lycut):

flatsky.utils.alm2bcl(bn, oL, nx, ny, D, alm1, spc='', alm2=None)¶

Compute angular power spectrum from Fourier modes, with multipole binning

Args:

alm1[nx,ny] (dcmplx):
bn (int):	number of multipole bin
oL[2] (int):	minimum and maximum multipoles of the output cl
nx, ny (int):	number of Lx and Ly grids
D[xy] (double):	map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
	Fourier mode, with bounds (nx,ny)

Args(optional):

alm2[nx,ny] (dcmplx):
	Fourier mode, with bounds (nx,ny), default to None
spc (str):	type of multipole binning, i.e., linear spacing (spc=’‘, default), or log spacing (spc=’log’)

Returns:

Cb[bin] (double):
	angular power spectrum with multipole binning, with bounds (bn)

Usage:

Cb = flatsky.utils.alm2bcl(bn,oL,nx,ny,D,alm1,alm2,spc):

flatsky.utils.c2d2bcl(nx, ny, D, c2d, bn, oL, spc='')¶

Return 1D angular power spectrum with multipole binning from a 2D power spectrum

Args:

c2d[nx,ny] (double):
nx, ny (int):	number of Lx and Ly grids
D[xy] (double):	map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
	2D power spectrum, with bounds (nx,ny)
bn (int):	number of multipole bin
oL[2] (int):	minimum and maximum multipoles of the output cl

Args(optional):

spc (str):	type of multipole binning, i.e., linear spacing (spc=’‘, default), or log spacing (spc=’log’)

Returns:

Cb[bin] (double):
	angular power spectrum with multipole binning, with bounds (bn)

Usage:

Cb = flatsky.utils.c2d2bcl(nx,ny,D,c2d,bn,oL,spc):

flatsky.utils.cl2c2d(nx, ny, D, lmin, lmax, Cl, method='linear')¶

Assign values of 1D angular power spectrum on to 2D grid with linear interpolation

Args:

nx, ny (int):	number of Lx and Ly grids
D[xy] (double):	map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
lmin (int):	minimum multipole of cl to be interpolated
lmax (int):	maximum multipole of cl to be interpolated
Cl[l] (double):	1D power spectrum, with bounds (0:lmax)

Args(optional):

method (str):	type of interpolation method, i.e., linear interpolation (method=’linear’, default), or step (method=’step’)

Returns:

c2d[nx,ny] (double):
	2D power spectrum, with bounds (nx,ny)

Usage:

c2d = flatsky.utils.cl2c2d(nx,ny,D,lmin,lmax,Cl,method):

flatsky.utils.cb2c2d(bn, bc, nx, ny, D, lmin, lmax, Cb, method='')¶

Assign values of 1D angular power spectrum on to 2D grid with linear interpolation

Args:

bc[bin] (double):
bn (int):	number of multipole bins
	multipole bin center, with bounds (bn)
nx, ny (int):	number of Lx and Ly grids
D[xy] (double):	map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
lmin (int):	minimum multipole of cl to be interpolated
lmax (int):	maximum multipole of cl to be interpolated
Cb[bin] (double):
	1D power spectrum with multipole binning, with bounds (bn)

Args(optional):

method (str):	interpolation method from binned to unbinned angular spectrum, i.e., spline (‘’, default), or linear (‘linear’) interpolation

Returns:

c2d[nx,ny] (double):
	2D power spectrum, with bounds (nx,ny)

Usage:

C2d = flatsky.utils.cb2c2d(bn,bc,nx,ny,D,lmin,lmax,Cb,method):

flatsky.utils.gauss1alm(nx, ny, D, lmin, lmax, Cl)¶

Generate random gaussian fields in 2D Fourier space for a given isotropic spectrum, satisfying a^*_l = a_{-l}

Args:

nx, ny (int):	number of Lx and Ly grids
D[xy] (double):	map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
lmin (int):	minimum multipole of cl to be interpolated
lmax (int):	maximum multipole of cl to be interpolated
Cl[l] (double):	1D power spectrum, with bounds (0:lmax)

Returns:

alm[lx,ly] (dcmplx):
	random gaussian fields on 2D Fourier plane, with bounds (nx,ny)

Usage:

alm = flatsky.utils.gauss1alm(nx,ny,D,lmin,lmax,Cl):

flatsky.utils.gauss2alm(nx, ny, D, lmin, lmax, TT, TE, EE)¶

Generate two correlated random gaussian fields in 2D Fourier space for a given isotropic spectrum

Args:

nx, ny (int):	number of Lx and Ly grids
D[xy] (double):	map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)
lmin (int):	minimum multipole of cl to be interpolated
lmax (int):	maximum multipole of cl to be interpolated
TT[l] (double):	the 1st 1D power spectrum, with bounds (0:lmax)
TE[l] (double):	the cross 1D power spectrum, with bounds (0:lmax)
EE[l] (double):	the 2nd 1D power spectrum, with bounds (0:lmax)

Returns:

tlm[lx,ly] (dcmplx):
	the 1st random gaussian fields on 2D Fourier plane, with bounds (nx,ny)
elm[lx,ly] (dcmplx):
	the 2nd random gaussian fields on 2D Fourier plane, with bounds (nx,ny)

Usage:

tlm,elm = flatsky.utils.gauss2alm(nx,ny,D,lmin,lmax,TT,TE,EE):

flatsky.utils.window_sin(nx, ny, D, ap=1, cut=1)¶

Return a sin window function.

Args:

nx, ny (int):	Number of Lx and Ly grids
D[xy] (double):	Map side length, or equivalent to dLx/2pi, dLy/2pi, with bounds (2)

Args(Optional):

ap (double):	Apodization parameter defined by apodized-range = (1-ap) x (cut)mapsize, from 0 (full apodization) to 1 (no apodization). Default to 1.
cut (double):	Map cut scale defined by cutmapsize = cut x mapsize, from 0 (full cut) to 1 (no cut). Default to 1.

Return:

W[x,y] (double):
	Window function, with bounds (nx,ny)

Usage:

W = flatsky.utils.window_sin(nx,ny,D,ap,cut):

flatsky.utils.window_norm(nx, ny, wind, num)¶

Usage:

wn = flatsky.utils.window_norm(nx,ny,wind,num):

flatsky.utils.window_norm_x(nx, ny, W1, W2, num)¶

Usage:

Wn = flatsky.utils.window_norm_x(nx,ny,W1,W2,num):

flatsky.utils.rotation(nx, ny, rot, QU, rtype)¶

Usage:

rQU = flatsky.utils.rotation(nx,ny,rot,QU,rtype):

flatsky.utils.get_angle(nx, ny, D)¶

Usage:

theta,phi = flatsky.utils.get_angle(nx,ny,D):

flatsky.utils.cutmap(ox, oy, cx, cy, omap)¶

Usage:

cmap = flatsky.utils.cutmap(ox,oy,cx,cy,omap):

flatsky – Flatsky analysis tools¶

rec_lens – quadratic lensing reconstruction¶

rec_rot – quadratic pol. rot. reconstruction¶

rec_tau – quadratic patchy tau reconstruction¶

rec_src – quadratic point-src reconstruction¶

norm_lens – normalization of quadratic lensing reconstruction¶

norm_rot – normalization of quadratic pol. rot. reconstruction¶

norm_tau – normalization of quadratic patchy tay reconstruction¶

bispec – bispectrum tools¶

utils – other tools¶

`flatsky` – Flatsky analysis tools¶

`rec_lens` – quadratic lensing reconstruction¶

`rec_rot` – quadratic pol. rot. reconstruction¶

`rec_tau` – quadratic patchy tau reconstruction¶

`rec_src` – quadratic point-src reconstruction¶

`norm_lens` – normalization of quadratic lensing reconstruction¶

`norm_rot` – normalization of quadratic pol. rot. reconstruction¶

`norm_tau` – normalization of quadratic patchy tay reconstruction¶

`bispec` – bispectrum tools¶

`utils` – other tools¶