flatsky – Flatsky analysis tools¶
rec_lens – quadratic lensing reconstruction¶
- cmblensplus.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:
- 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
- fC[lx,ly] (double):
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):
- cmblensplus.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:
- 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
- fC[lx,ly] (double):
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):
- cmblensplus.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:
- 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
- fC[lx,ly] (double):
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):
- cmblensplus.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:
- 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
- fC[lx,ly] (double):
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):
- cmblensplus.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:
- 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
- fC[lx,ly] (double):
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):
- cmblensplus.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:
- 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
- fC[lx,ly] (double):
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¶
- cmblensplus.flatsky.rec_rot.qte(nx, ny, D, rL, fC, T, E)¶
Reconstructing anisotropic pol. rot. angles from TE quadratic estimator
- 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)
- rL[2] (int):
Minimum and maximum multipole of CMB for reconstruction
- fC[lx,ly] (double):
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):
- cmblensplus.flatsky.rec_rot.qtb(nx, ny, D, rL, fC, T, B)¶
Reconstructing anisotropic pol. rot. angles from TB quadratic estimator
- 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)
- rL[2] (int):
Minimum and maximum multipole of CMB for reconstruction
- fC[lx,ly] (double):
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):
- cmblensplus.flatsky.rec_rot.qee(nx, ny, D, rL, fC, E1, E2)¶
Reconstructing anisotropic pol. rot. angles from EE quadratic estimator
- 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)
- rL[2] (int):
Minimum and maximum multipole of CMB for reconstruction
- fC[lx,ly] (double):
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):
- cmblensplus.flatsky.rec_rot.qeb(nx, ny, D, rL, EE, E, B, BB=0)¶
Reconstructing anisotropic pol. rot. angles from EB quadratic estimator
- 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)
- rL[2] (int):
Minimum and maximum multipole of CMB for reconstruction
- fC[lx,ly] (double):
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¶
- cmblensplus.flatsky.rec_tau.qtt(nx, ny, D, rL, fC, T1, T2)¶
Reconstructing patchy tau from the temperature quadratic estimator
- 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)
- rL[2] (int):
Minimum and maximum multipole of CMB for reconstruction
- fC[lx,ly] (double):
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):
- cmblensplus.flatsky.rec_tau.qte(nx, ny, D, rL, fC, T, E)¶
Reconstructing patchy tau from the suboptimal TE quadratic estimator
- 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)
- rL[2] (int):
Minimum and maximum multipole of CMB for reconstruction
- fC[lx,ly] (double):
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):
- cmblensplus.flatsky.rec_tau.qtb(nx, ny, D, rL, fC, T, B)¶
Reconstructing patchy tau from the TB quadratic estimator
- 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)
- rL[2] (int):
Minimum and maximum multipole of CMB for reconstruction
- fC[lx,ly] (double):
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):
- cmblensplus.flatsky.rec_tau.qee(nx, ny, D, rL, fC, E1, E2)¶
Reconstructing patchy tau from the EE quadratic estimator
- 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)
- rL[2] (int):
Minimum and maximum multipole of CMB for reconstruction
- fC[lx,ly] (double):
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):
- cmblensplus.flatsky.rec_tau.qeb(nx, ny, D, rL, fE, fB, E, B)¶
Reconstructing patchy tau from the EB quadratic estimator
- 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)
- rL[2] (int):
Minimum and maximum multipole of CMB for reconstruction
- fE[lx,ly] (double):
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¶
- cmblensplus.flatsky.rec_src.qtt(nx, ny, D, rL, T1, T2)¶
Reconstructing point source fields from the temperature quadratic estimator
- 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)
- rL[2] (int):
Minimum and maximum multipole of CMB for reconstruction
- fC[lx,ly] (double):
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):
- cmblensplus.flatsky.rec_src.qte(nx, ny, D, rL, T, E)¶
Reconstructing point source fields from the suboptimal TE quadratic estimator
- 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)
- rL[2] (int):
Minimum and maximum multipole of CMB for reconstruction
- fC[lx,ly] (double):
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):
- cmblensplus.flatsky.rec_src.qtb(nx, ny, D, rL, T, B)¶
Reconstructing point source fields from the TB quadratic estimator
- 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)
- rL[2] (int):
Minimum and maximum multipole of CMB for reconstruction
- fC[lx,ly] (double):
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):
- cmblensplus.flatsky.rec_src.qee(nx, ny, D, rL, E1, E2)¶
Reconstructing point source fields from the EE quadratic estimator
- 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)
- rL[2] (int):
Minimum and maximum multipole of CMB for reconstruction
- fC[lx,ly] (double):
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):
- cmblensplus.flatsky.rec_src.qeb(nx, ny, D, rL, E, B)¶
Reconstructing point source fields from the EB quadratic estimator
- 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)
- rL[2] (int):
Minimum and maximum multipole of CMB for reconstruction
- fC[lx,ly] (double):
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¶
- cmblensplus.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:
- 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
- OT[lx,ly] (double):
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):
- cmblensplus.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:
- 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
- OT[lx,ly] (double):
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):
- cmblensplus.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:
- 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
- OT[lx,ly] (double):
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):
- cmblensplus.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:
- 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
- OE[lx,ly] (double):
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):
- cmblensplus.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:
- 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
- OE[lx,ly] (double):
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¶
- cmblensplus.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:
- 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
- IE[lx,ly] (double):
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¶
- cmblensplus.flatsky.norm_tau.qtt(nx, ny, D, rL, OT, TT, eL)¶
Normalization of the temperature quadratic estimator for patchy tau
- 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)
- rL[2] (int):
Minimum and maximum multipole of CMB for reconstruction
- OT[lx,ly] (double):
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):
- cmblensplus.flatsky.norm_tau.qeb(nx, ny, D, rL, IE, IB, EE, eL)¶
Normalization of the EB quadratic estimator for patchy tau
- 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)
- rL[2] (int):
Minimum and maximum multipole of CMB for reconstruction
- IE[lx,ly] (double):
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¶
- cmblensplus.flatsky.bispec.bispec_norm(nx, ny, D, bp, dbin_max=-1, bn=1)¶
- Usage:
- norm = flatsky.bispec.bispec_norm(nx,ny,D,bp,dbin_max,bn):
- cmblensplus.flatsky.bispec.bispec_bin(kmap, bp, kn=1, bn=1, nx=0, ny=0, dbin_max=-1)¶
- Usage:
- bispec = flatsky.bispec.bispec_bin(kn,bn,nx,ny,kmap,bp,dbin_max):
- cmblensplus.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:
- 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)
- bp[bn+1] (double):
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):
- cmblensplus.flatsky.bispec.bispec_norm_1d(nx, ny, D, bfs, bn=1)¶
Normalization of the 1D binned bispectrum estimator
- Args:
- 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)
- bfs[3,bn,nx,ny] (double):
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):
- cmblensplus.flatsky.bispec.bispec_bin_1d(nx, ny, D, bfs, bnorm, alm, bn=1)¶
1D binned bispectrum estimator
- Args:
- 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)
- bfs[3,bn,nx,ny] (double):
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¶
- cmblensplus.flatsky.utils.map2alm(nx, ny, D, map)¶
DFT for 2D array.
- Args:
- nx, ny (int):
Number of x and y grids
- D[2] (double):
Side length (x and y) of map
- map[x,y] (double):
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):
- cmblensplus.flatsky.utils.alm2map(nx, ny, D, alm)¶
DFT for 2D array.
- Args:
- nx, ny (int):
Number of Lx and Ly grids
- D[2] (double):
Side length (x and y) of map
- alm[x,y] (dcmplx):
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):
- cmblensplus.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, (Lx**2+Ly**2)**0.5, with bounds (nx,ny)
- Usage:
- els = flatsky.utils.el2d(nx,ny,D):
- cmblensplus.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, (Lx**2+Ly**2)**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):
- cmblensplus.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):
- Returns:
- lmask[nx,ny] (double):
Mask, with bounds (nx,ny)
- Usage:
- lmask = flatsky.utils.elmask(nx,ny,D,lmin,lmax,lxcut,lycut):
- cmblensplus.flatsky.utils.alm2bcl(bn, oL, nx, ny, D, alm1, alm2=None, spc='')¶
Compute angular power spectrum from Fourier modes, with multipole binning
- Args:
- 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)
- alm1[nx,ny] (dcmplx):
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):
- cmblensplus.flatsky.utils.c2d2bcl(nx, ny, D, c2d, bn, oL, spc='')¶
Return 1D angular power spectrum with multipole binning from a 2D power 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)
- c2d[nx,ny] (double):
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):
- cmblensplus.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):
- cmblensplus.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:
- bn (int):
number of multipole bins
- bc[bin] (double):
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):
- cmblensplus.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):
- cmblensplus.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):
- cmblensplus.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):
- cmblensplus.flatsky.utils.window_norm(nx, ny, wind, num)¶
- Usage:
- wn = flatsky.utils.window_norm(nx,ny,wind,num):
- cmblensplus.flatsky.utils.window_norm_x(nx, ny, W1, W2, num)¶
- Usage:
- Wn = flatsky.utils.window_norm_x(nx,ny,W1,W2,num):
- cmblensplus.flatsky.utils.rotation(nx, ny, rot, QU, rtype)¶
- Usage:
- rQU = flatsky.utils.rotation(nx,ny,rot,QU,rtype):
- cmblensplus.flatsky.utils.get_angle(nx, ny, D)¶
- Usage:
- theta,phi = flatsky.utils.get_angle(nx,ny,D):
- cmblensplus.flatsky.utils.cutmap(ox, oy, cx, cy, omap)¶
- Usage:
- cmap = flatsky.utils.cutmap(ox,oy,cx,cy,omap):