Calibration Module

Calibration analysis module for LAT-SAT cross-spectrum studies.

This module provides classes for fitting calibration parameters (angles and amplitudes) using cross-correlations between Large Aperture Telescope (LAT) and Small Aperture Telescope (SAT) data from CMB observations.

class BaseSat4LatCross(spec_cross, sat_err, sat_lrange=(None, None), lat_lrange=(None, None), fit_per_split=True, spectra_selection='all', libdir_suffix='BaseSat4LatCross', num_sims=100, verbose=False)

Bases: ABC

Base class for LAT-SAT cross-spectrum calibration analyses.

Provides data loading, beam handling, and plotting logic. Subclasses must define:

• self.__pnames__ / self.__plabels__

• self.theory(theta)

• self.lnprior(theta)

Parameters:

• spec_cross (SpectraCross)

• sat_err (float)

• sat_lrange (Tuple[int | None, int | None])

• lat_lrange (Tuple[int | None, int | None])

• fit_per_split (bool)

• spectra_selection (str)

• libdir_suffix (str)

• num_sims (int)

• verbose (bool)

spec_cross

Cross-spectrum calculation object

sat_err

Satellite calibration error

sat_lrange

Satellite ell range for fitting

lat_lrange

LAT ell range for fitting

fit_per_split

Whether to fit per split or per frequency

spectra_selection

Which spectra to include (‘all’, ‘auto_only’, ‘cross_only’)

libdir

Directory for caching results

binner

Binning information object

Lmax

Maximum multipole

maptags

List of map tags

freq_groups

Dictionary mapping frequency bases to indices

freq_bases

List of frequency base names

mean_spec

Mean spectra from simulations

std_spec

Standard deviation of spectra

beam_arr

Beam transfer function array

__init__(spec_cross, sat_err, sat_lrange=(None, None), lat_lrange=(None, None), fit_per_split=True, spectra_selection='all', libdir_suffix='BaseSat4LatCross', num_sims=100, verbose=False)

Parameters:

• spec_cross (SpectraCross)

• sat_err (float)

• sat_lrange (Tuple[int | None, int | None])

• lat_lrange (Tuple[int | None, int | None])

• fit_per_split (bool)

• spectra_selection (str)

• libdir_suffix (str)

• num_sims (int)

• verbose (bool)

Return type:

None

abstract theory(theta)

Calculate theoretical model spectrum for given parameters.

Parameters:

theta (numpy.ndarray) – Parameter vector

Returns:

Model spectrum array with shape matching data

Return type:

numpy.ndarray

abstract lnprior(theta)

Calculate log prior probability for given parameters.

Parameters:

theta (numpy.ndarray) – Parameter vector

Returns:

Log prior probability

Return type:

float

chisq(theta)

Calculate chi-squared statistic for given parameters.

Parameters:

theta (numpy.ndarray) – Parameter vector

Returns:

Chi-squared value

Return type:

float

ln_likelihood(theta)

Calculate log likelihood for given parameters.

Parameters:

theta (numpy.ndarray)

Return type:

float

ln_prob(theta)

Calculate log posterior probability for given parameters.

Parameters:

theta (numpy.ndarray)

Return type:

float

run_mcmc(nwalkers=32, nsamples=2000, rerun=False, fiducial_params=None, fname=None)

Parameters:

• nwalkers (int)

• nsamples (int)

• rerun (bool)

• fiducial_params (numpy.ndarray | None)

• fname (str | None)

Return type:

numpy.ndarray

getdist_samples(nwalkers, nsamples, rerun=False, fiducial_params=None, label=None)

Parameters:

• nwalkers (int)

• nsamples (int)

• rerun (bool)

• fiducial_params (numpy.ndarray | None)

• label (str | None)

Return type:

getdist.MCSamples

plot_posteriors(nwalkers, nsamples, rerun=False, label=None, fiducial_params=None)

Parameters:

• nwalkers (int)

• nsamples (int)

• rerun (bool)

• label (str | None)

• fiducial_params (numpy.ndarray | None)

plot_spectra_matrix(theta=None, save_path=None, average_split=False)

Plots the mean data spectra with std deviation and optionally a theory curve in a matrix layout corresponding to all cross-correlations.

Parameters:

• theta (numpy.ndarray | None) – Parameter vector (alphas, beta, A_EB, etc.) for theory overlay.

• save_path (str | None) – If given, saves the figure instead of showing.

• average_split (bool) – If True, average spectra across splits per frequency.

Return type:

None

mle(nwalkers, nsamples, op=numpy.median)

class Sat4LatCross(spec_cross, sat_err, beta_fid, sat_lrange=(None, None), lat_lrange=(None, None), fit_per_split=True, spectra_selection='all', num_sims=100, verbose=False)

Bases: BaseSat4LatCross

Calibration model fitting for birefringence angle β.

This class implements a calibration analysis that fits calibration angles (alphas) and the cosmic birefringence angle β using EB cross-spectra between LAT and SAT.

Parameters:

• spec_cross (SpectraCross)

• sat_err (float)

• beta_fid (float)

• sat_lrange (Tuple[int | None, int | None])

• lat_lrange (Tuple[int | None, int | None])

• fit_per_split (bool)

• spectra_selection (str)

• num_sims (int)

• verbose (bool)

cl_len

Lensed CMB power spectra dictionary

__init__(spec_cross, sat_err, beta_fid, sat_lrange=(None, None), lat_lrange=(None, None), fit_per_split=True, spectra_selection='all', num_sims=100, verbose=False)

Initialize calibration analysis for birefringence angle fitting.

Parameters:

• spec_cross (SpectraCross) – Cross-spectrum calculation object

• sat_err (float) – Satellite calibration error

• beta_fid (float) – Fiducial birefringence angle for theory calculation

• sat_lrange (Tuple[int | None, int | None]) – Satellite ell range for fitting (lmin, lmax)

• lat_lrange (Tuple[int | None, int | None]) – LAT ell range for fitting (lmin, lmax)

• fit_per_split (bool) – Whether to fit per split or per frequency

• spectra_selection (str) – Which spectra to include (‘all’, ‘auto_only’, ‘cross_only’)

• verbose (bool) – Whether to enable verbose output

• num_sims (int)

Return type:

None

theory(theta)

Compute theoretical EB spectra between all map pairs using the exact birefringence + miscalibration formula:

C_ell^{E_iB_j} = cos(2α_i+2β)sin(2α_j+2β)C_EE

• sin(2α_i+2β)cos(2α_j+2β)C_BB

Parameters:

theta (numpy.ndarray)

Return type:

numpy.ndarray

lnprior(theta)

Calculate log prior probability for given parameters.

Parameters:

theta (numpy.ndarray) – Parameter vector

Returns:

Log prior probability

Return type:

float

property dof: int

Calculate degrees of freedom for chi-squared analysis.

Returns:

Number of data points minus number of fitted parameters

class Sat4LatCross_AmplitudeFit(spec_cross, sat_err, temp_model, temp_value, sat_lrange=(None, None), lat_lrange=(None, None), fit_per_split=True, spectra_selection='all', sim_idx=None, alpha_lat_prior='gaussian', fix_alpha=False, num_sims=100, verbose=False)

Bases: BaseSat4LatCross

Calibration model fitting for amplitude parameter A_EB.

This class implements a calibration analysis that fits calibration angles (alphas) and an amplitude parameter A_EB using EB cross-spectra between LAT and SAT.

Parameters:

• spec_cross (SpectraCross)

• sat_err (float)

• temp_model (str)

• temp_value (float)

• sat_lrange (Tuple[int | None, int | None])

• lat_lrange (Tuple[int | None, int | None])

• fit_per_split (bool)

• spectra_selection (str)

• sim_idx (int | None)

• alpha_lat_prior (str)

• fix_alpha (bool)

• num_sims (int)

• verbose (bool)

eb_template_unbinned

Unbinned EB template spectrum

binned_template

Binned EB template spectrum

cl_len

Lensed CMB power spectra dictionary

cl_diff_unbinned

Unbinned difference spectrum (EE - BB)/2

__init__(spec_cross, sat_err, temp_model, temp_value, sat_lrange=(None, None), lat_lrange=(None, None), fit_per_split=True, spectra_selection='all', sim_idx=None, alpha_lat_prior='gaussian', fix_alpha=False, num_sims=100, verbose=False)

Initialize calibration analysis for amplitude parameter fitting.

Parameters:

• spec_cross (SpectraCross) – Cross-spectrum calculation object

• sat_err (float) – Satellite calibration error

• temp_model (str) – Template model (‘iso’ or ‘iso_td’)

• temp_value (float) – Template parameter value (beta for ‘iso’, mass for ‘iso_td’)

• sat_lrange (Tuple[int | None, int | None]) – Satellite ell range for fitting (lmin, lmax)

• lat_lrange (Tuple[int | None, int | None]) – LAT ell range for fitting (lmin, lmax)

• fit_per_split (bool) – Whether to fit per split or per frequency

• spectra_selection (str) – Which spectra to include (‘all’, ‘auto_only’, ‘cross_only’)

• sim_idx (int | None) – Simulation index to use for data (default: 0)

• alpha_lat_prior (str) – Prior type for LAT alpha parameters (‘gaussian’ or ‘flat’)

• fix_alpha (bool) – Whether to fix alpha parameters (calibration angles) to zero

• verbose (bool) – Whether to enable verbose output

• num_sims (int)

Return type:

None

theory(theta)

Calculate theoretical model spectrum for given parameters.

Parameters:

theta (numpy.ndarray) – Parameter vector

Returns:

Model spectrum array with shape matching data

Return type:

numpy.ndarray

lnprior(theta)

Calculate log prior probability for given parameters.

Parameters:

theta (numpy.ndarray) – Parameter vector

Returns:

Log prior probability

Return type:

float

Helper Functions

_format_alpha_label(tag)

Format map tag like ‘LAT_93-1’ -> r’alpha_{LAT,93−1}’.

Parameters:

tag (str) – Map tag string to format

Returns:

Formatted alpha label for LaTeX rendering

Return type:

str

Base Classes

class BaseSat4LatCross(spec_cross, sat_err, sat_lrange=(None, None), lat_lrange=(None, None), fit_per_split=True, spectra_selection='all', libdir_suffix='BaseSat4LatCross', num_sims=100, verbose=False)

Base class for LAT-SAT cross-spectrum calibration analyses.

Provides data loading, beam handling, and plotting logic. Subclasses must define:

• self.__pnames__ / self.__plabels__

• self.theory(theta)

• self.lnprior(theta)

Parameters:

• spec_cross (SpectraCross)

• sat_err (float)

• sat_lrange (Tuple[int | None, int | None])

• lat_lrange (Tuple[int | None, int | None])

• fit_per_split (bool)

• spectra_selection (str)

• libdir_suffix (str)

• num_sims (int)

• verbose (bool)

spec_cross

Cross-spectrum calculation object

sat_err

Satellite calibration error

sat_lrange

Satellite ell range for fitting

lat_lrange

LAT ell range for fitting

fit_per_split

Whether to fit per split or per frequency

spectra_selection

Which spectra to include (‘all’, ‘auto_only’, ‘cross_only’)

libdir

Directory for caching results

binner

Binning information object

Lmax

Maximum multipole

maptags

List of map tags

freq_groups

Dictionary mapping frequency bases to indices

freq_bases

List of frequency base names

mean_spec

Mean spectra from simulations

std_spec

Standard deviation of spectra

beam_arr

Beam transfer function array

__init__(spec_cross, sat_err, sat_lrange=(None, None), lat_lrange=(None, None), fit_per_split=True, spectra_selection='all', libdir_suffix='BaseSat4LatCross', num_sims=100, verbose=False)

Parameters:

• spec_cross (SpectraCross)

• sat_err (float)

• sat_lrange (Tuple[int | None, int | None])

• lat_lrange (Tuple[int | None, int | None])

• fit_per_split (bool)

• spectra_selection (str)

• libdir_suffix (str)

• num_sims (int)

• verbose (bool)

Return type:

None

abstract theory(theta)

Calculate theoretical model spectrum for given parameters.

Parameters:

theta (numpy.ndarray) – Parameter vector

Returns:

Model spectrum array with shape matching data

Return type:

numpy.ndarray

abstract lnprior(theta)

Calculate log prior probability for given parameters.

Parameters:

theta (numpy.ndarray) – Parameter vector

Returns:

Log prior probability

Return type:

float

_build_likelihood_mask()

Build boolean mask for likelihood evaluation based on ell ranges.

Returns:

Boolean mask array with shape (n_tags, n_tags, n_bins)

Return type:

numpy.ndarray

_calc_mean_std(num_sims=100)

Calculate mean and standard deviation of spectra over simulations.

Parameters:

num_sims (int) – Number of simulations to use

Returns:

Tuple of (mean_spectrum, std_spectrum) arrays

Return type:

Tuple[numpy.ndarray, numpy.ndarray]

_get_beam_arr()

Calculate beam transfer function array for all map tag combinations.

Returns:

Beam array with shape (n_tags, n_tags, n_bins)

Return type:

numpy.ndarray

chisq(theta)

Calculate chi-squared statistic for given parameters.

Parameters:

theta (numpy.ndarray) – Parameter vector

Returns:

Chi-squared value

Return type:

float

ln_likelihood(theta)

Calculate log likelihood for given parameters.

Parameters:

theta (numpy.ndarray)

Return type:

float

ln_prob(theta)

Calculate log posterior probability for given parameters.

Parameters:

theta (numpy.ndarray)

Return type:

float

run_mcmc(nwalkers=32, nsamples=2000, rerun=False, fiducial_params=None, fname=None)

Parameters:

• nwalkers (int)

• nsamples (int)

• rerun (bool)

• fiducial_params (numpy.ndarray | None)

• fname (str | None)

Return type:

numpy.ndarray

getdist_samples(nwalkers, nsamples, rerun=False, fiducial_params=None, label=None)

Parameters:

• nwalkers (int)

• nsamples (int)

• rerun (bool)

• fiducial_params (numpy.ndarray | None)

• label (str | None)

Return type:

getdist.MCSamples

plot_posteriors(nwalkers, nsamples, rerun=False, label=None, fiducial_params=None)

Parameters:

• nwalkers (int)

• nsamples (int)

• rerun (bool)

• label (str | None)

• fiducial_params (numpy.ndarray | None)

plot_spectra_matrix(theta=None, save_path=None, average_split=False)

Plots the mean data spectra with std deviation and optionally a theory curve in a matrix layout corresponding to all cross-correlations.

Parameters:

• theta (numpy.ndarray | None) – Parameter vector (alphas, beta, A_EB, etc.) for theory overlay.

• save_path (str | None) – If given, saves the figure instead of showing.

• average_split (bool) – If True, average spectra across splits per frequency.

Return type:

None

mle(nwalkers, nsamples, op=numpy.median)

_abc_impl = <_abc._abc_data object>

Calibration Classes

class Sat4LatCross(spec_cross, sat_err, beta_fid, sat_lrange=(None, None), lat_lrange=(None, None), fit_per_split=True, spectra_selection='all', num_sims=100, verbose=False)

Bases: BaseSat4LatCross

Calibration model fitting for birefringence angle β.

This class implements a calibration analysis that fits calibration angles (alphas) and the cosmic birefringence angle β using EB cross-spectra between LAT and SAT.

Parameters:

• spec_cross (SpectraCross)

• sat_err (float)

• beta_fid (float)

• sat_lrange (Tuple[int | None, int | None])

• lat_lrange (Tuple[int | None, int | None])

• fit_per_split (bool)

• spectra_selection (str)

• num_sims (int)

• verbose (bool)

cl_len

Lensed CMB power spectra dictionary

__init__(spec_cross, sat_err, beta_fid, sat_lrange=(None, None), lat_lrange=(None, None), fit_per_split=True, spectra_selection='all', num_sims=100, verbose=False)

Initialize calibration analysis for birefringence angle fitting.

Parameters:

• spec_cross (SpectraCross) – Cross-spectrum calculation object

• sat_err (float) – Satellite calibration error

• beta_fid (float) – Fiducial birefringence angle for theory calculation

• sat_lrange (Tuple[int | None, int | None]) – Satellite ell range for fitting (lmin, lmax)

• lat_lrange (Tuple[int | None, int | None]) – LAT ell range for fitting (lmin, lmax)

• fit_per_split (bool) – Whether to fit per split or per frequency

• spectra_selection (str) – Which spectra to include (‘all’, ‘auto_only’, ‘cross_only’)

• verbose (bool) – Whether to enable verbose output

• num_sims (int)

Return type:

None

theory(theta)

Compute theoretical EB spectra between all map pairs using the exact birefringence + miscalibration formula:

C_ell^{E_iB_j} = cos(2α_i+2β)sin(2α_j+2β)C_EE

• sin(2α_i+2β)cos(2α_j+2β)C_BB

Parameters:

theta (numpy.ndarray)

Return type:

numpy.ndarray

lnprior(theta)

Calculate log prior probability for given parameters.

Parameters:

theta (numpy.ndarray) – Parameter vector

Returns:

Log prior probability

Return type:

float

property dof: int

Calculate degrees of freedom for chi-squared analysis.

Returns:

Number of data points minus number of fitted parameters

class Sat4LatCross_AmplitudeFit(spec_cross, sat_err, temp_model, temp_value, sat_lrange=(None, None), lat_lrange=(None, None), fit_per_split=True, spectra_selection='all', sim_idx=None, alpha_lat_prior='gaussian', fix_alpha=False, num_sims=100, verbose=False)

Bases: BaseSat4LatCross

Calibration model fitting for amplitude parameter A_EB.

This class implements a calibration analysis that fits calibration angles (alphas) and an amplitude parameter A_EB using EB cross-spectra between LAT and SAT.

Parameters:

• spec_cross (SpectraCross)

• sat_err (float)

• temp_model (str)

• temp_value (float)

• sat_lrange (Tuple[int | None, int | None])

• lat_lrange (Tuple[int | None, int | None])

• fit_per_split (bool)

• spectra_selection (str)

• sim_idx (int | None)

• alpha_lat_prior (str)

• fix_alpha (bool)

• num_sims (int)

• verbose (bool)

eb_template_unbinned

Unbinned EB template spectrum

binned_template

Binned EB template spectrum

cl_len

Lensed CMB power spectra dictionary

cl_diff_unbinned

Unbinned difference spectrum (EE - BB)/2

__init__(spec_cross, sat_err, temp_model, temp_value, sat_lrange=(None, None), lat_lrange=(None, None), fit_per_split=True, spectra_selection='all', sim_idx=None, alpha_lat_prior='gaussian', fix_alpha=False, num_sims=100, verbose=False)

Initialize calibration analysis for amplitude parameter fitting.

Parameters:

• spec_cross (SpectraCross) – Cross-spectrum calculation object

• sat_err (float) – Satellite calibration error

• temp_model (str) – Template model (‘iso’ or ‘iso_td’)

• temp_value (float) – Template parameter value (beta for ‘iso’, mass for ‘iso_td’)

• sat_lrange (Tuple[int | None, int | None]) – Satellite ell range for fitting (lmin, lmax)

• lat_lrange (Tuple[int | None, int | None]) – LAT ell range for fitting (lmin, lmax)

• fit_per_split (bool) – Whether to fit per split or per frequency

• spectra_selection (str) – Which spectra to include (‘all’, ‘auto_only’, ‘cross_only’)

• sim_idx (int | None) – Simulation index to use for data (default: 0)

• alpha_lat_prior (str) – Prior type for LAT alpha parameters (‘gaussian’ or ‘flat’)

• fix_alpha (bool) – Whether to fix alpha parameters (calibration angles) to zero

• verbose (bool) – Whether to enable verbose output

• num_sims (int)

Return type:

None

theory(theta)

Calculate theoretical model spectrum for given parameters.

Parameters:

theta (numpy.ndarray) – Parameter vector

Returns:

Model spectrum array with shape matching data

Return type:

numpy.ndarray

lnprior(theta)

Calculate log prior probability for given parameters.

Parameters:

theta (numpy.ndarray) – Parameter vector

Returns:

Log prior probability

Return type:

float