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, cov_mode='diagonal')[source]

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

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, cov_mode='diagonal')[source]
cov_mode controls how the data covariance is estimated:

‘diagonal’ – per-bin variance from sims (default, always safe). ‘block_diag’ – one (n_bins × n_bins) block per (i,j) map pair,

each block Hartlap-corrected. Needs N_sims >> n_bins (not N_sims >> n_data). Recommended when you want ell-ell correlations without full-matrix instability.

‘shrinkage’ – full (n_data × n_data) covariance shrunk toward the

identity via OAS. Well-conditioned at any N_sims.

‘full’ – raw sample covariance + Hartlap correction.

Requires N_sims > n_data + 2; raises ValueError otherwise.

Parameters:
Return type:

None

abstract theory(theta)[source]

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)[source]

Calculate log prior probability for given parameters.

Parameters:

theta (numpy.ndarray) – Parameter vector

Returns:

Log prior probability

Return type:

float

__all_spectra__(num_sims=100)[source]

Get all spectra data matrix for current ell ranges.

Returns:

Data matrix array with shape (n_tags, n_tags, n_bins)

Parameters:

num_sims (int)

Return type:

numpy.ndarray

chisq(theta)[source]

Calculate chi-squared statistic for given parameters.

When use_full_cov=True uses the full inverse covariance matrix; otherwise uses diagonal (per-bin) variances.

Parameters:

theta (numpy.ndarray)

Return type:

float

ln_likelihood(theta)[source]

Calculate log likelihood for given parameters.

Parameters:

theta (numpy.ndarray)

Return type:

float

ln_prob(theta)[source]

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, burnin=200, thin=20)[source]

Run (or extend/resume) MCMC using an emcee HDF5 backend.

The backend file grows as you call run_mcmc with larger nsamples — no samples are ever discarded from disk. burnin and thin only affect what is returned; you can change them freely without re-running.

Parameters:

  • nwalkers (int) – Number of walkers.

  • nsamples (int) – Target total number of steps stored in the backend. If the backend already has >= nsamples steps, the chain is returned immediately. If it has fewer, only the remaining steps are run (extending the existing chain).

  • rerun (bool) – If True, wipe the backend and start from scratch.

  • fiducial_params (numpy.ndarray | None) – Starting point for walkers (required on first run; ignored when resuming an existing chain).

  • fname (str | None) – Override the auto-generated backend path (.h5 file).

  • burnin (int) – Steps to discard from the front when returning the chain.

  • thin (int) – Thinning factor applied when returning the chain.

Return type:

numpy.ndarray

getdist_samples(nwalkers, nsamples, rerun=False, fiducial_params=None, label=None, burnin=200, thin=20)[source]
Parameters:
Return type:

getdist.MCSamples

plot_posteriors(nwalkers, nsamples, rerun=False, label=None, fiducial_params=None, burnin=200, thin=20)[source]
Parameters:
plot_spectra_matrix(theta=None, save_path=None, average_split=False)[source]

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)[source]
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, cov_mode='diagonal')[source]

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:
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, cov_mode='diagonal')[source]

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’)

  • num_sims (int) – Number of simulations for mean/std calculation

  • verbose (bool) – Whether to enable verbose output

  • cov_mode (str) – Covariance mode (‘diagonal’, ‘block_diag’, ‘shrinkage’, ‘full’)

Return type:

None

theory(theta)[source]

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

Optionally adds a dust foreground power law: A_dust * (ell/80)^alpha_dust

Parameters:

theta (numpy.ndarray)

Return type:

numpy.ndarray

lnprior(theta)[source]

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_FGFit(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, cov_mode='diagonal', fg_model='geometric', A_fg_max=2.0)[source]

Bases: BaseSat4LatCross

Calibration model fitting for birefringence angle β with shared per-frequency foreground amplitude parameters.

Fits calibration angles (alphas), the cosmic birefringence angle β, and per-frequency foreground scaling amplitudes (A_fg) using EB cross-spectra. Here frequency means only the band value (e.g. 93, 145), shared across LAT and SAT. Foreground EB templates are computed as full-sky power spectra from the saved dust Q/U maps and then binned with the same binner.

Before initialisation the class verifies that LAT and SAT were simulated with the same dust model; a ValueError is raised otherwise.

Parameters:
cl_len

Lensed CMB power spectra dictionary.

Type:

dict

freq_values

Unique frequency values extracted from map tags (e.g. ['93', '145']).

Type:

List[str]

fg_templates_binned

Binned foreground EB templates, shape (n_freq_values, n_freq_values, n_bins).

Type:

np.ndarray

__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, cov_mode='diagonal', fg_model='geometric', A_fg_max=2.0)[source]

Initialise calibration analysis with foreground amplitude fitting.

Parameters:

  • spec_cross (SpectraCross) – Cross-spectrum calculation object.

  • sat_err (float) – Satellite calibration angle prior width (degrees).

  • beta_fid (float) – Fiducial birefringence angle used to build the CMB template.

  • 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) – Fit one alpha per split-map (True) or per frequency (False).

  • spectra_selection (str) – Which spectra to include: 'all', 'auto_only', or 'cross_only'.

  • num_sims (int) – Number of simulations used for mean/std estimation.

  • verbose (bool) – Enable verbose logging.

  • cov_mode (str) – Covariance mode (‘diagonal’, ‘block_diag’, ‘shrinkage’, ‘full’).

  • fg_model (str) – Foreground amplitude parametrisation. 'geometric': one amplitude per frequency; cross-frequency scaling via geometric mean sqrt(A_i * A_j). 'per_pair': one independent amplitude per unique (freq_i, freq_j) pair — more robust, no factorizability assumption.

  • A_fg_max (float) – Hard upper bound (in absolute value) for all A_fg parameters. Flat prior on (-A_fg_max, A_fg_max).

Raises:

ValueError – If LAT and SAT use different dust foreground models.

Return type:

None

theory(theta)[source]

Theoretical EB model including miscalibration, birefringence, and foregrounds.

\[C_\ell^{E_i B_j} = \cos(2\alpha_i+2\beta)\sin(2\alpha_j+2\beta)\,C_{EE} - \sin(2\alpha_i+2\beta)\cos(2\alpha_j+2\beta)\,C_{BB} + \sqrt{A_{fg,i}A_{fg,j}}\,C_\ell^{fg,\,E_i B_j}\]

Parameters are ordered as: [alphas..., beta, A_fg_per_frequency...].

Parameters:

theta (numpy.ndarray)

Return type:

numpy.ndarray

lnprior(theta)[source]

Log prior probability.

  • Gaussian prior on SAT alpha angles (width = sat_err).

  • Flat prior on beta in (-0.5, 0.5) degrees.

  • Flat prior on each A_fg in (-A_fg_max, A_fg_max). For fg_model='geometric' A_fg is clipped to [0, A_fg_max] because the geometric mean requires non-negative values.

  • Hard bounds |alpha| < 0.5 degrees for all angles.

Parameters:

theta (numpy.ndarray)

Return type:

float

property dof: int

data points minus number of fitted parameters.

Type:

Degrees of freedom

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, cov_mode='diagonal')[source]

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:
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, cov_mode='diagonal')[source]

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

  • num_sims (int) – Number of simulations for mean/std calculation

  • verbose (bool) – Whether to enable verbose output

  • cov_mode (str) – Covariance mode (‘diagonal’, ‘block_diag’, ‘shrinkage’, ‘full’)

Return type:

None

theory(theta)[source]

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)[source]

Calculate log prior probability for given parameters.

Parameters:

theta (numpy.ndarray) – Parameter vector

Returns:

Log prior probability

Return type:

float

class LatCross(spec_cross, lat_err, beta_fid, lat_lrange=(None, None), fit_per_split=True, spectra_selection='all', num_sims=100, verbose=False, cov_mode='diagonal')[source]

Bases: BaseSat4LatCross

Calibration model fitting for birefringence angle β using LAT-only data.

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

Parameters:
cl_len

Lensed CMB power spectra dictionary

lat_err

LAT calibration error

__init__(spec_cross, lat_err, beta_fid, lat_lrange=(None, None), fit_per_split=True, spectra_selection='all', num_sims=100, verbose=False, cov_mode='diagonal')[source]

Initialize LAT-only calibration analysis for birefringence angle fitting.

Parameters:

  • spec_cross (SpectraCross) – Cross-spectrum calculation object (must be in LAT-only mode)

  • lat_err (float) – LAT calibration error

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

  • 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’)

  • num_sims (int) – Number of simulations for mean/std calculation

  • verbose (bool) – Whether to enable verbose output

  • cov_mode (str) – Covariance mode (‘diagonal’, ‘block_diag’, ‘shrinkage’, ‘full’)

Return type:

None

theory(theta)[source]

Compute theoretical EB spectra between all LAT 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)[source]

Calculate log prior for LAT-only analysis. Uses Gaussian prior on all alphas with LAT calibration error.

Parameters:

theta (numpy.ndarray)

Return type:

float

property dof: int

Calculate degrees of freedom for chi-squared analysis.

Returns:

Number of data points minus number of fitted parameters

Helper Functions

_format_alpha_label(tag)[source]

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, cov_mode='diagonal')[source]

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

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, cov_mode='diagonal')[source]
cov_mode controls how the data covariance is estimated:

‘diagonal’ – per-bin variance from sims (default, always safe). ‘block_diag’ – one (n_bins × n_bins) block per (i,j) map pair,

each block Hartlap-corrected. Needs N_sims >> n_bins (not N_sims >> n_data). Recommended when you want ell-ell correlations without full-matrix instability.

‘shrinkage’ – full (n_data × n_data) covariance shrunk toward the

identity via OAS. Well-conditioned at any N_sims.

‘full’ – raw sample covariance + Hartlap correction.

Requires N_sims > n_data + 2; raises ValueError otherwise.

Parameters:
Return type:

None

abstract theory(theta)[source]

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)[source]

Calculate log prior probability for given parameters.

Parameters:

theta (numpy.ndarray) – Parameter vector

Returns:

Log prior probability

Return type:

float

_build_likelihood_mask()[source]

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

__all_spectra__(num_sims=100)[source]

Get all spectra data matrix for current ell ranges.

Returns:

Data matrix array with shape (n_tags, n_tags, n_bins)

Parameters:

num_sims (int)

Return type:

numpy.ndarray

_calc_mean_std(num_sims=100)[source]

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()[source]

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

_calc_covariance(num_sims=100)[source]

Estimate and cache the data covariance under the likelihood mask.

The mode is controlled by self.cov_mode:

  • 'block_diag': independent (n_bins × n_bins) blocks per (i,j) map pair, each Hartlap-corrected. Only needs N_sims >> n_bins_per_pair.

  • 'shrinkage': full covariance regularised by OAS shrinkage toward the scaled identity. Well-conditioned for any N_sims.

  • 'full': raw sample covariance + Hartlap. Raises ValueError when N_sims ≤ n_data + 2.

Return type:

(cov, cov_inv, logdet_cov)

Parameters:

num_sims (int)

chisq(theta)[source]

Calculate chi-squared statistic for given parameters.

When use_full_cov=True uses the full inverse covariance matrix; otherwise uses diagonal (per-bin) variances.

Parameters:

theta (numpy.ndarray)

Return type:

float

ln_likelihood(theta)[source]

Calculate log likelihood for given parameters.

Parameters:

theta (numpy.ndarray)

Return type:

float

ln_prob(theta)[source]

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, burnin=200, thin=20)[source]

Run (or extend/resume) MCMC using an emcee HDF5 backend.

The backend file grows as you call run_mcmc with larger nsamples — no samples are ever discarded from disk. burnin and thin only affect what is returned; you can change them freely without re-running.

Parameters:

  • nwalkers (int) – Number of walkers.

  • nsamples (int) – Target total number of steps stored in the backend. If the backend already has >= nsamples steps, the chain is returned immediately. If it has fewer, only the remaining steps are run (extending the existing chain).

  • rerun (bool) – If True, wipe the backend and start from scratch.

  • fiducial_params (numpy.ndarray | None) – Starting point for walkers (required on first run; ignored when resuming an existing chain).

  • fname (str | None) – Override the auto-generated backend path (.h5 file).

  • burnin (int) – Steps to discard from the front when returning the chain.

  • thin (int) – Thinning factor applied when returning the chain.

Return type:

numpy.ndarray

getdist_samples(nwalkers, nsamples, rerun=False, fiducial_params=None, label=None, burnin=200, thin=20)[source]
Parameters:
Return type:

getdist.MCSamples

plot_posteriors(nwalkers, nsamples, rerun=False, label=None, fiducial_params=None, burnin=200, thin=20)[source]
Parameters:
plot_spectra_matrix(theta=None, save_path=None, average_split=False)[source]

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)[source]
_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, cov_mode='diagonal')[source]

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:
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, cov_mode='diagonal')[source]

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’)

  • num_sims (int) – Number of simulations for mean/std calculation

  • verbose (bool) – Whether to enable verbose output

  • cov_mode (str) – Covariance mode (‘diagonal’, ‘block_diag’, ‘shrinkage’, ‘full’)

Return type:

None

theory(theta)[source]

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

Optionally adds a dust foreground power law: A_dust * (ell/80)^alpha_dust

Parameters:

theta (numpy.ndarray)

Return type:

numpy.ndarray

lnprior(theta)[source]

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, cov_mode='diagonal')[source]

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:
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, cov_mode='diagonal')[source]

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

  • num_sims (int) – Number of simulations for mean/std calculation

  • verbose (bool) – Whether to enable verbose output

  • cov_mode (str) – Covariance mode (‘diagonal’, ‘block_diag’, ‘shrinkage’, ‘full’)

Return type:

None

theory(theta)[source]

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)[source]

Calculate log prior probability for given parameters.

Parameters:

theta (numpy.ndarray) – Parameter vector

Returns:

Log prior probability

Return type:

float