micmac.likelihood.harmonic module

class HarmonicMicmacSampler(nside, lmax, nstokes, frequency_array, freq_noise_c_ell, pos_special_freqs=[0, -1], n_components=3, lmin=2, n_iter=8, mask=None, spv_nodes_b=[], biased_version=False, boundary_Bf=None, boundary_r=None, step_size_r=0.0001, covariance_Bf=None, indexes_free_Bf=False, number_iterations_sampling=100, number_iterations_done=0, seed=0, disable_chex=True, instrument_name='SO_SAT')

Bases: SamplingFunctions

Main MICMAC Harmonic sampling object to initialize and launch the Metropolis-Hastings (MH) sampling in harmonic domain. The MH sampling will store Bf and r parameters.

Parameters:

nside : int

nside of the input frequency maps

lmax : int

maximum multipole for the spherical harmonics transforms and harmonic domain objects,

nstokes : int

number of Stokes parameters

frequency_array : array[float]

array of frequencies, in GHz

freq_noise_c_ell : array[float] of dimensions [frequencies, frequencies, lmax+1-lmin] or [frequencies, frequencies, lmax] (in which case it will be cut to lmax+1-lmin)

optional, noise power spectra for each frequency, in uK^2, dimensions

pos_special_freqs : list[int] (optional)

indexes of the special frequencies in the frequency array respectively for synchrotron and dust, default is [0,-1] for first and last frequencies

n_components : int (optional)

number of components for the mixing matrix, default 3

lmin : int (optional)

minimum multipole for the spherical harmonics transforms and harmonic domain objects, default 2

n_iter : int (optional)

number of iterations the spherical harmonics transforms (for map2alm transformations), default 8

mask : None or array[float] of dimensions [n_pix] (optional)

mask to use in the sampling ; if not given, no mask is used, default None Note: the mask WILL NOT be applied to the input maps, it will be only used for the propagated noise covariance WARNING: Masked input are not currently supported, expect E-to-B leakage

spv_nodes_b : list[dictionaries] (optional)

tree for the spatial variability, to generate from a yaml file, default [] in principle set up by get_nodes_b WARNING: The spatial variability is not currently supported, but will be passed to MicmacSampler obj when using create_Harmonic_MicmacSampler_from_MicmacSampler_obj

biased_version : bool (optional)

use the biased version of the likelihood, so no computation of the correction term, default False

boundary_Bf : None or array[float] (optional)

minimum and maximum Bf values accepted for Bf sample, set to [-inf,inf] for each Bf parameter if None, default None

boundary_r : None or array[float] (optional)

minimum and maximum r values accepted for r sample, set to [-inf,inf] if None, default None

step_size_r : float (optional)

step size for the Metropolis-Hastings sampling of r, default 1e-4

covariance_Bf : None or array[float] of dimensions [(n_frequencies-len(pos_special_freqs))*(n_components-1), (n_frequencies-len(pos_special_freqs))*(n_components-1)] (optional)

covariance for the Metropolis-Hastings sampling of Bf ; will be repeated if multiresoltion case, default None

number_iterations_sampling : int (optional)

maximum number of iterations for the sampling, default 100

number_iterations_done : int (optional)

number of iterations already accomplished, in case the chain is resuming from a previous run, usually set by exterior routines, default 0

seed : int or array[jnp.uint32] (optional)

seed for the JAX PRNG random number generator to start the chain or array of a previously computed seed, default 0

disable_chex : bool (optional)

disable chex tests (to improve speed)

instrument_name : str (optional)

name of the instrument as expected by cmbdb or given as ‘customized_instrument’ if redefined by user, default ‘SO_SAT’ see https://github.com/dpole/cmbdb/blob/master/cmbdb/experiments.yaml

__init__(nside, lmax, nstokes, frequency_array, freq_noise_c_ell, pos_special_freqs=[0, -1], n_components=3, lmin=2, n_iter=8, mask=None, spv_nodes_b=[], biased_version=False, boundary_Bf=None, boundary_r=None, step_size_r=0.0001, covariance_Bf=None, indexes_free_Bf=False, number_iterations_sampling=100, number_iterations_done=0, seed=0, disable_chex=True, instrument_name='SO_SAT')

Main MICMAC Harmonic sampling object to initialize and launch the Metropolis-Hastings (MH) sampling in harmonic domain. The MH sampling will store Bf and r parameters.

Parameters:

nside : int

nside of the input frequency maps

lmax : int

maximum multipole for the spherical harmonics transforms and harmonic domain objects,

nstokes : int

number of Stokes parameters

frequency_array : array[float]

array of frequencies, in GHz

freq_noise_c_ell : array[float] of dimensions [frequencies, frequencies, lmax+1-lmin] or [frequencies, frequencies, lmax] (in which case it will be cut to lmax+1-lmin)

optional, noise power spectra for each frequency, in uK^2, dimensions

pos_special_freqs : list[int] (optional)

indexes of the special frequencies in the frequency array respectively for synchrotron and dust, default is [0,-1] for first and last frequencies

n_components : int (optional)

number of components for the mixing matrix, default 3

lmin : int (optional)

minimum multipole for the spherical harmonics transforms and harmonic domain objects, default 2

n_iter : int (optional)

number of iterations the spherical harmonics transforms (for map2alm transformations), default 8

mask : None or array[float] of dimensions [n_pix] (optional)

mask to use in the sampling ; if not given, no mask is used, default None Note: the mask WILL NOT be applied to the input maps, it will be only used for the propagated noise covariance WARNING: Masked input are not currently supported, expect E-to-B leakage

spv_nodes_b : list[dictionaries] (optional)

tree for the spatial variability, to generate from a yaml file, default [] in principle set up by get_nodes_b WARNING: The spatial variability is not currently supported, but will be passed to MicmacSampler obj when using create_Harmonic_MicmacSampler_from_MicmacSampler_obj

biased_version : bool (optional)

use the biased version of the likelihood, so no computation of the correction term, default False

boundary_Bf : None or array[float] (optional)

minimum and maximum Bf values accepted for Bf sample, set to [-inf,inf] for each Bf parameter if None, default None

boundary_r : None or array[float] (optional)

minimum and maximum r values accepted for r sample, set to [-inf,inf] if None, default None

step_size_r : float (optional)

step size for the Metropolis-Hastings sampling of r, default 1e-4

covariance_Bf : None or array[float] of dimensions [(n_frequencies-len(pos_special_freqs))*(n_components-1), (n_frequencies-len(pos_special_freqs))*(n_components-1)] (optional)

covariance for the Metropolis-Hastings sampling of Bf ; will be repeated if multiresoltion case, default None

number_iterations_sampling : int (optional)

maximum number of iterations for the sampling, default 100

number_iterations_done : int (optional)

number of iterations already accomplished, in case the chain is resuming from a previous run, usually set by exterior routines, default 0

seed : int or array[jnp.uint32] (optional)

seed for the JAX PRNG random number generator to start the chain or array of a previously computed seed, default 0

disable_chex : bool (optional)

disable chex tests (to improve speed)

instrument_name : str (optional)

name of the instrument as expected by cmbdb or given as ‘customized_instrument’ if redefined by user, default ‘SO_SAT’ see https://github.com/dpole/cmbdb/blob/master/cmbdb/experiments.yaml

compute_covariance_from_samples()

Compute the covariance matrix from the sample chains of Bf and r

Returns:

covariance_Bf_r – covariance matrix of the samples of Bf and r

Return type:

array[float]

generate_CMB(return_spectra=True)

Returns CMB spectra of scalar modes only and tensor modes only (with r=1) Both CMB spectra are either returned in the usual form [number_correlations,lmax+1], or in the red_cov form if return_spectra == False

generate_input_freq_maps_from_fgs(freq_maps_fgs, r_true=0, return_only_freq_maps=True, return_only_maps=False)

Generate input frequency maps (CMB+foregrounds) from the input frequency foregrounds maps, return either the full frequency maps, the full frequency and CMB maps alone, or the full frequency and CMB maps with the theoretical reduced covariance matrices for the CMB scalar and tensor modes

Parameters:

freq_maps_fgs : array[float] of dimensions [n_frequencies,nstokes,n_pix]

input frequency foregrounds maps

return_only_freq_maps : bool (optional)

return only the full frequency maps, bool

return_only_maps : bool (optional)

return only the full frequency and CMB maps alone, bool

Returns:

• input_freq_maps (array[float] of dimensions [n_frequencies,nstokes,n_pix]) – input frequency maps

• input_cmb_maps (array[float] of dimensions [nstokes,n_pix]) – input CMB maps

• theoretical_red_cov_r0_total (array[float] of dimensions [lmax+1-lmin,nstokes,nstokes]) – theoretical reduced covariance matrix for the CMB scalar modes

• theoretical_red_cov_r1_tensor (array[float] of dimensions [lmax+1-lmin,nstokes,nstokes]) – theoretical reduced covariance matrix for the CMB tensor modes

get_alm_from_frequency_maps(input_freq_maps)

Get the alms from the input frequency maps using JAX

Parameters:

input_freq_maps : array[float] of dimensions [n_frequencies,nstokes,n_pix]

input frequency maps

Returns:

freq_alms_input_maps – alms from the input frequency maps the (lmax+1)*(lmax+2)//2 dimension is the flattened number of lm coefficients stored according to the Healpy convention

Return type:

array[float] of dimensions [n_frequencies,nstokes,(lmax+1)*(lmax+2)//2]

perform_harmonic_MH(input_freq_maps, c_ell_approx, init_params_mixing_matrix, theoretical_r0_total, theoretical_r1_tensor, initial_guess_r=0, covariance_Bf_r=None, input_freq_alms=None, print_bool=True)

Perform Metropolis Hastings to find the best r and Bf in harmonic domain. The chains will be stored as object attributes:

• all_samples_r for r

• all_params_mixing_matrix_samples for Bf

Parameters:

input_freq_maps : array[float] of dimensions [n_frequencies,nstokes,n_pix]

input frequency maps

c_ell_approx : array[float] of dimensions [number_correlations, lmax+1]

approximate CMB power spectra for the correction term

init_params_mixing_matrix : array[float] of dimensions [n_frequencies-len(pos_special_freqs), n_correlations-1]

initial parameters for the mixing matrix

theoretical_r0_total : array[float] of dimensions [lmax+1-lmin, number_correlations, number_correlations]

theoretical covariance matrix for the CMB scalar modes

theoretical_r1_tensor : array[float] of dimensions [lmax+1-lmin, number_correlations, number_correlations]

theoretical covariance matrix for the CMB tensor modes

initial_guess_r : float (optional)

initial guess for r, default 0

covariance_Bf_r : None or array[float] of dimensions [(n_frequencies-len(pos_special_freqs))*(n_correlations-1) + 1, (n_frequencies-len(pos_special_freqs))*(n_correlations-1) + 1] (optional)

covariance for the Metropolis-Hastings sampling of Bf and r, default None

input_freq_alms : array[float] of dimensions [n_frequencies,nstokes,(lmax + 1) * (lmax // 2 + 1)] (optional)

if provided, input_freq_alms is used instead of input_freq_maps for the MH steps

print_bool : bool (optional)

option for test prints, default True

perform_harmonic_minimize(input_freq_maps, c_ell_approx, init_params_mixing_matrix, theoretical_r0_total, theoretical_r1_tensor, initial_guess_r=0, method_used='ScipyMinimize', **options_minimizer)

Perform a minimization to find the best r and Bf in harmonic domain. The results will be returned as the best parameters found.

Parameters:

input_freq_maps : array[float] of dimensions [n_frequencies,nstokes,n_pix]

input frequency maps

c_ell_approx : array[float] of dimensions [number_correlations, lmax+1]

approximate CMB power spectra for the correction term

init_params_mixing_matrix : array[float] of dimensions [n_frequencies-len(pos_special_freqs), n_correlations-1]

initial parameters for the mixing matrix

theoretical_r0_total : array[float] of dimensions [lmax+1-lmin, number_correlations, number_correlations]

theoretical covariance matrix for the CMB scalar modes

theoretical_r1_tensor : array[float] of dimensions [lmax+1-lmin, number_correlations, number_correlations]

theoretical covariance matrix for the CMB tensor modes

initial_guess_r : float (optional)

initial guess for r, default 0

method_used : str (optional)

method used for the minimization, default ‘ScipyMinimize’

options_minimizer : dict (optional)

additional options dictionary for the minimizer

Returns:

params – best parameters found

Return type:

array[float] of dimensions [n_frequencies-len(pos_special_freqs)*(n_correlations-1) + 1]

update_samples_MH(all_samples)

Update the samples with new samples to add for r and Bf

Parameters:

all_samples : dictionary

dictionary of all the samples to update

update_variable(all_samples, new_samples_to_add)

Update the samples with new samples to add by stacking them

Parameters:

all_samples : array[float] of dimensions [n_samples,n_pix]

previous samples to update

new_samples_to_add : array[float] of dimensions [n_samples,n_pix]

new samples to add

Returns:

all_samples – updated samples

Return type:

array[float] of dimensions [n_samples+n_samples,n_pix]