Source code for comet.PTEmu

"""Main PTEmu module."""

import numpy as np
from scipy.interpolate import UnivariateSpline
from scipy.integrate import quad_vec, quad, dblquad
from scipy.special import eval_legendre
from astropy.io import fits
import pickle
from comet.cosmology import Cosmology
from comet.data import MeasuredData
from comet.tables import Tables
from comet.grid import Grid
from comet.bispectrum import Bispectrum
import os

base_dir = os.path.join(os.path.dirname(__file__))


[docs] class PTEmu: r"""Main class for the emulator of the power spectrum multipoles. The emulator makes use of evolution mapping (`Sanchez 2020 <https://journals.aps.org/prd/abstract/10.1103/PhysRevD.102.123511>`_, `Sanchez et al 2021 <https://arxiv.org/abs/2108.12710>`_,) to compress the information of evolution parameters :math:`\mathbf{\Theta_{e}}` (e.g. :math:`h,\,\Omega_\mathrm{K},\,w_0,\,w_\mathrm{a},\,A_\mathrm{s},\, \ldots`) into the single quantity :math:`\sigma_{12}`, defined as the rms fluctuation of the linear density contrast :math:`\delta` within spheres of radius :math:`R=8\,\mathrm{Mpc}`. This parameter, together with the parameters affecting the shape of the power spectrum :math:`\mathbf{\Theta_{s}}` (e.g. :math:`\omega_\mathrm{b},\,\omega_\mathrm{c},\,n_\mathrm{s}`), and the linear growth rate :math:`f`, are used as base of the emulator. The redshift-dependency of the multipoles can also be treated similarly to the impact that different evolution parameters have on the power spectrum, that is, by a simple rescaling of the amplitude of the power spectrum in order to match the desired value of :math:`\sigma_{12}`. Internally to the emulator, the pair :math:`\left[k,P(k)\right]` is expressed in :math:`\left[\mathrm{Mpc}^{-1},\mathrm{Mpc}^3\right]` units, since this is the only set of units for which the evolution parameter degeneracy is present. If the user wishes to use the more conventional unit set :math:`\left[h\,\mathrm{Mpc}^{-1},h^{-3}\,\mathrm{Mpc}^3\right]`, they can do so by specifying it in the proper class attribute flag. In this case, the input/output are converted into :math:`\mathrm{Mpc}` units before being used/returned. Geometrical distortions (AP corrections) are included a posteriori without the need of including them in the emulation. This process is carried out by first reconstructing the full anisotropic 2d galaxy power spectrum :math:`P_\mathrm{gg}(k,\mu)`, summing up all the even multipoles up to :math:`\ell=6`, applying distortions to :math:`k` and :math:`\mu`, and then projecting again over the Legendre polynomials. """ def __init__(self, model, use_Mpc=True, bias_basis='EggScoSmi', counterterm_basis='Comet'): r"""Class constructor. Parameters ---------- model: str Identifier of the selected model. use_Mpc: bool, optional Flag that determines if the input and output quantities are specified in :math:`\mathrm{Mpc}` (**True**) or :math:`h^{-1}\mathrm{Mpc}` (**False**) units. Defaults to **True**. bias_basis: str, optional Identifier for the bias basis convention, possible choices are "EggScoSmi" (default), "AssBauGre", and "AmiGleKok". counterterm_basis: str, optional Identifier for the counterterm basis convention, possible choices are "Comet" (default) and "ClassPT". """ self.bias_basis = bias_basis self.counterterm_basis = counterterm_basis if self.bias_basis == 'EggScoSmi': self.bias_params_list = ['b1', 'b2', 'g2', 'g21', 'c0', 'c2', 'c4', 'cnlo', 'cnloB', 'NP0', 'NP20', 'NP22', 'NB0', 'MB0', 'cB1', 'cB2'] elif self.bias_basis == 'AssBauGre': self.bias_params_list = ['b1', 'b2', 'bG2', 'bGam3', 'c0', 'c2', 'c4', 'cnlo', 'cnloB', 'NP0', 'NP20', 'NP22', 'NB0', 'MB0', 'cB1', 'cB2'] elif self.bias_basis == 'AmiGleKok': self.bias_params_list = ['b1t', 'b2t', 'b3t', 'b4t', 'c0', 'c2', 'c4', 'cnlo', 'cnloB', 'NP0', 'NP20', 'NP22', 'NB0', 'MB0', 'cB1', 'cB2'] else: print('Warning. Bias basis not recognised, defaulting to ' '"EggScoSmi".') self.bias_basis = 'EggScoSmi' self.bias_params_list = ['b1', 'b2', 'g2', 'g21', 'c0', 'c2', 'c4', 'cnlo', 'cnloB', 'NP0', 'NP20', 'NP22', 'NB0', 'MB0', 'cB1', 'cB2'] self.RSD_params_list = [] self.de_model_params_list = { 'lambda': ['h', 'As', 'Ok', 'z'], 'w0': ['h', 'As', 'Ok', 'w0', 'z'], 'w0wa': ['h', 'As', 'Ok', 'w0', 'wa', 'z']} self.cnloB_type = 'EggLeeSco' self.n_diagrams = 19 self.diagrams_emulated = ['P0L_b1b1', 'PNL_b1', 'PNL_id', 'Pctr_c0', 'Pctr_c2', 'Pctr_c4', 'Pctr_b1b1cnlo', 'Pctr_b1cnlo', 'Pctr_cnlo', 'P1L_b1b1', 'P1L_b1b2', 'P1L_b1g2', 'P1L_b1g21', 'P1L_b2b2', 'P1L_b2g2', 'P1L_g2g2', 'P1L_b2', 'P1L_g2', 'P1L_g21'] self.diagrams_all = ['P0L_b1b1', 'PNL_b1', 'PNL_id', 'Pctr_c0', 'Pctr_c2', 'Pctr_c4', 'Pctr_b1b1cnlo', 'Pctr_b1cnlo', 'Pctr_cnlo', 'P1L_b1b1', 'P1L_b1b2', 'P1L_b1g2', 'P1L_b1g21', 'P1L_b2b2', 'P1L_b2g2', 'P1L_g2g2', 'P1L_b2', 'P1L_g2', 'P1L_g21', 'Pnoise_NP0', 'Pnoise_NP20', 'Pnoise_NP22'] self.use_Mpc = use_Mpc self.nbar = 1.0 # in units of Mpc^3 or (Mpc/h)^3 depending on use_Mpc self.training = {} self.emu = {} self.cosmo = Cosmology(0.3, 67.0) # Initialise with arbitrary values self.Pk_lin = None self.Pk_ratios = {0: None, 2: None, 4: None} self.Pell_spline = {} self.Pell_lowk_extrapolation = {} self.Pell_highk_extrapolation = {} self.Pell_min = {} self.Pell_max = {} self.neff_min = {} self.neff_max = {} self.PX_ell_spline = {X: {} for X in self.diagrams_all} self.PX_ell_min = {X: {} for X in self.diagrams_all} self.PX_ell_max = {X: {} for X in self.diagrams_all} self.X_neff_min = {X: {} for X in self.diagrams_all} self.X_neff_max = {X: {} for X in self.diagrams_all} self.PX_ell_list = {} self.k_table_min = {} self.k_table_max = {} self.gl_x, self.gl_weights = np.polynomial.legendre.leggauss(10) self.gl_x = 0.5 * self.gl_x + 0.5 self.data = {} self.grid = None self.splines_up_to_date = False self.dw_spline_up_to_date = False self.X_splines_up_to_date = {X: False for X in self.diagrams_all} self.X_obs_id = None self.X_binning = None self.Bisp_binning = None self._Bisp_binning_last = {} self._Bisp_tri_has_changed = False self.emu_params_updated = False self.chi2_decomposition = None self.Bisp_chi2_decomposition = None self._load_emulator_data( fname=base_dir+'/data_dir/tables/{}.fits'.format(model)) self._load_emulator( fname_base=base_dir+'/data_dir/models/{}'.format(model))
[docs] def init_params_dict(self): r"""Initialize params dictionary. Sets up the internal class attribute which stores the complete list of model parameters. This includes cosmological parameters as well as biases, noises, counterterms, and other nuisance parameters. """ self.params = {p: 0.0 for p in self.params_list + self.bias_params_list + self.RSD_params_list + self.de_model_params_list['w0wa']} self.params['w0'] = -1.0 self.params['q_tr'] = 1.0 self.params['q_lo'] = 1.0
def _load_emulator_data(self, fname): r"""Load tables of the emulator. Loads a fits file, reads the tables and stores them as class attributes, as instances of the **Tables** class. Additionally sets up the internal dictionary that stores the full list of model parameters, by calling **init_params_dict**. Determine if the emulator is for real- or redshift-space, checking if the growth rate :math:`f` is part of the parameter sample or not. Parameters ---------- fname: str Name of the output fits file to read from. """ hdul = fits.open(fname) self.params_shape_list = ([ hdul['PARAMS_SHAPE'].header['TTYPE{}'.format(n+1)] for n in range(hdul['PARAMS_SHAPE'].header['TFIELDS'])]) self.params_list = ([ hdul['PARAMS_FULL'].header['TTYPE{}'.format(n+1)] for n in range(hdul['PARAMS_FULL'].header['TFIELDS'])]) self.real_space = False if 'f' in self.params_list else True self.emu_LCDM_params = ({ p: hdul['PRIMARY'].header['TRAINING:{}'.format(p)] for p in ['wc', 'wb', 'ns', 'h', 'As', 'z']}) self.params_shape_ranges = {} self.params_ranges = {} for p in self.params_shape_list: min = hdul['PARAMS_SHAPE'].header['MIN:{}'.format(p)] max = hdul['PARAMS_SHAPE'].header['MAX:{}'.format(p)] self.params_shape_ranges[p] = [min, max] for p in self.params_list: min = hdul['PARAMS_FULL'].header['MIN:{}'.format(p)] max = hdul['PARAMS_FULL'].header['MAX:{}'.format(p)] self.params_ranges[p] = [min, max] self.training['SHAPE'] = Tables(self.params_shape_list) self.training['FULL'] = Tables(self.params_list) self.k_table = hdul['K_TABLE'].data['bins'] self.nk = self.k_table.shape[0] self.nkloop = sum(self.k_table > hdul['K_TABLE'].header['k1loop']) self.RSD_model = hdul['MODEL_FULL'].header['RSD_model'] if self.RSD_model == 'VDG_infty': self.RSD_params_list += ['avir','avirB'] self.init_params_dict() if self.RSD_model == 'EFT': self.Bisp_diagrams_all = ['B0L_b1b1b1', 'B0L_b1b1', 'B0L_b1', 'B0L_b1b1b1cnloB', 'B0L_b1b1cnloB', 'B0L_b1cnloB', 'B0L_b1b1b2', 'B0L_b1b2', 'B0L_b2', 'B0L_b1b1b2cnloB', 'B0L_b1b2cnloB', 'B0L_b2cnloB', 'B0L_b1b1g2', 'B0L_b1g2', 'B0L_g2', 'B0L_b1b1g2cnloB', 'B0L_b1g2cnloB', 'B0L_g2cnloB', 'B0L_id', 'B0L_cnloB', 'Bnoise_MB0b1b1', 'Bnoise_MB0b1', 'Bnoise_NP0', 'Bnoise_NB0'] else: self.Bisp_diagrams_all = ['B0L_b1b1b1', 'B0L_b1b1', 'B0L_b1', 'B0L_b1b1b2', 'B0L_b1b2', 'B0L_b2', 'B0L_b1b1g2', 'B0L_b1g2', 'B0L_g2', 'B0L_id', 'Bnoise_MB0b1b1', 'Bnoise_MB0b1', 'Bnoise_NP0', 'Bnoise_NB0'] self.training['SHAPE'].assign_samples(hdul['PARAMS_SHAPE']) self.training['SHAPE'].assign_table(hdul['MODEL_SHAPE'], self.nk, self.nkloop) self.training['FULL'].assign_samples(hdul['PARAMS_FULL']) self.training['FULL'].assign_table(hdul['MODEL_FULL'], self.nk, self.nkloop) if not self.real_space: self.s12_for_P6 = hdul['MODEL_Pell6'].header['SIG12'] self.P6 = hdul['MODEL_Pell6'].data['P_all'] # better compute P6 table for full k-range... nkdiff = self.nk-self.nkloop for i in range(3,25): dly = np.log10( np.abs(self.P6[nkdiff+2,i]/self.P6[nkdiff,i])) dlx = np.log10( np.abs(self.k_table[nkdiff+2]/self.k_table[nkdiff])) neff = dly/dlx self.P6[:nkdiff,i] = self.P6[nkdiff,i] \ * (self.k_table[:nkdiff]/self.k_table[nkdiff])**neff self.Bisp = Bispectrum(self.real_space, self.RSD_model, self.use_Mpc) def _load_emulator(self, fname_base): r"""Load the emulator from pickle file. Loads an emulator object from a file (pickle format) and adds it to the internal dictionary containing the emulators. Parameters ---------- fname_base: str Root name of the input pickle file. data_type: str, optional Type of the table which refers to the input emulator. If **None**, it loads the emulators for all the tables that are stored as class attributes. Defaults to **None**. """ self.emu['shape'] = pickle.load( open('{}_scikit_s12svPL.pickle'.format(fname_base), "rb")) self.emu['ratios'] = pickle.load( open('{}_scikit_ratios.pickle'.format(fname_base), "rb"))
[docs] def define_units(self, use_Mpc): r"""Define units for the power spectrum and number density. Sets the internal class attribute **use_Mpc**, clears all the data objects (if defined), and resets the number density to 1 in the units corresponding to the input flag. The number density value can be subsequently explicitly changed calling **define_nbar**. Parameters ---------- use_Mpc: bool Flag that determines if the input and output quantities are specified in :math:`\mathrm{Mpc}` (**True**) or :math:`h^{-1}\,\mathrm{Mpc}` (**False**) units. """ if use_Mpc != self.use_Mpc: self.use_Mpc = use_Mpc self.nbar = 1.0 # units of Mpc^3 or (Mpc/h)^3 depending on use_Mpc for obs_id in self.data.keys(): self.data[obs_id].clear_data() self.splines_up_to_date = False self.dw_spline_up_to_date = False self.Bisp.define_units(self.use_Mpc) self.Bisp.define_nbar(self.nbar) nbar_unit = '(1/Mpc)^3' if self.use_Mpc else '(h/Mpc)^3' self.H_fid = None self.Dm_fid = None print("Number density resetted to nbar = 1 {}. Fiducial background " "cosmology and data sets (if defined)" "cleared.".format(nbar_unit))
[docs] def change_bias_basis(self, bias_basis): if self.bias_basis != bias_basis: self.bias_basis = bias_basis if self.bias_basis == 'EggScoSmi': self.bias_params_list = ['b1', 'b2', 'g2', 'g21', 'c0', 'c2', 'c4', 'cnlo', 'cnloB', 'NP0', 'NP20', 'NP22', 'NB0', 'MB0', 'cB1', 'cB2'] elif self.bias_basis == 'AssBauGre': self.bias_params_list = ['b1', 'b2', 'bG2', 'bGam3', 'c0', 'c2', 'c4', 'cnlo', 'cnloB', 'NP0', 'NP20', 'NP22', 'NB0', 'MB0', 'cB1', 'cB2'] elif self.bias_basis == 'AmiGleKok': self.bias_params_list = ['b1t', 'b2t', 'b3t', 'b4t', 'c0', 'c2', 'c4', 'cnlo', 'cnloB', 'NP0', 'NP20', 'NP22', 'NB0', 'MB0', 'cB1', 'cB2'] else: print('Warning. Bias basis not recognised, choose between ' '"EggScoSmi" (default), "AssBauGre", or "AmiGleKok".') self.init_params_dict() self.splines_up_to_date = False self.dw_spline_up_to_date = False
[docs] def change_counterterm_basis(self, counterterm_basis): if counterterm_basis in ['Comet','ClassPT']: if self.counterterm_basis != counterterm_basis: self.counterterm_basis = counterterm_basis self.init_params_dict() self.splines_up_to_date = False self.dw_splines_up_to_date = False else: print('Warning. Counterterm basis not recognised, choose between ' '"Comet" (default), or "ClassPT".')
[docs] def change_gauss_legendre_degree(self, degree): self.gl_x, self.gl_weights = np.polynomial.legendre.leggauss(degree) self.gl_x = 0.5 * self.gl_x + 0.5
[docs] def change_cnloB_type(self, type): if type in ['EggLeeSco','IvaPhiNis']: self.cnloB_type = type self.Bisp.change_cnlo_type(type) else: print('Warning. Type not recognised, choose between ' '"EggLeeSco" (default), or "IvaPhiNis".')
[docs] def define_nbar(self, nbar): r"""Define the number density of the sample. Sets the internal class attribute **nbar** to the value provided as input. The latter is intended to be in the set of units currently used by the emulator, that can be specified at class instanciation, or using the method **define_units**. Parameters ---------- nbar: float Number density of the sample, in units of :math:`\mathrm{Mpc}^{-3}` or :math:`h^3\,\mathrm{Mpc}^{-3}`, depending on the value of the class attribute **use_Mpc**. """ self.nbar = np.copy(nbar) self.Bisp.define_nbar(self.nbar) self.splines_up_to_date = False
[docs] def define_data_set(self, obs_id, **kwargs): r"""Define data sample. If the identifier of the data sample is not present in the internal data dictionary, it assigns a new **MeasuredData** object to it. Otherwise it updates the already existing entry. Parameters ---------- obs_id: str Identifier of the data sample. **kwargs: dict Dictionary of keyword arguments (check docs of **MeasuredData** class for the list of allowed keyword arguments). """ if obs_id not in self.data: self.data[obs_id] = MeasuredData(**kwargs) else: self.data[obs_id].update(**kwargs) self.chi2_decomposition = None self.Bisp_chi2_decomposition = None
[docs] def define_fiducial_cosmology(self, HDm_fid=None, params_fid=None, de_model='lambda'): r"""Define fiducial cosmology. Sets the internal attributes of the class to store the parameters of the fiducial cosmology, required for the calculation of the AP corrections. Parameters ---------- HDm_fid: list or numpy.ndarray, optional List containing the fiducial expansion factor :math:`H(z)` and angular diameter distance :math:`D_\mathrm{A}(z)`, in the units defined by the class attribute **use_Mpc**. If **None**, this method expects to find a dictionary containing the parameters of the fiducial cosmology (see **params_fid** below). Defaults to **None**. params_fid: dict, optional Dictionary containing the parameters of the fiducial cosmology, used to compute the expansion factor :math:`H(z)` and angular diameter distance :math:`D_\mathrm{A}(z)`, in the units defined by the class attribute **use_Mpc**. Defaults to **None**. de_model: str, optional String that determines the dark energy equation of state. Can be chosen form the list [`"lambda"`, `"w0"`, `"w0wa"`]. Defaults to `"lambda"`. """ if HDm_fid is not None: self.H_fid = HDm_fid[0] self.Dm_fid = HDm_fid[1] else: Om0 = (params_fid['wc']+params_fid['wb'])/params_fid['h']**2 H0 = params_fid['h']*100.0 Ok0 = 0.0 if 'Ok' not in params_fid else params_fid['Ok'] if de_model == 'lambda': w0 = -1.0 wa = 0.0 elif de_model == 'w0': w0 = params_fid['w0'] wa = 0.0 elif de_model == 'w0wa': w0 = params_fid['w0'] wa = params_fid['wa'] self.cosmo.update_cosmology(Om0, H0, Ok0=Ok0, de_model=de_model, w0=w0, wa=wa) self.H_fid = self.cosmo.Hz(params_fid['z']) self.Dm_fid = \ self.cosmo.comoving_transverse_distance(params_fid['z']) if not self.use_Mpc: self.H_fid /= params_fid['h'] self.Dm_fid *= params_fid['h']
def _update_params(self, params, de_model=None): r"""Update parameters of the emulator. Sets the internal attributes of the class to store the parameters of the emulator, based on the input argument, and resets to **None** the internal dictionary containing the model ingredients. Parameters ---------- params: dict Dictionary containing the list of total model parameters which are internally used by the emulator. The keyword/value pairs of the dictionary specify the names and the values of the parameters, respectively. de_model: str, optional String that determines the dark energy equation of state. Can be chosen from the list [`"lambda"`, `"w0"`, `"w0wa"`] to work with the standard cosmological parameters, or be left undefined to use only :math:`\sigma_{12}`. Defaults to **None**. """ def check_ranges(params_list): for p in params_list: if not self.params_ranges[p][0] <= self.params[p] \ <= self.params_ranges[p][1]: print('Warning! Leaving emulator range' + \ 'for parameter {}'.format(p)) try: if de_model is None and self.use_Mpc: emu_params_updated = any([params[p] != self.params[p] for p in self.params_list]) for p in self.params_list: self.params[p] = params[p] self.params['As'] = 0.0 self.params['z'] = 0.0 check_ranges(self.params_list) elif de_model is None and not self.use_Mpc: emu_params_updated = any([params[p] != self.params[p] for p in self.params_list+['h']]) for p in self.params_list+['h']: self.params[p] = params[p] self.params['As'] = 0.0 self.params['z'] = 0.0 check_ranges(self.params_list) else: expected_params = self.params_shape_list \ + self.de_model_params_list[de_model] if 'Ok' not in params: expected_params.remove('Ok') emu_params_updated = any([params[p] != self.params[p] for p in expected_params]) for p in expected_params: self.params[p] = params[p] if de_model == 'lambda' and \ (self.params['w0'] != -1.0 or self.params['wa'] != 0.0): self.params['w0'] = -1.0 self.params['wa'] = 0.0 emu_params_updated = True elif de_model == 'w0' and self.params['wa'] != 0.0: self.params['wa'] = 0.0 emu_params_updated = True check_ranges(self.params_shape_list) except KeyError: print('Not all required parameter values have been defined.') if emu_params_updated: self.Pk_ratios = {0: None, 2: None, 4: None} self.splines_up_to_date = False self.dw_spline_up_to_date = False self.X_splines_up_to_date = {X: False for X in self.diagrams_all} self.chi2_decomposition = None self.Bisp_chi2_decomposition = None RSD_params_updated = any([params[p] != self.params[p] for p in list(set(params) \ & set(self.RSD_params_list))]) if RSD_params_updated: self.chi2_decomposition = None self.Bisp_chi2_decomposition = None self._update_bias_params(params, include_RSD_params=True) return emu_params_updated def _update_bias_params(self, params, include_RSD_params=False): params_list = self.bias_params_list.copy() if include_RSD_params: params_list += self.RSD_params_list for p in params_list: if p in params.keys(): self.params[p] = params[p] else: self.params[p] = 0.0 if self.RSD_model == 'VDG_infty': self.params['cnlo'] = 0.0 self.params['cnloB'] = 0.0 self.params['cB1'] = 0.0 self.params['cB2'] = 0.0 if self.bias_basis == 'AssBauGre': self.params['g2'] = self.params['bG2'] self.params['g21'] = -4.0/7.0 * (self.params['bG2'] + self.params['bGam3']) elif self.bias_basis == 'AmiGleKok': self.params['b1'] = self.params['b1t'] self.params['b2'] = 2.0 * (-self.params['b1t'] + self.params['b2t'] + self.params['b4t']) self.params['g2'] = -2.0/7.0 * (self.params['b1t'] - self.params['b2t']) self.params['g21'] = -2.0/147.0 * (11*self.params['b1t'] - 18*self.params['b2t'] + 9*self.params['b3t']) def _update_AP_params(self, params, de_model=None, q_tr_lo=None): r"""Update AP parameters. Sets the internal attributes of the class to store the AP parameters. Parameters ---------- params: dict Dictionary containing the list of total model parameters which are internally used by the emulator. The keyword/value pairs of the dictionary specify the names and the values of the parameters, respectively. de_model: str, optional String that determines the dark energy equation of state. Can be chosen from the list [`"lambda"`, `"w0"`, `"w0wa"`] to work with the standard cosmological parameters, or be left undefined to use only :math:`\sigma_{12}`. Defaults to **None**. q_tr_lo: list or numpy.ndarray, optional List containing the user-provided AP parameters, in the form :math:`(q_\perp, q_\parallel)`. If provided, prevents computation from correct formulas (ratios of expansion factors and angular diameter distance). Defaults to **None**. """ if de_model is not None and q_tr_lo is None: Om0 = (self.params['wc']+self.params['wb'])/self.params['h']**2 H0 = 100.0*self.params['h'] self.cosmo.update_cosmology( Om0=Om0, H0=H0, Ok0=self.params['Ok'], de_model=de_model, w0=self.params['w0'], wa=self.params['wa']) self.params['q_lo'] = \ self.H_fid/self.cosmo.Hz(self.params['z']) self.params['q_tr'] = self.cosmo.comoving_transverse_distance( self.params['z'])/self.Dm_fid if not self.use_Mpc: self.params['q_lo'] *= self.params['h'] self.params['q_tr'] *= self.params['h'] elif de_model is not None: self.params['q_lo'] = q_tr_lo[1] self.params['q_tr'] = q_tr_lo[0] elif (de_model is None and 'q_lo' in params and 'q_tr' in params): self.params['q_lo'] = params['q_lo'] self.params['q_tr'] = params['q_tr'] def _get_bias_coeff(self): r"""Get bias coefficients for the emulated terms. Each term of the :math:`P_{\ell}` expansion is multiplied by a combination of bias parameters. This method returns such combinations in an array format. Returns ------- params_comb: numpy.ndarray Combinations of bias parameters that multiply each term of the expansion of the multipole of order :math:`\ell`. The output corresponds to .. math:: :nowrap: \begin{flalign*} & P_{\delta\delta}^\mathrm{tree} \rightarrow b_1^2 \\ & P_{\delta\theta}^\mathrm{tree+1\mbox{-}loop} \ \rightarrow b_1 \\ & P_{\theta\theta}^\mathrm{tree+1\mbox{-}loop} \ \rightarrow 1 \\ & P_{\mathrm{ctr},k^2} \rightarrow \ [c_0,\: c_2,\: c_4] \\ & P_{\mathrm{ctr},k^4} \rightarrow \ [b_1^2c_\mathrm{nlo},\: b_1c_\mathrm{nlo},\: \ c_\mathrm{nlo}] \\ & P_{\delta\delta}^\mathrm{1\mbox{-}loop} \ \rightarrow b_1^2 \\ & P_{b_\mathrm{X}b_\mathrm{Y}} \rightarrow [b_1b_2, \ \: b_1\gamma_2,\: b_1\gamma_{21},\: \ b_2^2,\: b_2\gamma_2,\: \gamma_2^2,\: b_2,\: \ \gamma_2,\: \gamma_{21}] \end{flalign*} """ b1 = self.params['b1'] b2 = self.params['b2'] g2 = self.params['g2'] g21 = self.params['g21'] c0 = self.params['c0'] if self.use_Mpc \ else self.params['c0']/self.params['h']**2 c2 = self.params['c2'] if self.use_Mpc \ else self.params['c2']/self.params['h']**2 c4 = self.params['c4'] if self.use_Mpc \ else self.params['c4']/self.params['h']**2 cnlo = self.params['cnlo'] if self.use_Mpc \ else self.params['cnlo']/self.params['h']**4 b1sq = b1**2 return np.array([b1sq, b1, 1., c0, c2, c4, b1sq*cnlo, b1*cnlo, cnlo, b1sq, b1*b2, b1*g2, b1*g21, b2**2, b2*g2, g2**2, b2, g2, g21]) def _get_bias_coeff_for_P6(self): r"""Get bias coefficients for the emulated terms of the octopole. Differently from the lower-order multipoles :math:`P_{0,2,4}`, the shape parameters of :math:`P_6` are kept fixed to the best values from Planck 2018 (TT+TE+EE+lowE+lensing), while each of the terms is rescaled by the current value of the growth rate :math:`f` and :math:`\sigma_{12}`. Each term of the :math:`P_6` expansion is therefore multiplied by a combination of growth rate and bias parameters. This method returns such combinations in an array format. Returns ------- params_comb: numpy.ndarray Combinations of bias parameters that multiply each term of the expansion of the multipole of order 6. The output corresponds to .. math:: :nowrap: \begin{flalign*} &P^\mathrm{tree}\rightarrow[b_1^2,\: fb_1,\: f^2] \\ &P^\mathrm{1\mbox{-}loop}\rightarrow[b_1^2,\: fb_1^2,\ \: f^2b_1^2,\: fb_1,\: f^2b_1,\: f^3b_1,\: f^2,\: \ f^3,\: f^4, \\ &\hspace{2.3cm} b_1b_2,\: fb_1b_2,\: b_1\gamma_2, \ \: fb_1\gamma_2,\: b_1\gamma_{21},\: b_2^2,\: \ b_2\gamma_2, \\ &\hspace{2.3cm} \gamma_2^2,\: fb_2,\: f^2b_2,\: \ f\gamma_2,\: f^2\gamma_2,\: f\gamma_{21}] \\ &P_{\mathrm{ctr},k^4}\rightarrow[f^4b_1^2 \ c_\mathrm{nlo},\: f^5b_1c_\mathrm{nlo},\: \ f^6c_\mathrm{nlo}] \end{flalign*} """ b1 = self.params['b1'] b2 = self.params['b2'] g2 = self.params['g2'] g21 = self.params['g21'] cnlo = self.params['cnlo'] if self.use_Mpc \ else self.params['cnlo']/self.params['h']**4 f = self.params['f'] b1sq = b1**2 b1f = b1*f f2 = f**2 f3 = f**3 f4 = f**4 bb_tree = np.array([b1sq, b1*f, f2]) bb_loop = np.array([b1sq, b1sq*f, b1sq*f2, b1f, b1f*f, b1f*f2, f2, f3, f4, b1*b2, b1f*b2, b1*g2, b1f*g2, b1*g21, b2**2, b2*g2, g2**2, b2*f, b2*f2, g2*f, g2*f2, g21*f]) bb_k4ctr = np.array([b1sq*f4, b1f*f4, f2*f4])*cnlo s12ratio = (self.params['s12']/self.s12_for_P6)**2 bb_tree *= s12ratio bb_loop *= s12ratio**2 bb_k4ctr *= s12ratio return np.hstack([bb_tree, bb_loop, bb_k4ctr]) def _get_bias_coeff_for_chi2_decomposition(self): r"""Get bias coefficients for the :math:`\chi^2` tables. In order to speed up the evaluation of the likelihood, the total :math:`\chi^2` is factorised into separate contributions scaling with different combinations of the bias and shot-noise parameters (the latter are expressed in units of the sample mean number density :math:`\bar{n}`). This method returns such combinations in an array format. Returns ------- params_comb: numpy.ndarray Combinations of bias and noise parameters that multiply each term of the factorisation of the total :math:`\chi^2` into individual terms. The output correpsonds to .. math:: :nowrap: \begin{flalign*} & P_{\delta\delta}^\mathrm{tree} \rightarrow b_1^2 \\ & P_{\delta\theta}^\mathrm{tree+1\mbox{-}loop} \ \rightarrow b_1 \\ & P_{\theta\theta}^\mathrm{tree+1\mbox{-}loop} \ \rightarrow 1 \\ & P_{\mathrm{ctr},k^2} \rightarrow [c_0,\: c_2,\: \ c_4] \\ & P_{\mathrm{ctr},k^4} \rightarrow \ [b_1^2c_\mathrm{nlo},\: b_1c_\mathrm{nlo},\: \ c_\mathrm{nlo}] \\ & P_{\delta\delta}^\mathrm{1\mbox{-}loop} \ \rightarrow b_1^2 \\ & P_{b_\mathrm{X}b_\mathrm{Y}} \rightarrow [b_1b_2, \ \: b_1\gamma_2,\: b_1\gamma_{21},\: \ b_2^2,\: b_2\gamma_2,\: \gamma_2^2,\: b_2,\: \ \gamma_2,\: \gamma_{21}] \\ & P_\mathrm{noise} \rightarrow [N_0/\bar{n},\: \ N_{20}/\bar{n},\: N_{22}/\bar{n}] \end{flalign*} """ b1 = self.params['b1'] b2 = self.params['b2'] g2 = self.params['g2'] g21 = self.params['g21'] c0 = self.params['c0'] if self.use_Mpc \ else self.params['c0']/self.params['h']**2 c2 = self.params['c2'] if self.use_Mpc \ else self.params['c2']/self.params['h']**2 c4 = self.params['c4'] if self.use_Mpc \ else self.params['c4']/self.params['h']**2 cnlo = self.params['cnlo'] if self.use_Mpc \ else self.params['cnlo']/self.params['h']**4 N0 = self.params['NP0'] if self.use_Mpc \ else self.params['NP0']/self.params['h']**3 N20 = self.params['NP20'] if self.use_Mpc \ else self.params['NP20']/self.params['h']**5 N22 = self.params['NP22'] if self.use_Mpc \ else self.params['NP22']/self.params['h']**5 b1sq = b1**2 return np.array([b1sq, b1, 1., c0, c2, c4, b1sq*cnlo, b1*cnlo, cnlo, b1sq, b1*b2, b1*g2, b1*g21, b2**2, b2*g2, g2**2, b2, g2, g21, N0/self.nbar, N20/self.nbar, N22/self.nbar]) def _get_bias_coeff_for_Bisp_chi2_decomposition(self): r"""Get bias coefficients for the bispectrum :math:`\chi^2` tables. In order to speed up the evaluation of the likelihood, the total :math:`\chi^2` is factorised into separate contributions scaling with different combinations of the bias and shot-noise parameters (the latter are expressed in units of the sample mean number density :math:`\bar{n}`). This method returns such combinations in an array format. Returns ------- params_comb: numpy.ndarray Combinations of bias and noise parameters that multiply each term of the factorisation of the total :math:`\chi^2` into individual terms. """ b1 = self.params['b1'] b2 = self.params['b2'] g2 = self.params['g2'] cnloB = self.params['cnloB']*self.params['f']**2 MB0 = self.params['MB0'] NB0 = self.params['NB0'] NP0 = self.params['NP0'] b1sq = b1**2 if self.RSD_model == 'EFT': params_comb = np.array([b1sq*b1, b1sq, b1, b1sq*b1*cnloB, b1sq*cnloB, b1*cnloB, b1sq*b2, b1*b2, b2, b1sq*b2*cnloB, b1*b2*cnloB, b2*cnloB, b1sq*g2, b1*g2, g2, b1sq*g2*cnloB, b1*g2*cnloB, g2*cnloB, 1.0, cnloB, MB0*b1sq/self.nbar, (MB0+NP0)*b1/self.nbar, NP0/self.nbar, NB0/self.nbar**2]) else: params_comb = np.array([b1sq*b1, b1sq, b1, b1sq*b2, b1*b2, b2, b1sq*g2, b1*g2, g2, 1.0, MB0*b1sq/self.nbar, (MB0+NP0)*b1/self.nbar, NP0/self.nbar, NB0/self.nbar**2]) return params_comb def _eval_emulator(self, params, ell, de_model=None): r"""Evaluate the emulators for the different terms. Sets up the internal parameters of the class, and evaluate the emulators for the various ingredients of the model, that are then stored as class attributes. The list of emulated quantities comprises the linear power spectrum :math:`P_\mathrm{L}(k)` (function of the shape parameters :math:`\mathbf{\Theta_{s}}`), the value of :math:`\sigma_{12}` (function of the shape parameters :math:`\mathbf{\Theta_{s}}`), and all the integral tables consisting of ratios between individual contributions to the one-loop galaxy power spectrum and the linear one (function of shape parameters :math:`\mathbf{\Theta_{s}}`, the growth rate :math:`f`, and :math:`\sigma_{12}`). For the `VDG_infty` model, an additional emulator is evaluated to obtain the value of the pairwise velocity dispersion, i.e. :math:`\sigma_\mathrm{v}`. Parameters ---------- params: dict Dictionary containing the list of total model parameters which are internally used by the emulator. The keyword/value pairs of the dictionary specify the names and the values of the parameters, respectively. ell: list or numpy.ndarray Specific multipole order :math:`\ell`. Can be chosen from the list [0,2,4], whose entries correspond to monopole (:math:`\ell=0`), quadrupole (:math:`\ell=2`) and hexadecapole (:math:`\ell=4`). de_model: str, optional String that determines the dark energy equation of state. Can be chosen from the list [`"lambda"`, `"w0"`, `"w0wa"`] to work with the standard cosmological parameters, or be left undefined to use only :math:`\sigma_{12}`. Defaults to **None**. """ emu_params_updated = self._update_params(params, de_model=de_model) params_shape = np.array( [self.params[p] for p in self.params_shape_list]) if de_model is None: params_all = np.array([self.params[p] for p in self.params_list]) if self.Pk_lin is None or emu_params_updated: shape_all = self.emu['shape'].predict(params_shape[None, :]) sigma12 = self.training['SHAPE'].transform_inv( shape_all[0,0], 's12') self.Pk_lin = self.training['SHAPE'].transform_inv( shape_all[0,2:], 'PL') self.Pk_lin *= (self.params['s12']/sigma12)**2 if self.RSD_model == 'VDG_infty': self.params['sv'] = self.training['SHAPE'].transform_inv( shape_all[0,1], 'sv') self.params['sv'] *= self.params['s12']/sigma12 if not self.use_Mpc: self.params['sv'] *= self.params['h'] ratios_all = self.emu['ratios'].predict(params_all[None, :]) for i,m in enumerate(ell): self.Pk_ratios[m] = self.training['FULL'].transform_inv( ratios_all[0,i*1754:(i+1)*1754], m) else: if self.Pk_lin is None or emu_params_updated: shape_all = self.emu['shape'].predict(params_shape[None, :]) sigma12 = self.training['SHAPE'].transform_inv( shape_all[0,0], 's12') self.Pk_lin = self.training['SHAPE'].transform_inv( shape_all[0,2:], 'PL') # compute growth factors corresponding to fiducial and target # parameters + growth rate Om0_fid = (self.params['wc']+self.params['wb']) \ / self.emu_LCDM_params['h']**2 H0_fid = 100.0*self.emu_LCDM_params['h'] self.cosmo.update_cosmology(Om0=Om0_fid, H0=H0_fid) Dfid = self.cosmo.growth_factor(self.emu_LCDM_params['z']) Om0 = (self.params['wc']+self.params['wb'])/self.params['h']**2 H0 = 100.0*self.params['h'] self.cosmo.update_cosmology( Om0=Om0, H0=H0, Ok0=self.params['Ok'], de_model=de_model, w0=self.params['w0'], wa=self.params['wa']) D, f = self.cosmo.growth_factor(self.params['z'], get_growth_rate=True) # rescale linear power spectrum and sigma12 amplitude_scaling = np.sqrt( self.params['As']/self.emu_LCDM_params['As'])*D/Dfid self.Pk_lin *= amplitude_scaling**2 self.params['s12'] = sigma12*amplitude_scaling self.params['f'] = f for p in list(set(['s12','f']) & set(self.params_list)): if not self.params_ranges[p][0] <= self.params[p] \ <= self.params_ranges[p][1]: print('Warning! Leaving emulator range' + \ 'for parameter {}'.format(p)) if self.RSD_model == 'VDG_infty': self.params['sv'] = self.training['SHAPE'].transform_inv( shape_all[0,1], 'sv') self.params['sv'] *= amplitude_scaling if not self.use_Mpc: self.params['sv'] *= self.params['h'] params_all = np.array([self.params[p] for p in self.params_list], dtype=object) ratios_all = self.emu['ratios'].predict(params_all[None, :]) for i,m in enumerate(ell): self.Pk_ratios[m] = self.training['FULL'].transform_inv( ratios_all[0,i*1754:(i+1)*1754], m) if self.counterterm_basis == 'ClassPT': self.params['c2'] = 2.0/3.0 * self.params['f'] * self.params['c2'] self.params['c4'] = 8.0/35.0 * self.params['f']**2 * self.params['c4'] self.params['cnlo'] = - self.params['cnlo'] self.params['NP20'] = self.params['NP20'] + 1.0/3.0 * self.params['NP22'] self.params['NP22'] = 2.0/3.0 * self.params['NP22']
[docs] def W_kurt(self, k, mu): r"""Large scale limit of the velocity difference generating function. Method used exclusively if the `VDG_infty` model is specified. In the large scale limit, :math:`r\rightarrow\infty`, the velocity difference generating function :math:`W_\mathrm{G}` becomes scale-independent, with a gaussian limit given by .. math:: W_\infty(\lambda)=e^{-\lambda^2\sigma_\mathrm{v}^2}, where :math:`\lambda=fk\mu`, and :math:`\sigma_\mathrm{v}` is the pairwise velocity dispersion. This method returns a modified version of the gaussian limit, which also allows for non-zero kurtosis of the pairwise velocity distribution, .. math:: W_\infty(\lambda)=\frac{1}{\sqrt(1+a_\mathrm{vir}^2\lambda^2)} e^{-\frac{\lambda^2\sigma_\mathrm{v}^2} {1+a_\mathrm{vir}^2\lambda^2}}, where :math:`a_\mathrm{vir}` is a free parameter of the model, that can be specified in the list of model parameters when instantiating or updating the class. Parameters ---------- k: float Value of the wavemode :math:`k`. mu: float Value of the cosine :math:`\mu` of the angle between the pair separation and the line of sight. Returns ------- Winfty: float Value of the pairwise velocity generating function in the large scale limit. """ t1 = (self.params['f']*k*mu)**2 t2 = 1.0 + t1*self.params['avir']**2 return 1.0/np.sqrt(t2)*np.exp(-t1*self.params['sv']**2/t2)
[docs] def get_kmu_products(self, tri, mu1, mu2, mu3): r"""Computes the products k1*mu1, k2*mu2, and k3*mu3. The method returns the products in a format needed for the computation of the bispectrum damping function. It also applies Alcock-Paczynski distortions to the wave modes and cosines. Parameters ---------- tri: numpy.ndarray Wavemodes :math:`k_1`, :math:`k_2`, :math:`k_3`. mu1: numpy.ndarray Cosines of the angle between :math:`k_1` and the LOS. mu2: numpy.ndarray Cosines of the angle between :math:`k_2` and the LOS. mu3: numpy.ndarray Cosines of the angle between :math:`k_3` and the LOS. Returns ------- kmu1: numpy.ndarray Product of k1 and mu1. kmu2: numpy.ndarray Product of k2 and mu2. kmu2: numpy.ndarray Product of k3 and mu3. """ k1 = tri[:,0].reshape((-1,1)) k2 = tri[:,1].reshape((-1,1)) k3 = tri[:,2].reshape((-1,1)) kmu1 = np.outer(k1,mu1)/self.params['q_lo'] kmu2 = k2*mu2/self.params['q_lo'] kmu3 = k3*mu3/self.params['q_lo'] return kmu1, kmu2, kmu3
[docs] def WB_kurt(self, tri, mu1, mu2, mu3): # including AP effect! k1 = tri[:,0].reshape((-1,1)) k2 = tri[:,1].reshape((-1,1)) k3 = tri[:,2].reshape((-1,1)) lsq = 0.5 * (self.params['f']/self.params['q_lo'])**2 \ * (np.outer(k1,mu1)**2 + (k2*mu2)**2 + (k3*mu3)**2) t = 1.0 + lsq*self.params['avirB']**2 return 1.0/np.sqrt(t**3) * np.exp(-lsq*self.params['sv']**2/t)
def _build_Pell_spline(self, Pell, ell): r"""Build spline object for power spectrum multipoles. Generates a cubic spline object for the specified power spectrum multipole, including the computation of effective indexes for the low- and high-:math:`k` tails of the multipole, and stores it as class attribute. Parameters ---------- Pell: list or numpy.ndarray Array containing the power spectrum multipole of order :math:`\ell`, evaluated at the wavemodes defined by the class attribute **k_table**. ell: int Specific multipole order :math:`\ell`. Can be chosen from the list [0,2,4,6], whose entries correspond to monopole (:math:`\ell=0`), quadrupole (:math:`\ell=2`), hexadecapole (:math:`\ell=4`) and octopole (:math:`\ell=6`). """ id_min = 0 if not ell == 6 else self.nk-self.nkloop id_max = -1 if self.use_Mpc: self.Pell_spline[ell] = UnivariateSpline(self.k_table, Pell, k=3, s=0) self.k_table_min[ell] = self.k_table[id_min] self.k_table_max[ell] = self.k_table[id_max] else: Pell *= self.params['h']**3 self.Pell_spline[ell] = UnivariateSpline( self.k_table/self.params['h'], Pell, k=3, s=0) self.k_table_min[ell] = self.k_table[id_min]/self.params['h'] self.k_table_max[ell] = self.k_table[id_max]/self.params['h'] # low-k extrapolation self.Pell_min[ell] = Pell[id_min] dlP_min = np.log10(np.abs(Pell[id_min+2]/Pell[id_min])) dlk_min = np.log10(self.k_table[id_min+2]/self.k_table[id_min]) self.neff_min[ell] = dlP_min/dlk_min self.Pell_lowk_extrapolation[ell] = lambda k: self.Pell_min[ell] \ * (k/self.k_table_min[ell])**self.neff_min[ell] # high-k extrapolation if np.abs(Pell[id_max]/Pell[id_max-2]) < 2 \ and np.abs(Pell[id_max-2]/Pell[id_max]) < 2: self.Pell_max[ell] = Pell[id_max] dlP_max = np.log10(np.abs(Pell[id_max]/Pell[id_max-2])) dlk_max = np.log10(self.k_table[id_max]/self.k_table[id_max-2]) self.neff_max[ell] = dlP_max/dlk_max self.Pell_highk_extrapolation[ell] = lambda k: self.Pell_max[ell] \ * (k/self.k_table_max[ell])**self.neff_max[ell] else: a = (Pell[id_max] - Pell[id_max-2]) \ / (self.k_table[id_max] - self.k_table[id_max-2]) b = Pell[id_max-2] - a*self.k_table[id_max-2] if not self.use_Mpc: a *= self.params['h'] self.Pell_highk_extrapolation[ell] = lambda k: a*k + b def _build_Pdw_spline(self, Pdw): r"""Build spline object for multipoles of linear de-wiggled power spectrum. Generates a cubic spline object for the linear de-wiggled power spectrum, including the computation of effective indexes for the low- and high-:math:`k` tails, and stores it as class attribute. Parameters ---------- Pdw: list or numpy.ndarray Array containing the de-wiggled linear power spectrum evaluated at the wavemodes defined by the class attribute **k_table**. """ id_min = 0 if self.use_Mpc: self.Pdw_spline = UnivariateSpline(self.k_table, Pdw, k=3, s=0) self.Pdw_min = Pdw[id_min] self.Pdw_max = Pdw[-1] self.k_table_min[0] = self.k_table[id_min] self.k_table_max[0] = self.k_table[-1] dlP_min = np.log10(np.abs(Pdw[id_min+2]/Pdw[id_min])) dlP_max = np.log10(np.abs(Pdw[-1]/Pdw[-3])) dlk_min = np.log10(self.k_table[id_min+2]/self.k_table[id_min]) dlk_max = np.log10(self.k_table[-1]/self.k_table[-3]) self.neff_dw_min = dlP_min/dlk_min self.neff_dw_max = dlP_max/dlk_max else: Pdw *= self.params['h']**3 self.Pdw_spline = UnivariateSpline(self.k_table/self.params['h'], Pdw, k=3, s=0) self.Pdw_min = Pdw[id_min] self.Pdw_max = Pdw[-1] self.k_table_min[0] = self.k_table[id_min]/self.params['h'] self.k_table_max[0] = self.k_table[-1]/self.params['h'] dlP_min = np.log10(np.abs(Pdw[id_min+2]/Pdw[id_min])) dlP_max = np.log10(np.abs(Pdw[-1]/Pdw[-3])) dlk_min = np.log10(self.k_table[id_min+2]/self.k_table[id_min]) dlk_max = np.log10(self.k_table[-1]/self.k_table[-3]) self.neff_dw_min = dlP_min/dlk_min self.neff_dw_max = dlP_max/dlk_max def _eval_Pell_spline(self, k, ell): r"""Evaluate the spline of the specified power spectrum multipole. Calls the spline object stored as class attribute for the power spectrum multipole of given order :math:`\ell` on the input wavemodes :math:`k`. The called interpolator results in a cubic spline or in a power-law extrapolation, depending if the value of :math:`k` is within or outside the original boundary spcified by the training table. Parameters ---------- k: numpy.ndarray Values of the requested wavemodes :math:`k`. ell: int Specific multipole order :math:`\ell`. Can be chosen from the list [0,2,4,6], whose entries correspond to monopole (:math:`\ell=0`), quadrupole (:math:`\ell=2`), hexadecapole (:math:`\ell=4`) and octopole (:math:`\ell=6`). Returns ------- spline: numpy.ndarray Interpolated power spectrum multipole of order :math:`\ell` at the requested wavemodes :math:`k`. """ spline = \ np.where(k < self.k_table_min[ell], self.Pell_lowk_extrapolation[ell](k), np.where(k > self.k_table_max[ell], self.Pell_highk_extrapolation[ell](k), self.Pell_spline[ell](k))) return spline def _eval_Pdw_spline(self, k): r"""Evaluate the spline of the linear de-wiggled power spectrum. Calls the spline object stored as class attribute for the linear de-wiggled power spectrum on the input wavemodes :math:`k`. The called interpolator results in a cubic spline or in a power-law extrapolation, depending if the value of :math:`k` is within or outside the original boundary spcified by the training table. Parameters ---------- k: numpy.ndarray Values of the requested wavemodes :math:`k`. Returns ------- spline: numpy.ndarray Interpolated linear de-wiggled power spectrum at the requested wavemodes :math:`k`. """ mask_low = k < self.k_table_min[0] mask_high = k > self.k_table_max[0] spline = np.hstack( [self.Pdw_min * (k[mask_low]/self.k_table_min[0])**self.neff_dw_min, self.Pdw_spline(k[np.invert(mask_low) & np.invert(mask_high)]), self.Pdw_max * (k[mask_high]/self.k_table_max[0])**self.neff_dw_max] ) return spline
[docs] def PL(self, k, params, de_model=None): r"""Compute the linear power spectrum predictions. Evaluates the emulator calling **_eval_emulator**, and returns the linear power spectrum :math:`P_\mathrm{L}(k)` at the specified wavemodes. Parameters ---------- k: float or numpy.ndarray Value of the requested wavemodes :math:`k`. params: dict Dictionary containing the list of total model parameters which are internally used by the emulator. The keyword/value pairs of the dictionary specify the names and the values of the parameters, respectively. de_model: str, optional String that determines the dark energy equation of state. Can be chosen from the list [`"lambda"`, `"w0"`, `"w0wa"`] to work with the standard cosmological parameters, or be left undefined to use only :math:`\sigma_{12}`. Defaults to **None**. Returns ------- PL: float or numpy.ndarray Linear power spectrum :math:`P_\mathrm{L}(k)` evaluated at the input wavemodes :math:`k`. """ self._eval_emulator(params, ell=[], de_model=de_model) if self.use_Mpc: PL_spline = UnivariateSpline(self.k_table, self.Pk_lin, k=3, s=0) else: PL_spline = UnivariateSpline(self.k_table/self.params['h'], self.Pk_lin*self.params['h']**3, k=3, s=0) return PL_spline(k)
[docs] def Pdw_2d(self, k, mu, params, de_model=None, ell_for_recon=None): r"""Compute the anisotropic leading order IR-resummed power spectrum. Evaluates the emulator calling **_eval_emulator**, and returns the anisotropic leading order IR-resummed power spectrum :math:`P_\mathrm{IR-res}^\mathrm{LO}(k,\mu)`, defined as .. math:: P_\mathrm{IR-res}^\mathrm{LO}(k,\mu) = P_\mathrm{nw}(k) + \ e^{-k^2\Sigma^2(f,\mu)}P_\mathrm{w}(k), where :math:`P_\mathrm{nw}` and :math:`P_\mathrm{w}` are the no-wiggle and wiggle-only component of the linear matter power spectrum, and :math:`\Sigma(f,\mu)` is the anisotropic BAO damping factor due to infrared modes. Notice how this function does not include the leading order Kaiser effect due to the impact of the velocity field on the amplitude of the power spectrum. Parameters ---------- k: float or numpy.ndarray Value of the requested wavemodes :math:`k`. mu: float or numpy.ndarray Value of the cosine :math:`\mu` of the angle between the pair separation and the line of sight. params: dict Dictionary containing the list of total model parameters which are internally used by the emulator. The keyword/value pairs of the dictionary specify the names and the values of the parameters, respectively. de_model: str, optional String that determines the dark energy equation of state. Can be chosen from the list [`"lambda"`, `"w0"`, `"w0wa"`] to work with the standard cosmological parameters, or be left undefined to use only :math:`\sigma_{12}`. Defaults to **None**. ell_for_recon: list, optional List of :math:`\ell` values used for the reconstruction of the 2d leading-order IR-resummed power spectrum. If **None**, all the even multipoles up to :math:`\ell=6` are used in the reconstruction. Defaults to **None**. Returns ------- Pdw_2d: numpy.ndarray Leading-order infrared resummed power spectrum :math:`P_\mathrm{IR-res}^\mathrm{LO}(k,\mu)` evaluated at the input wavemodes :math:`k` and angles :math:`\mu`. """ if ell_for_recon is None: ell_for_recon = [0, 2, 4, 6] if not self.real_space else [0] ell_eval_emu = ell_for_recon.copy() if 6 in ell_eval_emu: ell_eval_emu.remove(6) self._eval_emulator(params, ell=ell_eval_emu, de_model=de_model) Pdw_ell = np.zeros([self.nk, len(ell_for_recon)]) for i, ell in enumerate(ell_for_recon): if ell != 6: Pdw_ell[:, i] = self.Pk_ratios[ell][:self.nk] else: Pdw_ell[:, i] = self.P6[:, 0] Pdw_ell[:, :len(ell_eval_emu)] = (Pdw_ell[:, :len(ell_eval_emu)].T * self.Pk_lin).T Pdw_spline = {} for i, ell in enumerate(ell_for_recon): if self.use_Mpc: Pdw_spline[ell] = UnivariateSpline(self.k_table, Pdw_ell[:, i], k=3, s=0) else: Pdw_spline[ell] = UnivariateSpline( self.k_table/self.params['h'], Pdw_ell[:, i]*self.params['h']**3, k=3, s=0) Pdw_2d = 0.0 for ell in ell_for_recon: Pdw_2d += np.outer(Pdw_spline[ell](k), eval_legendre(ell, mu)) return Pdw_2d
[docs] def Pdw(self, k, params, de_model=None, ell_for_recon=None): r"""Compute the real space leading order IR-resummed power spectrum. Evaluates the emulator calling **_eval_emulator**, and returns the real space (:math:`\mu = 0`) leading order IR-resummed power spectrum :math:`P_\mathrm{IR-res}^\mathrm{LO}(k,\mu)`, defined as .. math:: P_\mathrm{IR-res}^\mathrm{LO}(k,\mu) = P_\mathrm{nw}(k) + \ e^{-k^2\Sigma^2(f,\mu)}P_\mathrm{w}(k), where :math:`P_\mathrm{nw}` and :math:`P_\mathrm{w}` are the no-wiggle and wiggle-only component of the linear matter power spectrum, and :math:`\Sigma(f,\mu)` is the anisotropic BAO damping factor due to infrared modes. Notice how this function does not include the leading order Kaiser effect due to the impact of the velocity field on the amplitude of the power spectrum. Parameters ---------- k: float or numpy.ndarray Value of the requested wavemodes :math:`k`. mu: float or numpy.ndarray Value of the cosine :math:`\mu` of the angle between the pair separation and the line of sight. params: dict Dictionary containing the list of total model parameters which are internally used by the emulator. The keyword/value pairs of the dictionary specify the names and the values of the parameters, respectively. de_model: str, optional String that determines the dark energy equation of state. Can be chosen from the list [`"lambda"`, `"w0"`, `"w0wa"`] to work with the standard cosmological parameters, or be left undefined to use only :math:`\sigma_{12}`. Defaults to **None**. ell_for_recon: list, optional List of :math:`\ell` values used for the reconstruction of the 2d leading-order IR-resummed power spectrum. If **None**, all the even multipoles up to :math:`\ell=6` are used in the reconstruction. Defaults to **None**. Returns ------- Pdw_2d: numpy.ndarray Leading-order infrared resummed power spectrum :math:`P_\mathrm{IR-res}^\mathrm{LO}(k,\mu)` evaluated at the input wavemodes :math:`k` and angles :math:`\mu`. """ if ell_for_recon is None: ell_for_recon = [0, 2, 4, 6] if not self.real_space else [0] ell_eval_emu = ell_for_recon.copy() if 6 in ell_eval_emu: ell_eval_emu.remove(6) self._eval_emulator(params, ell=ell_eval_emu, de_model=de_model) if not self.dw_spline_up_to_date: Pdw_ell = np.zeros([self.nk, len(ell_for_recon)]) for i, ell in enumerate(ell_for_recon): if ell != 6: Pdw_ell[:, i] = self.Pk_ratios[ell][:self.nk] else: Pdw_ell[:, i] = self.P6[:, 0] Pdw_ell[:, :len(ell_eval_emu)] = (Pdw_ell[:, :len(ell_eval_emu)].T * self.Pk_lin).T Pdw = 0.0 for i, ell in enumerate(ell_for_recon): Pdw += Pdw_ell[:,i]*eval_legendre(ell, 0.6) self._build_Pdw_spline(Pdw) self.dw_spline_up_to_date = True Pdw = self._eval_Pdw_spline(k) return Pdw
def _Pell_fid_ktable(self, params, ell, de_model=None): r"""Compute the power spectrum multipoles at the training wavemodes. Returns the specified multipole at a fixed :math:`k` grid corresponding to the wavemodes used to train the emulator (without the need to recur to a spline interpolation in :math:`k`). The output power spectrum multipole is not corrected for AP distortions. Used for validation purposes. Parameters ---------- params: dict Dictionary containing the list of total model parameters which are internally used by the emulator. The keyword/value pairs of the dictionary specify the names and the values of the parameters, respectively. ell: int Specific multipole order :math:`\ell`. Can be chosen from the list [0,2,4,6], whose entries correspond to monopole (:math:`\ell=0`), quadrupole (:math:`\ell=2`), hexadecapole (:math:`\ell=4`) and octopole (:math:`\ell=6`). de_model: str, optional String that determines the dark energy equation of state. Can be chosen from the list [`"lambda"`, `"w0"`, `"w0wa"`] to work with the standard cosmological parameters, or be left undefined to use only :math:`\sigma_{12}`. Defaults to **None**. Returns ------- Pell: numpy.ndarray Power spectrum multipole of order :math:`\ell` at the fixed :math:`k` grid used for the training of the emulator. """ ell = [ell] if not isinstance(ell, list) else ell ell_eval_emu = ell.copy() if 6 in ell_eval_emu: ell_eval_emu.remove(6) self._eval_emulator(params, ell_eval_emu, de_model=de_model) bij = self._get_bias_coeff() Pell = np.zeros([self.nk, len(ell)]) for i, m in enumerate(ell): if m != 6: Pk_bij = np.zeros([self.nk, self.n_diagrams]) Pk_bij[:, :9] = np.multiply( self.Pk_ratios[m][:9*self.nk].reshape((9, self.nk)), self.Pk_lin).T Pk_bij[(self.nk-self.nkloop):, 9:19] = np.multiply( self.Pk_ratios[m][9*self.nk:].reshape((10, self.nkloop)), self.Pk_lin[(self.nk-self.nkloop):]).T Pell[:, i] = np.dot(bij, Pk_bij.T) # add shot noise (now done in Pell) # if m == 0: # N0 = self.params['NP0'] if self.use_Mpc \ # else self.params['NP0']/self.params['h']**3 # N20 = self.params['NP20'] if self.use_Mpc \ # else self.params['NP20']/self.params['h']**5 # Pell[:, i] += (np.ones_like(self.k_table)*N0/self.nbar + # self.k_table**2*N20/self.nbar) # elif m == 2: # N22 = self.params['NP22'] if self.use_Mpc \ # else self.params['NP22']/self.params['h']**5 # Pell[:, i] += self.k_table**2*N22/self.nbar else: bij_for_P6 = self._get_bias_coeff_for_P6() Pell[:, i] = np.dot(bij_for_P6, self.P6.T) return Pell
[docs] def Pell_quad(self, k, params, ell, de_model=None, binning=None, obs_id=None, q_tr_lo=None, W_damping=None, ell_for_recon=None): r"""Compute the power spectrum multipoles. Main method to compute the galaxy power spectrum multipoles. Returns the specified multipole at the given wavemodes :math:`k`. Parameters ---------- k: float or list or numpy.ndarray Wavemodes :math:`k` at which to evaluate the multipoles. If a list is passed, it has to match the size of `ell`, and in that case each wavemode refer to a given multipole. params: dict Dictionary containing the list of total model parameters which are internally used by the emulator. The keyword/value pairs of the dictionary specify the names and the values of the parameters, respectively. ell: int or list Specific multipole order :math:`\ell`. Can be chosen from the list [0,2,4,6], whose entries correspond to monopole (:math:`\ell=0`), quadrupole (:math:`\ell=2`), hexadecapole (:math:`\ell=4`) and octopole (:math:`\ell=6`). de_model: str, optional String that determines the dark energy equation of state. Can be chosen from the list [`"lambda"`, `"w0"`, `"w0wa"`] to work with the standard cosmological parameters, or be left undefined to use only :math:`\sigma_{12}`. Defaults to **None**. binning: dict, optional obs_id: str, optional If not **None** the returned power spectrum will be convolved with a survey window function. In that case the string must be a valid data set identifier and the window function mixing matrix must have been loaded beforehand. Defaults to **None**. q_tr_lo: list or numpy.ndarray, optional List containing the user-provided AP parameters, in the form :math:`(q_\perp, q_\parallel)`. If provided, prevents computation from correct formulas (ratios of angular diameter distances and expansion factors wrt to the corresponding quantities of the fiducial cosmology). Defaults to **None**. W_damping: Callable[[float, float], float], optional Function returning the shape of the pairwise velocity generating function in the large scale limit, :math:`r\rightarrow\infty`. The function accepts two floats as arguments, corresponding to the wavemode :math:`k` and the cosinus of the angle between pair separation and line of sight :math:`\mu`, and returns a float. This function is used only with the **VDG_infty** model. If **None**, it uses the free kurtosis distribution defined by **W_kurt**. Defaults to **None**. ell_for_recon: list, optional List of :math:`\ell` values used for the reconstruction of the 2d leading-order IR-resummed power spectrum. If **None**, all the even multipoles up to :math:`\ell=6` are used in the reconstruction. Defaults to **None**. Returns ------- Pell_dict: dict Dictionary containing all the requested power spectrum multipoles of order :math:`\ell` at the specified :math:`k`. """ if ell_for_recon is None: ell_for_recon = [0, 2, 4, 6] if not self.real_space else [0] ell = [ell] if not isinstance(ell, list) else ell if isinstance(k, list): if len(k) != len(ell): raise ValueError("If 'k' is given as a list, it must match the" " length of 'ell'.") else: k_list = k k = np.unique(np.hstack(k_list)) else: k_list = [k]*len(ell) k = np.unique(np.hstack(k_list)) use_effective_modes = False if binning is not None: if self.grid is None: self.grid = Grid(binning['kfun'], binning['dk']) else: self.grid.update(binning['kfun'], binning['dk']) self.grid.find_discrete_modes(k, **binning) if binning.get('effective') is not None: use_effective_modes = binning['effective'] if use_effective_modes: self.grid.compute_effective_modes(k, **binning) keff = self.grid.keff if use_effective_modes else k def P2d(q, mu): t = 0.0 for m in ell_for_recon: t += eval_legendre(m, mu) * self._eval_Pell_spline(q, m) return t def P2d_stoch(q, mu): t = self.params['NP0'] + q**2 * (self.params['NP20'] \ + self.params['NP22']*eval_legendre(2,mu)) return t/self.nbar if self.RSD_model == 'EFT': if binning is None or use_effective_modes: def integrand(mu): mu2 = mu**2 APfac = np.sqrt(mu2/self.params['q_lo']**2 + (1.0 - mu2)/self.params['q_tr']**2) kp = keff*APfac mup = mu/self.params['q_lo']/APfac P2d_tot = P2d(kp, mup) + P2d_stoch(kp, mup) return np.outer(P2d_tot, eval_legendre(ell, mu)) else: def shell_average(): mu2 = self.grid.mu**2 APfac = np.sqrt(mu2/self.params['q_lo']**2 + (1.0 - mu2)/self.params['q_tr']**2) kp = self.grid.k*APfac mup = self.grid.mu/self.params['q_lo']/APfac legendre = np.array([eval_legendre(l, self.grid.mu) for l in ell]) prod = (P2d(kp, mup) + P2d_stoch(kp, mup)) * legendre avg = np.zeros([len(self.grid.nmodes)-1, len(ell)]) for i in range(len(self.grid.nmodes)-1): n1 = self.grid.nmodes[i] n2 = self.grid.nmodes[i+1] avg[i] = np.average(prod[:,n1:n2], axis=1, weights=self.grid.weights[n1:n2]) return avg elif self.RSD_model == 'VDG_infty': if W_damping is None: W_damping = self.W_kurt if binning is None or use_effective_modes: def integrand(mu): mu2 = mu**2 APfac = np.sqrt(mu2/self.params['q_lo']**2 + (1.0 - mu2)/self.params['q_tr']**2) kp = keff*APfac mup = mu/self.params['q_lo']/APfac P2d_damped = P2d(kp, mup) * W_damping(kp, mup) P2d_tot = P2d_damped + P2d_stoch(kp, mup) return np.outer(P2d_tot, eval_legendre(ell, mu)) else: def shell_average(): mu2 = self.grid.mu**2 APfac = np.sqrt(mu2/self.params['q_lo']**2 + (1.0 - mu2)/self.params['q_tr']**2) kp = self.grid.k*APfac mup = self.grid.mu/self.params['q_lo']/APfac legendre = np.array([eval_legendre(l, self.grid.mu) for l in ell]) P2d_damped = P2d(kp, mup) * W_damping(kp, mup) prod = (P2d_damped + P2d_stoch(kp, mup)) * legendre avg = np.zeros([len(self.grid.nmodes)-1, len(ell)]) for i in range(len(self.grid.nmodes)-1): n1 = self.grid.nmodes[i] n2 = self.grid.nmodes[i+1] avg[i] = np.average(prod[:,n1:n2], axis=1, weights=self.grid.weights[n1:n2]) return avg else: raise ValueError('Unsupported RSD model.') if obs_id is None: params_updated = [params[p] != self.params[p] for p in params.keys()] params_nonzero = [x for x in self.bias_params_list + self.RSD_params_list if self.params[x] != 0] if (any(params_updated) or any(p not in params.keys() for p in params_nonzero) or not self.splines_up_to_date): Pell = self._Pell_fid_ktable(params, ell=ell_for_recon, de_model=de_model) for i, m in enumerate(ell_for_recon): self._build_Pell_spline(Pell[:, i], m) self.splines_up_to_date = True # self.X_splines_up_to_date = {X: False for X in self.diagrams_all} # self.chi2_decomposition = None self._update_AP_params(params, de_model=de_model, q_tr_lo=q_tr_lo) q3 = self.params['q_tr']**2 * self.params['q_lo'] if binning is None or use_effective_modes: Pell_model = quad_vec(integrand, 0.0, 1.0)[0] else: Pell_model = shell_average() Pell_model *= (2.0*np.array(ell)+1.0) / q3 Pell_dict = {} for i, m in enumerate(ell): ids = np.intersect1d(k, k_list[i], return_indices=True)[1] Pell_dict['ell{}'.format(m)] = Pell_model[ids, i] else: mixing_matrix_exists = True try: self.data[obs_id].bins_mixing_matrix except AttributeError: mixing_matrix_exists = False try: self.data[obs_id].W_mixing_matrix except AttributeError: mixing_matrix_exists = False if mixing_matrix_exists: ell_for_mixing_matrix = [0,2,4] if not self.real_space else [0] Pell_model = self.Pell( self.data[obs_id].bins_mixing_matrix_compressed, params, ell_for_mixing_matrix, de_model, obs_id=None, q_tr_lo=q_tr_lo, W_damping=W_damping, ell_for_recon=ell_for_recon) Pell_list = [] for l in ell_for_mixing_matrix: spline = UnivariateSpline( self.data[obs_id].bins_mixing_matrix_compressed, Pell_model['ell{}'.format(l)], k=3, s=0) Pell_list = np.hstack( [Pell_list, spline(self.data[obs_id].bins_mixing_matrix[1])]) Pell_convolved = np.dot(self.data[obs_id].W_mixing_matrix, Pell_list) nb = len(self.data[obs_id].bins_mixing_matrix[0]) Pell_dict = {} if k.size != np.intersect1d( k, self.data[obs_id].bins_mixing_matrix[0]).size: for i, m in enumerate(ell): spline = UnivariateSpline( self.data[obs_id].bins_mixing_matrix[0], Pell_convolved[int(m/2)*nb:(int(m/2)+1)*nb], k=3, s=0) Pell_dict['ell{}'.format(m)] = spline(k_list[i]) else: for i, m in enumerate(ell): ids = np.intersect1d( k_list[i], self.data[obs_id].bins_mixing_matrix[0], return_indices=True)[1] Pell_dict['ell{}'.format(m)] = Pell_convolved[ids + int(m/2)*nb] else: print('Warning! Bins for mixing matrix and/or mixing matrix ' 'itself not provided. Returning unconvolved power ' 'spectrum.') Pell_dict = self.Pell(k, params, ell, de_model, binning, None, q_tr_lo, W_damping, ell_for_recon) return Pell_dict
[docs] def Pell(self, k, params, ell, de_model=None, binning=None, obs_id=None, q_tr_lo=None, W_damping=None, ell_for_recon=None): r"""Compute the power spectrum multipoles. Main method to compute the galaxy power spectrum multipoles. Returns the specified multipole at the given wavemodes :math:`k`. Parameters ---------- k: float or list or numpy.ndarray Wavemodes :math:`k` at which to evaluate the multipoles. If a list is passed, it has to match the size of `ell`, and in that case each wavemode refer to a given multipole. params: dict Dictionary containing the list of total model parameters which are internally used by the emulator. The keyword/value pairs of the dictionary specify the names and the values of the parameters, respectively. ell: int or list Specific multipole order :math:`\ell`. Can be chosen from the list [0,2,4,6], whose entries correspond to monopole (:math:`\ell=0`), quadrupole (:math:`\ell=2`), hexadecapole (:math:`\ell=4`) and octopole (:math:`\ell=6`). de_model: str, optional String that determines the dark energy equation of state. Can be chosen from the list [`"lambda"`, `"w0"`, `"w0wa"`] to work with the standard cosmological parameters, or be left undefined to use only :math:`\sigma_{12}`. Defaults to **None**. binning: dict, optional obs_id: str, optional If not **None** the returned power spectrum will be convolved with a survey window function. In that case the string must be a valid data set identifier and the window function mixing matrix must have been loaded beforehand. Defaults to **None**. q_tr_lo: list or numpy.ndarray, optional List containing the user-provided AP parameters, in the form :math:`(q_\perp, q_\parallel)`. If provided, prevents computation from correct formulas (ratios of angular diameter distances and expansion factors wrt to the corresponding quantities of the fiducial cosmology). Defaults to **None**. W_damping: Callable[[float, float], float], optional Function returning the shape of the pairwise velocity generating function in the large scale limit, :math:`r\rightarrow\infty`. The function accepts two floats as arguments, corresponding to the wavemode :math:`k` and the cosinus of the angle between pair separation and line of sight :math:`\mu`, and returns a float. This function is used only with the **VDG_infty** model. If **None**, it uses the free kurtosis distribution defined by **W_kurt**. Defaults to **None**. ell_for_recon: list, optional List of :math:`\ell` values used for the reconstruction of the 2d leading-order IR-resummed power spectrum. If **None**, all the even multipoles up to :math:`\ell=6` are used in the reconstruction. Defaults to **None**. Returns ------- Pell_dict: dict Dictionary containing all the requested power spectrum multipoles of order :math:`\ell` at the specified :math:`k`. """ if ell_for_recon is None: ell_for_recon = [0, 2, 4, 6] if not self.real_space else [0] ell = [ell] if not isinstance(ell, list) else ell if isinstance(k, list): if len(k) != len(ell): raise ValueError("If 'k' is given as a list, it must match the " "length of 'ell'.") else: k_list = k k = np.unique(np.hstack(k_list)) else: k_list = [k]*len(ell) k = np.unique(np.hstack(k_list)) use_effective_modes = False if binning is not None: if self.grid is None: self.grid = Grid(binning['kfun'], binning['dk']) else: self.grid.update(binning['kfun'], binning['dk']) self.grid.find_discrete_modes(k, **binning) if binning.get('effective') is not None: use_effective_modes = binning['effective'] if use_effective_modes: self.grid.compute_effective_modes(k, **binning) keff = self.grid.keff if use_effective_modes else k def P2d(q, mu): t = 0.0 for m in ell_for_recon: t += self._eval_Pell_spline(q, m).reshape(q.shape) \ * eval_legendre(m, mu) return t def P2d_stoch(q, mu): t = self.params['NP0'] + q**2 * (self.params['NP20'] \ + self.params['NP22']*eval_legendre(2,mu)) return t/self.nbar if self.RSD_model == 'EFT': if binning is None or use_effective_modes: def integrand(mu): mu2 = mu**2 APfac = np.sqrt(mu2/self.params['q_lo']**2 + (1.0 - mu2)/self.params['q_tr']**2) kp = np.outer(keff, APfac) mup = mu/self.params['q_lo']/APfac P2d_tot = P2d(kp, mup) + P2d_stoch(kp, mup) legendre = np.array([eval_legendre(l, mu) for l in ell]) return np.einsum("ab,cb->acb", P2d_tot, legendre) else: def shell_average(): mu2 = self.grid.mu**2 APfac = np.sqrt(mu2/self.params['q_lo']**2 + (1.0 - mu2)/self.params['q_tr']**2) kp = self.grid.k*APfac mup = self.grid.mu/self.params['q_lo']/APfac legendre = np.array([eval_legendre(l, self.grid.mu) for l in ell]) prod = (P2d(kp, mup) + P2d_stoch(kp, mup)) * legendre avg = np.zeros([len(self.grid.nmodes)-1, len(ell)]) for i in range(len(self.grid.nmodes)-1): n1 = self.grid.nmodes[i] n2 = self.grid.nmodes[i+1] avg[i] = np.average(prod[:,n1:n2], axis=1, weights=self.grid.weights[n1:n2]) return avg elif self.RSD_model == 'VDG_infty': if W_damping is None: W_damping = self.W_kurt if binning is None or use_effective_modes: def integrand(mu): mu2 = mu**2 APfac = np.sqrt(mu2/self.params['q_lo']**2 + (1.0 - mu2)/self.params['q_tr']**2) kp = np.outer(keff, APfac) mup = mu/self.params['q_lo']/APfac P2d_damped = P2d(kp, mup) * W_damping(kp, mup) P2d_tot = P2d_damped + P2d_stoch(kp, mup) legendre = np.array([eval_legendre(l, mu) for l in ell]) return np.einsum("ab,cb->acb", P2d_tot, legendre) else: def shell_average(): mu2 = self.grid.mu**2 APfac = np.sqrt(mu2/self.params['q_lo']**2 + (1.0 - mu2)/self.params['q_tr']**2) kp = self.grid.k*APfac mup = self.grid.mu/self.params['q_lo']/APfac legendre = np.array([eval_legendre(l, self.grid.mu) for l in ell]) P2d_damped = P2d(kp, mup) * W_damping(kp, mup) prod = (P2d_damped + P2d_stoch(kp, mup)) * legendre avg = np.zeros([len(self.grid.nmodes)-1, len(ell)]) for i in range(len(self.grid.nmodes)-1): n1 = self.grid.nmodes[i] n2 = self.grid.nmodes[i+1] avg[i] = np.average(prod[:,n1:n2], axis=1, weights=self.grid.weights[n1:n2]) return avg else: raise ValueError('Unsupported RSD model.') if obs_id is None: params_updated = [params[p] != self.params[p] for p in params.keys()] params_nonzero = [x for x in self.bias_params_list + self.RSD_params_list if self.params[x] != 0] if (any(params_updated) or any(p not in params.keys() for p in params_nonzero) or not self.splines_up_to_date): Pell = self._Pell_fid_ktable(params, ell=ell_for_recon, de_model=de_model) for i, m in enumerate(ell_for_recon): self._build_Pell_spline(Pell[:, i], m) self.splines_up_to_date = True # self.X_splines_up_to_date = {X: False for X in self.diagrams_all} # self.chi2_decomposition = None self._update_AP_params(params, de_model=de_model, q_tr_lo=q_tr_lo) q3 = self.params['q_tr']**2 * self.params['q_lo'] if binning is None or use_effective_modes: Pell_model = 0.5 * np.dot(integrand(self.gl_x), self.gl_weights) else: Pell_model = shell_average() Pell_model *= (2.0*np.array(ell)+1.0) / q3 Pell_dict = {} for i, m in enumerate(ell): ids = np.intersect1d(k, k_list[i], return_indices=True)[1] Pell_dict['ell{}'.format(m)] = Pell_model[ids, i] else: mixing_matrix_exists = True try: self.data[obs_id].bins_mixing_matrix except AttributeError: mixing_matrix_exists = False try: self.data[obs_id].W_mixing_matrix except AttributeError: mixing_matrix_exists = False if mixing_matrix_exists: ell_for_mixing_matrix = [0,2,4] if not self.real_space else [0] Pell_model = self.Pell( self.data[obs_id].bins_mixing_matrix_compressed, params, ell_for_mixing_matrix, de_model, obs_id=None, q_tr_lo=q_tr_lo, W_damping=W_damping, ell_for_recon=ell_for_recon) Pell_list = [] for l in ell_for_mixing_matrix: spline = UnivariateSpline( self.data[obs_id].bins_mixing_matrix_compressed, Pell_model['ell{}'.format(l)], k=3, s=0) Pell_list = np.hstack( [Pell_list, spline(self.data[obs_id].bins_mixing_matrix[1])]) Pell_convolved = np.dot(self.data[obs_id].W_mixing_matrix, Pell_list) nb = len(self.data[obs_id].bins_mixing_matrix[0]) Pell_dict = {} if k.size != np.intersect1d( k, self.data[obs_id].bins_mixing_matrix[0]).size: for i, m in enumerate(ell): spline = UnivariateSpline( self.data[obs_id].bins_mixing_matrix[0], Pell_convolved[int(m/2)*nb:(int(m/2)+1)*nb], k=3, s=0) Pell_dict['ell{}'.format(m)] = spline(k_list[i]) else: for i, m in enumerate(ell): ids = np.intersect1d( k_list[i], self.data[obs_id].bins_mixing_matrix[0], return_indices=True)[1] Pell_dict['ell{}'.format(m)] = Pell_convolved[ids + int(m/2)*nb] else: print('Warning! Bins for mixing matrix and/or mixing matrix ' 'itself not provided. Returning unconvolved power ' 'spectrum.') Pell_dict = self.Pell(k, params, ell, de_model, binning, None, q_tr_lo, W_damping, ell_for_recon) return Pell_dict
[docs] def Pell_fixed_cosmo_boost(self, k, params, ell, de_model=None, binning=None, obs_id=None, q_tr_lo=None, W_damping=None, ell_for_recon=None): r"""Compute the power spectrum multipoles (fast for fixed cosmology). Main method to compute the galaxy power spectrum multipoles. Returns the specified multipole at the given wavemodes :math:`k`. Differently from **Pell**, if the cosmology has not been varied from the last call, this method simply reconstruct the final multipoles by multiplying the stored model ingredients (which, at fixed cosmology are the same) by the new bias parameters. Parameters ---------- k: float or list or numpy.ndarray Wavemodes :math:`k` at which to evaluate the multipoles. If a list is passed, it has to match the size of `ell`, and in that case each wavemode refer to a given multipole. params: dict Dictionary containing the list of total model parameters which are internally used by the emulator. The keyword/value pairs of the dictionary specify the names and the values of the parameters, respectively. ell: int or list pecific multipole order :math:`\ell`. Can be chosen from the list [0,2,4,6], whose entries correspond to monopole (:math:`\ell=0`), quadrupole (:math:`\ell=2`), hexadecapole (:math:`\ell=4`) and octopole (:math:`\ell=6`). de_model: str, optional String that determines the dark energy equation of state. Can be chosen from the list [`"lambda"`, `"w0"`, `"w0wa"`] to work with the standard cosmological parameters, or be left undefined to use only :math:`\sigma_{12}`. Defaults to **None**. binning: dict, optional obs_id: str, optional If not **None** the returned power spectrum will be convolved with a survey window function. In that case the string must be a valid data set identifier and the window function mixing matrix must have been loaded beforehand. Defaults to **None**. q_tr_lo: list or numpy.ndarray, optional List containing the user-provided AP parameters, in the form :math:`(q_\perp, q_\parallel)`. If provided, prevents computation from correct formulas (ratios of angular diameter distances and expansion factors wrt to the corresponding quantities of the fiducial cosmology). Defaults to **None**. W_damping: Callable[[float, float], float], optional Function returning the shape of the pairwise velocity generating function in the large scale limit, :math:`r\rightarrow\infty`. The function accepts two floats as arguments, corresponding to the wavemode :math:`k` and the cosinus of the angle between pair separation and line of sight :math:`\mu`, and returns a float. This function is used only with the **VDG_infty** model. If **None**, it uses the free kurtosis distribution defined by **W_kurt**. Defaults to **None**. ell_for_recon: list, optional List of :math:`\ell` values used for the reconstruction of the 2d leading-order IR-resummed power spectrum. If **None**, all the even multipoles up to :math:`\ell=6` are used in the reconstruction. Defaults to **None**. Returns ------- Pell_dict: dict Dictionary containing all the requested power spectrum multipoles of order :math:`\ell` at the specified :math:`k`. """ ell = [ell] if not isinstance(ell, list) else ell if isinstance(k, list): if len(k) != len(ell): raise ValueError("If 'k' is given as a list, it must match the" " length of 'ell'.") else: k_list = k k = np.unique(np.hstack(k_list)) else: k_list = [k]*len(ell) if de_model is None and self.use_Mpc: check_params = self.params_list + self.RSD_params_list elif de_model is None and not self.use_Mpc: check_params = self.params_list + ['h'] + self.RSD_params_list else: check_params = self.params_shape_list \ + self.de_model_params_list[de_model] \ + self.RSD_params_list if 'Ok' not in params: check_params.remove('Ok') for p in self.RSD_params_list: if p not in params: check_params.remove(p) if obs_id != self.X_obs_id: self.X_splines_up_to_date = {X: False for X in self.diagrams_all} self.X_obs_id = obs_id if binning != self.X_binning: self.X_splines_up_to_date = {X: False for X in self.diagrams_all} self.X_binning = binning if (any(params[p] != self.params[p] for p in check_params) or not all(self.X_splines_up_to_date.values())): self.PX_ell_list = { 'ell{}'.format(m): np.zeros( [k_list[i].shape[0], len(self.diagrams_all)]) for i, m in enumerate(ell)} for i, X in enumerate(self.diagrams_all): PX_ell = self.PX_ell(k_list, params, ell, X, de_model=de_model, binning=self.X_binning, obs_id=self.X_obs_id, q_tr_lo=q_tr_lo, W_damping=W_damping, ell_for_recon=ell_for_recon) for m in PX_ell.keys(): self.PX_ell_list[m][:, i] = PX_ell[m] for p in self.bias_params_list: if p in params.keys(): self.params[p] = params[p] else: self.params[p] = 0.0 # self.splines_up_to_date = False # self.dw_spline_up_to_date = False bX = self._get_bias_coeff_for_chi2_decomposition() Pell_dict = {} for i, m in enumerate(ell): Pell_dict['ell{}'.format(m)] = np.dot( self.PX_ell_list['ell{}'.format(m)], bX) return Pell_dict
[docs] def PX(self, k, mu, params, X, de_model=None): r"""Compute the individual contribution X to the galaxy power spectrum. Returns the individual anisotropic contribution X to the galaxy power spectrum :math:`P_\mathrm{gg}(k,\mu)`. Parameters ---------- k: float or list or numpy.ndarray Wavemodes :math:`k` at which to evaluate the X contribution. mu: float or list or numpy.ndarray Cosinus :math:`\mu` between the pair separation and the line of sight at which to evaluate the X contribution. params: dict Dictionary containing the list of total model parameters which are internally used by the emulator. The keyword/value pairs of the dictionary specify the names and the values of the parameters, respectively. X: str Identifier of the contribution to the galaxy power spectrum. Can be chosen from the list [`"P0L_b1b1"`, `"PNL_b1"`, `"PNL_id"`, `"Pctr_c0"`, `"Pctr_c2"`, `"Pctr_c4"`, `"Pctr_b1b1cnlo"`, `"Pctr_b1cnlo"`, `"Pctr_cnlo"`, `"P1L_b1b1"`, `"P1L_b1b2"`, `"P1L_b1g2"`, `"P1L_b1g21"`, `"P1L_b2b2"`, `"P1L_b2g2"`, `"P1L_g2g2"`, `"P1L_b2"`, `"P1L_g2"`, `"P1L_g21"`]. de_model: str, optional String that determines the dark energy equation of state. Can be chosen from the list [`"lambda"`, `"w0"`, `"w0wa"`] to work with the standard cosmological parameters, or be left undefined to use only :math:`\sigma_{12}`. Defaults to **None**. Returns ------- PX_2d: numpy.ndarray 2-d array containing the X contribution to the galaxy power spectrum at the specified :math:`k` and :math:`\mu`. """ ids = None for n, diagram in enumerate(self.diagrams_emulated): if diagram == X: if n < 9: ids = [n*self.nk, (n+1)*self.nk] else: ids = [9*self.nk + (n-9)*self.nkloop, 9*self.nk + (n-8)*self.nkloop] if ids is not None: ell_for_recon = [0, 2, 4] if not self.real_space else [0] self._eval_emulator(params, ell=ell_for_recon, de_model=de_model) PX_ell = np.zeros([self.nk, 3]) for i, ell in enumerate(ell_for_recon): PX_ell[self.nk - (ids[1]-ids[0]):, i] = \ self.Pk_ratios[ell][ids[0]:ids[1]] PX_ell = (PX_ell.T*self.Pk_lin).T PX_spline = {} for i, ell in enumerate(ell_for_recon): if self.use_Mpc: PX_spline[ell] = UnivariateSpline(self.k_table, PX_ell[:, i], k=3, s=0) else: PX_spline[ell] = UnivariateSpline( self.k_table/self.params['h'], PX_ell[:, i]*self.params['h']**3, k=3, s=0) PX_2d = 0.0 for ell in ell_for_recon: PX_2d += np.outer(PX_spline[ell](k), eval_legendre(ell, mu)) else: raise ValueError('{}: invalid identifier.'.format(X)) return PX_2d
def _PX_ell6_novir_noAP(self, X): r"""Compute the individual contribution X to the octopole. Returns the individual contribution X to the octopole :math:`P_6(k)` of the training sample, multiplying it by the correspondent bias and growth coefficients. Parameters ---------- X: str Identifier of the contribution to the octopole of the galaxy power spectrum. Can be chosen from the list [`"P0L_b1b1"`, `"PNL_b1"`, `"PNL_id"`, `"Pctr_b1b1cnlo"`, `"Pctr_b1cnlo"`, `"Pctr_cnlo"`, `"P1L_b1b1"`, `"P1L_b1b2"`, `"P1L_b1g2"`, `"P1L_b1g21"`, `"P1L_b2b2"`, `"P1L_b2g2"`, `"P1L_g2g2"`, `"P1L_b2"`, `"P1L_g2"`, `"P1L_g21"`]. Returns ------- P6X: numpy.ndarray Array containing the X contribution to the octopole :math:`P_6(k)`. """ s12ratio = (self.params['s12']/self.s12_for_P6)**2 s12ratio_sq = s12ratio**2 f = self.params['f'] if X == 'P0L_b1b1': P6X = self.P6[:, 0]*s12ratio elif X == 'PNL_b1': fvec = np.array([f*s12ratio, f*s12ratio_sq, f**2*s12ratio_sq, f**3*s12ratio_sq]) P6X = np.dot(self.P6[:, [1, 6, 7, 8]], fvec) elif X == 'PNL_id': f2 = f**2 fvec = np.array([f2*s12ratio, f2*s12ratio_sq, f*f2*s12ratio_sq, f2**2*s12ratio_sq]) P6X = np.dot(self.P6[:, [2, 9, 10, 11]], fvec) elif X == 'P1L_b1b1': fvec = np.array([1, f, f**2]) P6X = np.dot(self.P6[:, [3, 4, 5]], fvec)*s12ratio_sq elif X == 'P1L_b1b2': fvec = np.array([1, f]) P6X = np.dot(self.P6[:, [12, 13]], fvec)*s12ratio_sq elif X == 'P1L_b1g2': fvec = np.array([1, f]) P6X = np.dot(self.P6[:, [14, 15]], fvec)*s12ratio_sq elif X == 'P1L_b1g21': P6X = self.P6[:, 16]*s12ratio_sq elif X == 'P1L_b2b2': P6X = self.P6[:, 17]*s12ratio_sq elif X == 'P1L_b2g2': P6X = self.P6[:, 18]*s12ratio_sq elif X == 'P1L_g2g2': P6X = self.P6[:, 19]*s12ratio_sq elif X == 'P1L_b2': fvec = np.array([f, f**2]) P6X = np.dot(self.P6[:, [20, 21]], fvec)*s12ratio_sq elif X == 'P1L_g2': fvec = np.array([f, f**2]) P6X = np.dot(self.P6[:, [22, 23]], fvec)*s12ratio_sq elif X == 'P1L_g21': P6X = f*self.P6[:, 24]*s12ratio_sq elif X == 'Pctr_b1b1cnlo': P6X = f**4*self.P6[:, 25]*s12ratio elif X == 'Pctr_b1cnlo': P6X = f**5*self.P6[:, 26]*s12ratio elif X == 'Pctr_cnlo': P6X = f**6*self.P6[:, 27]*s12ratio return P6X
[docs] def PX_ell(self, k, params, ell, X, de_model=None, binning=None, obs_id=None, q_tr_lo=None, W_damping=None, ell_for_recon=None): r"""Get the individual contribution to the power spectrum multipoles. Computes the individual contribution X to the galaxy power spectrum multipoles. Returns the contribution to the specified multipole at the specified wavemodes :math:`k`. Parameters ---------- k: float or list or numpy.ndarray Wavemodes :math:`k` at which to evaluate the multipoles. If a list is passed, it has to match the size of `ell`, and in that case each wavemode refer to a given multipole. params: dict Dictionary containing the list of total model parameters which are internally used by the emulator. The keyword/value pairs of the dictionary specify the names and the values of the parameters, respectively. ell: int or list pecific multipole order :math:`\ell`. Can be chosen from the list [0,2,4,6], whose entries correspond to monopole (:math:`\ell=0`), quadrupole (:math:`\ell=2`), hexadecapole (:math:`\ell=4`) and octopole (:math:`\ell=6`). X: str Identifier of the contribution to the galaxy power spectrum. Can be chosen from the list [`"P0L_b1b1"`, `"PNL_b1"`, `"PNL_id"`, `"Pctr_c0"`, `"Pctr_c2"`, `"Pctr_c4"`, `"Pctr_b1b1cnlo"`, `"Pctr_b1cnlo"`, `"Pctr_cnlo"`, `"P1L_b1b1"`, `"P1L_b1b2"`, `"P1L_b1g2"`, `"P1L_b1g21"`, `"P1L_b2b2"`, `"P1L_b2g2"`, `"P1L_g2g2"`, `"P1L_b2"`, `"P1L_g2"`, `"P1L_g21"`, `"Pnoise_NP0"`, `"Pnoise_NP20"`, `"Pnoise_NP22"`]. de_model: str, optional String that determines the dark energy equation of state. Can be chosen from the list [`"lambda"`, `"w0"`, `"w0wa"`] to work with the standard cosmological parameters, or be left undefined to use only :math:`\sigma_{12}`. Defaults to **None**. binning: dict, optional obs_id: str, optional If not **None** the returned power spectrum contribution will be convolved with a survey window function. In that case the string must be a valid data set identifier and the window function mixing matrix must have been loaded beforehand. Defaults to **None**. q_tr_lo: list or numpy.ndarray, optional List containing the user-provided AP parameters, in the form :math:`(q_\perp, q_\parallel)`. If provided, prevents computation from correct formulas (ratios of angular diameter distances and expansion factors wrt to the corresponding quantities of the fiducial cosmology). Defaults to **None**. W_damping: Callable[[float, float], float], optional Function returning the shape of the pairwise velocity generating function in the large scale limit, :math:`r\rightarrow\infty`. The function accepts two floats as arguments, corresponding to the wavemode :math:`k` and the cosinus of the angle between pair separation and line of sight :math:`\mu`, and returns a float. This function is used only with the **VDG_infty** model. If **None**, it uses the free kurtosis distribution defined by **W_kurt**. Defaults to **None**. ell_for_recon: list, optional List of :math:`\ell` values used for the reconstruction of the 2d leading-order IR-resummed power spectrum. If **None**, all the even multipoles up to :math:`\ell=6` are used in the reconstruction. Defaults to **None**. Returns ------- PX_ell_dict: dict Dictionary containing the contributions to all the requested power spectrum multipoles of order :math:`\ell` at the specified :math:`k`. """ if ell_for_recon is None: ell_for_recon = [0, 2, 4, 6] if not self.real_space else [0] ell_eval_emu = ell_for_recon.copy() try: ell_eval_emu.remove(6) except Exception: pass ell = [ell] if not isinstance(ell, list) else ell if isinstance(k, list): if len(k) != len(ell): raise ValueError("If 'k' is given as a list, it must match the" " length of 'ell'.") else: k_list = k k = np.unique(np.hstack(k_list)) else: k_list = [k]*len(ell) use_effective_modes = False if binning is not None: if self.grid is None: self.grid = Grid(binning['kfun'], binning['dk']) else: self.grid.update(binning['kfun'], binning['dk']) if binning.get('do_rounding') is None: self.grid.find_discrete_modes(k) if binning.get('effective') is not None: use_effective_modes = binning['effective'] if use_effective_modes: self.grid.compute_effective_modes(k) else: self.grid.find_discrete_modes(k, binning['do_rounding'], binning['decimals']) if binning.get('effective') is not None: use_effective_modes = binning['effective'] if use_effective_modes: self.grid.compute_effective_modes(k, binning['do_rounding'], binning['decimals']) keff = self.grid.keff if use_effective_modes else k def P2d(q, mu): t = 0.0 for m in ell_for_recon: t += self.PX_ell_spline[X][m](q).reshape(q.shape) \ * eval_legendre(m, mu) return t if self.RSD_model == 'EFT': if binning is None or use_effective_modes: def integrand(mu): mu2 = mu**2 APfac = np.sqrt(mu2/self.params['q_lo']**2 + (1.0 - mu2)/self.params['q_tr']**2) kp = np.outer(keff, APfac) mup = mu/self.params['q_lo']/APfac legendre = np.array([eval_legendre(l, mu) for l in ell]) return np.einsum("ab,cb->acb", P2d(kp, mup), legendre) else: def shell_average(): mu2 = self.grid.mu**2 APfac = np.sqrt(mu2/self.params['q_lo']**2 + (1.0 - mu2)/self.params['q_tr']**2) kp = self.grid.k*APfac mup = self.grid.mu/self.params['q_lo']/APfac legendre = np.array([eval_legendre(l, self.grid.mu) for l in ell]) prod = P2d(kp, mup) * legendre avg = np.zeros([len(self.grid.nmodes)-1, len(ell)]) for i in range(len(self.grid.nmodes)-1): n1 = self.grid.nmodes[i] n2 = self.grid.nmodes[i+1] avg[i] = np.average(prod[:,n1:n2], axis=1, weights=self.grid.weights[n1:n2]) return avg elif self.RSD_model == 'VDG_infty': if W_damping is None: W_damping = self.W_kurt if X in ['Pnoise_NP0', 'Pnoise_NP20', 'Pnoise_NP22']: W_damping = lambda k,mu: 1.0 if binning is None or use_effective_modes: def integrand(mu): mu2 = mu**2 APfac = np.sqrt(mu2/self.params['q_lo']**2 + (1.0 - mu2)/self.params['q_tr']**2) kp = np.outer(keff, APfac) mup = mu/self.params['q_lo']/APfac P2d_damped = P2d(kp, mup) * W_damping(kp, mup) legendre = np.array([eval_legendre(l, mu) for l in ell]) return np.einsum("ab,cb->acb", P2d_damped, legendre) else: def shell_average(): mu2 = self.grid.mu**2 APfac = np.sqrt(mu2/self.params['q_lo']**2 + (1.0 - mu2)/self.params['q_tr']**2) kp = self.grid.k*APfac mup = self.grid.mu/self.params['q_lo']/APfac legendre = np.array([eval_legendre(l, self.grid.mu) for l in ell]) prod = P2d(kp, mup) * W_damping(kp, mup) * legendre avg = np.zeros([len(self.grid.nmodes)-1, len(ell)]) for i in range(len(self.grid.nmodes)-1): n1 = self.grid.nmodes[i] n2 = self.grid.nmodes[i+1] avg[i] = np.average(prod[:,n1:n2], axis=1, weights=self.grid.weights[n1:n2]) return avg else: raise ValueError('Unsupported RSD model.') if obs_id is None: PX_ell = np.zeros([self.nk, len(ell_for_recon)]) X_emu = X if X_emu in self.diagrams_emulated: for n, diagram in enumerate(self.diagrams_emulated): if diagram == X_emu: if n < 9: ids = [n*self.nk, (n+1)*self.nk] else: ids = [9*self.nk + (n-9)*self.nkloop, 9*self.nk + (n-8)*self.nkloop] self._eval_emulator(params, ell=ell_eval_emu, de_model=de_model) if X_emu in ['Pctr_c0', 'Pctr_c2', 'Pctr_c4']: for i, m in enumerate(ell_eval_emu): PX_ell[self.nk - (ids[1]-ids[0]):, i] = \ self.Pk_ratios[m][ids[0]:ids[1]] else: for i, m in enumerate(ell_for_recon): if m != 6: PX_ell[self.nk - (ids[1]-ids[0]):, i] = \ self.Pk_ratios[m][ids[0]:ids[1]] else: PX_ell[:, i] = self._PX_ell6_novir_noAP(X_emu) PX_ell[:,:len(ell_eval_emu)] = (PX_ell[:,:len(ell_eval_emu)].T \ * self.Pk_lin).T else: if X_emu == 'Pnoise_NP0': PX_ell[:, 0] = np.ones_like(self.k_table) elif X_emu == 'Pnoise_NP20': PX_ell[:, 0] = self.k_table**2 elif X_emu == 'Pnoise_NP22' and len(ell_for_recon) > 1: PX_ell[:, 1] = self.k_table**2 for i, m in enumerate(ell_for_recon): if self.use_Mpc: self.PX_ell_spline[X][m] = UnivariateSpline(self.k_table, PX_ell[:, i], k=3, s=0) else: self.PX_ell_spline[X][m] = UnivariateSpline( self.k_table/self.params['h'], PX_ell[:, i]*self.params['h']**3, k=3, s=0) self.X_splines_up_to_date[X] = True self._update_AP_params(params, de_model=de_model, q_tr_lo=q_tr_lo) q3 = self.params['q_tr']**2 * self.params['q_lo'] if binning is None or use_effective_modes: PX_ell_model = 0.5 * np.dot(integrand(self.gl_x), self.gl_weights) else: PX_ell_model = shell_average() PX_ell_model *= (2.0*np.array(ell)+1.0) / q3 PX_ell_dict = {} for i, m in enumerate(ell): ids = np.intersect1d(k, k_list[i], return_indices=True)[1] PX_ell_dict['ell{}'.format(m)] = PX_ell_model[ids, i] else: mixing_matrix_exists = True try: self.data[obs_id].bins_mixing_matrix except AttributeError: mixing_matrix_exists = False try: self.data[obs_id].W_mixing_matrix except AttributeError: mixing_matrix_exists = False if mixing_matrix_exists: ell_for_mixing_matrix = [0,2,4] if not self.real_space else [0] PX_ell_model = self.PX_ell( self.data[obs_id].bins_mixing_matrix_compressed, params, ell_for_mixing_matrix, X, de_model, obs_id=None, q_tr_lo=q_tr_lo, W_damping=W_damping, ell_for_recon=ell_for_recon) PX_ell_list = [] for l in ell_for_mixing_matrix: spline = UnivariateSpline( self.data[obs_id].bins_mixing_matrix_compressed, PX_ell_model['ell{}'.format(l)], k=3, s=0) PX_ell_list = np.hstack( [PX_ell_list, spline(self.data[obs_id].bins_mixing_matrix[1])]) PX_ell_convolved = np.dot(self.data[obs_id].W_mixing_matrix, PX_ell_list) nb = len(self.data[obs_id].bins_mixing_matrix[0]) PX_ell_dict = {} if k.size != np.intersect1d( k, self.data[obs_id].bins_mixing_matrix[0]).size: for i, m in enumerate(ell): spline = UnivariateSpline( self.data[obs_id].bins_mixing_matrix[0], PX_ell_convolved[int(m/2)*nb:(int(m/2)+1)*nb], k=3, s=0) PX_ell_dict['ell{}'.format(m)] = spline(k_list[i]) else: for i, m in enumerate(ell): ids = np.intersect1d( k_list[i], self.data[obs_id].bins_mixing_matrix[0], return_indices=True)[1] PX_ell_dict['ell{}'.format(m)] = PX_ell_convolved[ids + int(m/2)*nb] else: print('Warning! Bins for mixing matrix and/or mixing matrix ' 'itself not provided. Returning unconvolved power ' 'spectrum.') PX_ell_dict = self.PX_ell(k, params, ell, X, de_model, binning, None, q_tr_lo, W_damping, ell_for_recon) return PX_ell_dict
[docs] def Bell(self, tri, params, ell, de_model=None, kfun=None, binning=None, q_tr_lo=None, W_damping=None, ell_for_recon=None, gl_deg=8, cnloB_mapping=None): ell = [ell] if not isinstance(ell, list) else ell if tri.ndim == 1: tri = tri[None,:] tri_sorted = np.flip(np.sort(tri, axis=1), axis=1) if np.any(tri != tri_sorted): tri = tri_sorted print('Warning. Triangle configurations sorted such that ' 'k1 >= k2 >= k3.') if self.RSD_model == 'VDG_infty': if W_damping is None: W_damping = self.WB_kurt else: W_damping = None tri_has_changed, binning_has_changed = \ self.Bisp.set_tri(tri, ell, kfun, gl_deg, binning) if binning: tri_unique = self.Bisp.tri_eff_unique if not binning.get('effective', False) \ and (tri_has_changed or binning_has_changed): self.Bisp.set_fiducial_cosmology(params) Pdw_eff = self.Pdw(tri_unique, self.Bisp.fiducial_cosmology, de_model, ell_for_recon) self.Bisp.init_Pdw_eff(Pdw_eff) if self.Bisp.generate_discrete_kernels: # print('Recompute (binned) kernels!') Pdw = np.array([ self.Pdw(self.Bisp.grid.kmu123[:,j], self.Bisp.fiducial_cosmology, de_model, ell_for_recon) for j in range(3) ]).T self.Bisp.init_Pdw(Pdw, ell) self.Bisp.compute_kernels_shell_average(max(ell)) else: # print('Load (binned) kernels!') self.Bisp.load_kernels_shell_average() else: tri_unique = self.Bisp.tri_unique Pdw = self.Pdw(tri_unique, params, de_model=de_model, ell_for_recon=ell_for_recon) if self.real_space: neff = None else: neff = tri_unique*self.Pdw_spline.derivative(n=1)(tri_unique)/Pdw if binning and self.RSD_model == 'VDG_infty': if cnloB_mapping is not None: coeff = cnloB_mapping([self.params['avirB'], self.params['sv'].squeeze()]) self.params['cnloB'] = \ - (coeff[0]*self.params['avirB']**self.Bisp.pow_ctr \ + 0.5*self.params['sv']**self.Bisp.pow_ctr) self._update_AP_params(params, de_model=de_model, q_tr_lo=q_tr_lo) Bell_dict = self.Bisp.Bell(Pdw, neff, self.params, ell, W_damping) return Bell_dict
[docs] def Avg_covariance(self, l1, l2, k, Pl, sigma_d, avg_los=3): def kxx_int(th, ph,l1, l2, k, b, inv_nbar, Pl, sigma_d): costh2 = np.sin(th)*np.cos(ph) costh1 = np.cos(th) sinth1 = np.sin(th) f= self.cosmo.growth_rate(self.params["z"]) beta = f/b func = sinth1*(b**2 * (1 + beta*costh1**2) * \ (1 + beta*costh2**2) * Pl + inv_nbar * np.exp( -k**2 * ( costh1**2 + costh2**2) * f**2*sigma_d**2/2 ))**2 * eval_legendre(l1, costh1) \ *eval_legendre(l2, costh2) return func def kll_int(th,l1, l2, k, b, inv_nbar, Pl, sigma_d): sinth1 = np.sin(th) costh1 = np.cos(th) f= self.cosmo.growth_rate(self.params["z"]) beta = f/b func = 2*np.pi* sinth1 * ( b**2*(1 + beta*costh1**2)**2*Pl \ + inv_nbar )**2 * eval_legendre(l1, costh1)* \ eval_legendre(l2,costh1) return func kxx_l1l2 = np.asarray([ dblquad(kxx_int, 0, 2*np.pi, lambda ph: 0, lambda th: 1*np.pi, args=(l1,l2, k[i], self.params["b1"], 1/self.nbar, Pl[i], sigma_d) )[0] for i in range(len(k)) ]) kll_l1l2 = np.asarray([ quad(kll_int,0, np.pi, args=(l1, l2, k[i], self.params["b1"], 1/self.nbar, Pl[i], sigma_d))[0] for i in range(len(k)) ]) if avg_los==3: return (1+2*(kxx_l1l2/kll_l1l2))/3 elif avg_los==2: return (1+(kxx_l1l2/kll_l1l2))/2
def _Gaussian_covariance(self, l1, l2, k, dk, Pell, volume, Nmodes=None, avg_cov=False, avg_los=3): r"""Compute the gaussian covariance of the power spectrum multipoles. Returns the gaussian covariance predictions for the specified power spectrum multipoles (of order :math:`\ell_1` and :math:`\ell_2`), at the specified wavemodes :math:`k`, and for the given volume. Parameters ---------- l1: int Order of first power spectrum multipole. l2: int Order of second power spectrum multipole. k: numpy.ndarray Wavemodes :math:`k` at which to evaluate the gaussian covariance. dk: float Width of the :math:`k` bins. Pell: dict Dictionary containing the monopole, quadrupole and hexadecapole of the power spectrum. volume: float Reference volume to be used in the calculation of the gaussian covariance. Nmodes: numpy.ndarray, optional Number of modes contained in each :math:`k` bin. If not provided, its calculation is carried out based on the value of :math:`k` and :math:`\mathrm{d}k`. Defaults to **None**. Returns ------- cov: numpy.ndarray Gaussian covariance of the selected power spectrum multipoles. """ if Nmodes is None: Nmodes = volume/3.0/(2.0*np.pi**2)*((k+dk/2.0)**3 - (k-dk/2.0)**3) if not self.real_space: P0 = Pell['ell0'] P2 = Pell['ell2'] P4 = Pell['ell4'] if l1 == l2 == 0: cov = P0**2 + 1.0/5.0*P2**2 + 1.0/9.0*P4**2 elif l1 == 0 and l2 == 2: cov = (2.0*P0*P2 + 2.0/7.0*P2**2 + 4.0/7.0*P2*P4 + 100.0/693.0*P4**2) elif l1 == l2 == 2: cov = (5.0*P0**2 + 20.0/7.0*P0*P2 + 20.0/7.0*P0*P4 + 15.0/7.0*P2**2 + 120.0/77.0*P2*P4 + 8945.0/9009.0*P4**2) elif l1 == 0 and l2 == 4: cov = (2.0*P0*P4 + 18.0/35.0*P2**2 + 40.0/77.0*P2*P4 + 162.0/1001.0*P4**2) elif l1 == 2 and l2 == 4: cov = (36.0/7.0*P0*P2 + 200.0/77.0*P0*P4 + 108.0/77.0*P2**2 + 3578.0/1001.0*P2*P4 + 900.0/1001.0*P4**2) elif l1 == l2 == 4: cov = (9.0*P0**2 + 360.0/77.0*P0*P2 + 2916.0/1001.0*P0*P4 + 16101.0/5005.0*P2**2 + 3240.0/1001.0*P2*P4 + 42849.0/17017.0*P4**2) else: cov = Pell['ell0']**2 if avg_cov: Pl = self.PL(k,self.params, de_model="lambda") sigma_d = np.sqrt(quad(self.PL, np.min(k), np.max(k) , args=(self.params, "lambda") )[0] / (6*np.pi**2) ) avg = self.Avg_covariance(l1, l2, k, Pl, sigma_d, avg_los) else: avg=1. cov *= 2.0/Nmodes*avg return cov
[docs] def Pell_covariance(self, k, params, ell, dk, de_model=None, q_tr_lo=None, W_damping=None, volume=None, zmin=None, zmax=None, fsky=15000.0/(360.0**2/np.pi), Nmodes=None, volfac=1.0, avg_cov=False, avg_los=3): r"""Compute the Gaussian covariance of the power spectrum multipoles. Generates the selected power spectrum multipoles for the specified set of parameters, and returns their Gaussian covariance predictions at the specified wavemodes :math:`k`. Parameters ---------- k: float or list or numpy.ndarray Wavemodes :math:`k` at which to evaluate the multipoles. If a list is passed, it has to match the size of `ell`, and in that case each wavemode refer to a given multipole. params: dict Dictionary containing the list of total model parameters which are internally used by the emulator. The keyword/value pairs of the dictionary specify the names and the values of the parameters, respectively. ell: int or list pecific multipole order :math:`\ell`. Can be chosen from the list [0,2,4,6], whose entries correspond to monopole (:math:`\ell=0`), quadrupole (:math:`\ell=2`), hexadecapole (:math:`\ell=4`) and octopole (:math:`\ell=6`). dk: float Width of the :math:`k` bins. de_model: str, optional String that determines the dark energy equation of state. Can be chosen from the list [`"lambda"`, `"w0"`, `"w0wa"`] to work with the standard cosmological parameters, or be left undefined to use only :math:`\sigma_{12}`. Defaults to **None**. q_tr_lo: list or numpy.ndarray, optional List containing the user-provided AP parameters, in the form :math:`(q_\perp, q_\parallel)`. If provided, prevents computation from correct formulas (ratios of angular diameter distances and expansion factors wrt to the corresponding quantities of the fiducial cosmology). Defaults to **None**. W_damping: Callable[[float, float], float], optional Function returning the shape of the pairwise velocity generating function in the large scale limit, :math:`r\rightarrow\infty`. The function accepts two floats as arguments, corresponding to the wavemode :math:`k` and the cosinus of the angle between pair separation and line of sight :math:`\mu`, and returns a float. This function is used only with the **VDG_infty** model. If **None**, it uses the free kurtosis distribution defined by **W_kurt**. Defaults to **None**. volume: float, optional Reference volume to be used in the calculation of the gaussian covariance. Defaults to **None**. zmin: float, optional Minimum redshift of the volume used in the calculation of the gaussian covariance. Defaults to **None**. zmin: float, optional Maximum redshift of the volume used in the calculation of the gaussian covariance. Defaults to **None**. fsky: float, optional Sky fraction of the volume used in the calculation of the gaussian covariance (in units of radians). Defaults to :math:`15000\mathrm{deg}^2`. Nmodes: numpy.ndarray, optional Number of fundamental modes per :math:`k-shell. The size of the array should match the size of ``k``. Defaults to :math:`4\pi/3\,\left[(k+\Delta k/2)^3 - (k-\Delta k/2)^3\right] /k_f^3`, where :math:`k_f^3 = (2 \pi)^3/V`. volfac: float, optional Rescaling volume fraction. Defaults to :math:`1`. Returns ------- cov: numpy.ndarray Gaussian covariance of the selected power spectrum multipoles. """ ell = [ell] if not isinstance(ell, list) else ell if not isinstance(k, list): k = [np.array(k)]*len(ell) elif isinstance(k, list) and len(k) != len(ell): raise ValueError("If 'k' is given as a list, it must match the " "length of 'ell'.") else: k = [np.array(x) for x in k] nbins = [x.shape[0] for x in k] cov = np.zeros([sum(nbins), sum(nbins)]) k_all = np.unique(np.hstack(k)) ell_for_cov = [0, 2, 4] if not self.real_space else 0 Pell = self.Pell(k_all, params, ell=ell_for_cov, de_model=de_model, q_tr_lo=q_tr_lo, W_damping=W_damping) Pell['ell0'] += 1.0/self.nbar if de_model is not None and volume is None: Om0 = (self.params['wc']+self.params['wb'])/self.params['h']**2 H0 = 100.0*self.params['h'] self.cosmo.update_cosmology(Om0=Om0, H0=H0, Ok0=self.params['Ok'], de_model=de_model, w0=self.params['w0'], wa=self.params['wa']) volume = volfac*self.cosmo.comoving_volume(zmin, zmax, fsky) if not self.use_Mpc: volume *= self.params['h']**3 elif de_model is None and volume is None: raise ValueError("If no dark energy model is specified, a value " "for the volume must be provided.") for i, l1 in enumerate(ell): for j, l2 in enumerate(ell): if j >= i: kij, id1, id2 = np.intersect1d(k[i], k[j], return_indices=True) ids_ij = np.intersect1d(k_all, kij, return_indices=True)[1] cov_l1l2 = self._Gaussian_covariance( l1, l2, k_all, dk, Pell, volume, Nmodes, avg_cov=avg_cov, avg_los=avg_los)[ids_ij] cov[sum(nbins[:i]):sum(nbins[:i+1]), sum(nbins[:j]):sum(nbins[:j+1])][id1, id2] = cov_l1l2 else: cov[sum(nbins[:i]):sum(nbins[:i+1]), sum(nbins[:j]):sum(nbins[:j+1])] = \ cov[sum(nbins[:j]):sum(nbins[:j+1]), sum(nbins[:i]):sum(nbins[:i+1])].T return cov
[docs] def Bell_covariance(self, tri, params, ell, dk, de_model=None, kfun=None, q_tr_lo=None, W_damping=None, volume=None, zmin=None, zmax=None, fsky=15000.0/(360.0**2/np.pi), Ntri=None, volfac=1.0): r"""Compute the Gaussian covariance of the bispectrum multipoles. Returns the Gaussian covariance predictions for the specified multipole numbers at the given parameters and triangle configurations :math:`k_1`, :math:`k_2`, :math:`k_3`. Parameters ---------- tri: numpy.ndarray or list of numpy.ndarray Wavemodes :math:`k_1`, :math:`k_2`, :math:`k_3` at which to evaluate the predictions. If a list is passed, it has to match the size of `ell`, and in that case each set of configurations refers to a given multipole. params: dict Dictionary containing the list of total model parameters which are internally used by the emulator. The keyword/value pairs of the dictionary specify the names and the values of the parameters, respectively. ell: int or list pecific multipole order :math:`\ell`. Can be chosen from the list [0,2,4], whose entries correspond to monopole (:math:`\ell=0`), quadrupole (:math:`\ell=2`), hexadecapole (:math:`\ell=4`) and octopole (:math:`\ell=6`). dk: float Width of the :math:`k` bins. de_model: str, optional String that determines the dark energy equation of state. Can be chosen from the list [`"lambda"`, `"w0"`, `"w0wa"`] to work with the standard cosmological parameters, or be left undefined to use only :math:`\sigma_{12}`. Defaults to **None**. k_fun: float, optional Fundamental frequency of the grid that was used to compute the bispectrum measurements. This is useful to specify if the triangle configurations are not given in multiples of the fundamental frequency, in which case a compression of the unique :math:`k` modes is performed. Should not be much larger than the bin width. Defaults to :math:`\Delta k`. q_tr_lo: list or numpy.ndarray, optional List containing the user-provided AP parameters, in the form :math:`(q_\perp, q_\parallel)`. If provided, prevents computation from correct formulas (ratios of angular diameter distances and expansion factors wrt to the corresponding quantities of the fiducial cosmology). Defaults to **None**. W_damping: Callable[[float, float], float], optional Function returning the shape of the pairwise velocity generating function in the large scale limit, :math:`r\rightarrow\infty`. The function accepts two floats as arguments, corresponding to the wavemode :math:`k` and the cosinus of the angle between pair separation and line of sight :math:`\mu`, and returns a float. This function is used only with the **VDG_infty** model. If **None**, it uses the free kurtosis distribution defined by **W_kurt**. Defaults to **None**. volume: float, optional Reference volume to be used in the calculation of the gaussian covariance. Defaults to **None**. zmin: float, optional Minimum redshift of the volume used in the calculation of the gaussian covariance. Defaults to **None**. zmin: float, optional Maximum redshift of the volume used in the calculation of the gaussian covariance. Defaults to **None**. fsky: float, optional Sky fraction of the volume used in the calculation of the gaussian covariance (in units of radians). Defaults to :math:`15000\mathrm{deg}^2`. Ntri: numpy.ndarray, optional Number of fundamental triangles per bin. The size of this array should match the size of ``tri``, or the longest array in ``tri`` if given as a list. Defaults to :math:`8 \pi^2 k_1\,k_2\,k_3\,\Delta k^3\k_f^6`, where :math:`k_f^3 = (2\pi)^3/V`. volfac: float, optional Rescaling volume fraction. Defaults to :math:`1`. Returns ------- cov: numpy.ndarray Gaussian covariance of the selected bispectrum multipoles. """ ell = [ell] if not isinstance(ell, list) else ell if not isinstance(tri, list): tri = [tri]*len(ell) elif isinstance(tri, list) and len(tri) != len(ell): raise ValueError("If 'k' is given as a list, it must match the " "length of 'ell'.") for i in range(len(ell)): if tri[i].ndim == 1: tri[i] = tri[i][None,:] tri_sorted = np.flip(np.sort(tri[i], axis=1), axis=1) if np.any(tri[i] != tri_sorted): tri[i] = tri_sorted print('Warning. Triangle configurations sorted such that ' 'k1 >= k2 >= k3.') if not tri[i].flags['CONTIGUOUS']: tri[i] = np.ascontiguousarray(tri[i]) if not np.all(self.Bisp.tri == max(tri, key=len)): if kfun is None: kfun = dk print('kfun not specified. Using kfun = {}'.format(kfun)) self.Bisp.set_tri(tri, ell, kfun) nbins = [x.shape[0] for x in tri] cov = np.zeros([sum(nbins), sum(nbins)]) ell_for_cov = [0, 2, 4] if not self.real_space else 0 Pell = self.Pell(self.Bisp.tri_unique, params, ell=ell_for_cov, de_model=de_model, q_tr_lo=q_tr_lo, W_damping=W_damping) Pell['ell0'] += 1.0/self.nbar if de_model is not None and volume is None: Om0 = (self.params['wc']+self.params['wb'])/self.params['h']**2 H0 = 100.0*self.params['h'] self.cosmo.update_cosmology(Om0=Om0, H0=H0, Ok0=self.params['Ok'], de_model=de_model, w0=self.params['w0'], wa=self.params['wa']) volume = volfac*self.cosmo.comoving_volume(zmin, zmax, fsky) if not self.use_Mpc: volume *= self.params['h']**3 elif de_model is None and volume is None: raise ValueError("If no dark energy model is specified, a value " "for the volume must be provided.") tri_dtype = {'names':['f{}'.format(i) for i in range(3)], 'formats':3 * [self.Bisp.tri.dtype]} for i, l1 in enumerate(ell): for j, l2 in enumerate(ell): if j >= i: tri_ij, id1, id2 = np.intersect1d(tri[i].view(tri_dtype), tri[j].view(tri_dtype), return_indices=True) ids_ij = np.intersect1d(self.Bisp.tri.view(tri_dtype), tri_ij, return_indices=True)[1] cov_l1l2 = self.Bisp.Gaussian_covariance( l1, l2, dk, Pell, volume, Ntri)[ids_ij] cov[sum(nbins[:i]):sum(nbins[:i+1]), sum(nbins[:j]):sum(nbins[:j+1])][id1, id2] = cov_l1l2 else: cov[sum(nbins[:i]):sum(nbins[:i+1]), sum(nbins[:j]):sum(nbins[:j+1])] = \ cov[sum(nbins[:j]):sum(nbins[:j+1]), sum(nbins[:i]):sum(nbins[:i+1])].T return cov
[docs] def chi2(self, obs_id, params, kmax, de_model=None, binning=None, convolve_window=False, q_tr_lo=None, W_damping=None, chi2_decomposition=False, ell_for_recon=None, cnloB_mapping=None): r"""Compute the :math:`\chi^2 for the given configurations`. Generates the selected power spectrum multipoles for the specified set of parameters, and returns the :math:`\chi^2` evaluated with the specified :math:`k_\mathrm{max}` for the specified data sample. Parameters ---------- obs_id: str Identifier of the data sample. params: dict Dictionary containing the list of total model parameters which are internally used by the emulator. The keyword/value pairs of the dictionary specify the names and the values of the parameters, respectively. kmax: float or list Maximum wavemode up to which the :math:`\chi^2` is computed. If a float is passed, this is used for all the multipoles, else each value refers to a given multipoles. de_model: str, optional String that determines the dark energy equation of state. Can be chosen from the list [`"lambda"`, `"w0"`, `"w0wa"`] to work with the standard cosmological parameters, or be left undefined to use only :math:`\sigma_{12}`. Defaults to **None**. binning: dict, optional convolve_window: bool, optional q_tr_lo: list or numpy.ndarray, optional List containing the user-provided AP parameters, in the form :math:`(q_\perp, q_\parallel)`. If provided, prevents computation from correct formulas (ratios of angular diameter distances and expansion factors wrt to the corresponding quantities of the fiducial cosmology). Defaults to **None**. W_damping: Callable[[float, float], float], optional Function returning the shape of the pairwise velocity generating function in the large scale limit, :math:`r\rightarrow\infty`. The function accepts two floats as arguments, corresponding to the wavemode :math:`k` and the cosinus of the angle between pair separation and line of sight :math:`\mu`, and returns a float. This function is used only with the **VDG_infty** model. If **None**, it uses the free kurtosis distribution defined by **W_kurt**. Defaults to **None**. chi2_decomposition: bool, optional Flag to determine if the :math:`\chi^2` is computed using the fast :math:`\chi^2` decomposition (**True**) or not (**False**). Defaults to **False**. ell_for_recon: list, optional List of :math:`\ell` values used for the reconstruction of the 2d leading-order IR-resummed power spectrum. If **None**, all the even multipoles up to :math:`\ell=6` are used in the reconstruction. Defaults to **None**. Returns ------- chi2: float Value of the :math:`\chi^2`. """ obs_id = [obs_id] if not isinstance(obs_id, list) else obs_id if not isinstance(kmax, dict): kmax_dict = {} for oi in obs_id: kmax_dict[oi] = kmax kmax = kmax_dict if binning is None: binning = {oi:None for oi in obs_id} if not np.any([oi in binning.keys() for oi in obs_id]): binning = {oi:binning for oi in obs_id} else: for oi in obs_id: if oi not in binning.keys(): binning[oi] = None # deactivating chi2-decomposition if the bispectrum is involved # [TODO: include counterterms in stochastic contributions for EFT/VDG] for oi in obs_id: if self.data[oi].stat == 'bispectrum': chi2_decomposition = False ell = {} for oi in obs_id: # kmax_updated = False if (not self.data[oi].kmax_is_set or (self.data[oi].kmax != kmax[oi] and self.data[oi].kmax != [kmax[oi] for i in range(self.data[oi].n_ell)])): self.data[oi].set_kmax(kmax[oi]) if self.data[oi].stat == 'powerspectrum': self.chi2_decomposition = None elif self.data[oi].stat == 'bispectrum': self.Bisp_chi2_decomposition = None # kmax_updated = True ell[oi] = self.data[oi].ell if self.data[oi].stat == 'bispectrum': # if self.Bisp.tri is not None: # ntri = list(self.Bisp.ntri_ell.values()) # else: # ntri = None # if kmax_updated or self.Bisp.tri is None or \ # ntri != self.data[oi].nbins or \ # self.Bisp.kfun != self.data[oi].kfun: # self.Bisp_binning = binning # self.Bisp.set_tri(self.data[oi].bins_kmax, ell[oi], # self.data[oi].kfun, binning=binning[oi]) # self._Bisp_tri_has_changed = True tri_has_changed, binning_has_changed = \ self.Bisp.set_tri(self.data[oi].bins_kmax, ell[oi], self.data[oi].kfun, binning=binning[oi]) if W_damping is None: W_damping = {} for oi in obs_id: if self.data[oi].stat == 'powerspectrum': W_damping[oi] = self.W_kurt elif self.data[oi].stat == 'bispectrum': W_damping[oi] = self.WB_kurt if not chi2_decomposition: chi2 = 0.0 for oi in obs_id: if self.data[oi].stat == 'powerspectrum': if self.RSD_model == 'VDG_infty': if W_damping[oi] is None: W_damping[oi] = self.W_kurt convolve_oi = oi if convolve_window else None Pell = self.Pell(self.data[oi].bins_kmax, params, ell[oi], de_model=de_model, binning=binning[oi], obs_id=convolve_oi, q_tr_lo=q_tr_lo, W_damping=W_damping[oi], ell_for_recon=ell_for_recon) Pell_list = np.hstack([Pell[m] for m in Pell.keys()]) diff = Pell_list - self.data[oi].signal_kmax chi2 += diff @ self.data[oi].inverse_cov_kmax @ diff.T elif self.data[oi].stat == 'bispectrum': if self.RSD_model == 'VDG_infty': if W_damping[oi] is None: W_damping[oi] = self.WB_kurt if binning[oi]: tri_unique = self.Bisp.tri_eff_unique if not binning[oi].get('effective', False) \ and (tri_has_changed or binning_has_changed): self.Bisp.set_fiducial_cosmology(params) Pdw_eff = self.Pdw(tri_unique, self.Bisp.fiducial_cosmology, de_model, ell_for_recon) self.Bisp.init_Pdw_eff(Pdw_eff) if self.Bisp.generate_discrete_kernels: # print('Recompute (binned) kernels!') Pdw = np.array([ self.Pdw(self.Bisp.grid.kmu123[:,j], self.Bisp.fiducial_cosmology, de_model, ell_for_recon) for j in range(3) ]).T self.Bisp.init_Pdw(Pdw, ell[oi]) self.Bisp.compute_kernels_shell_average( max(ell[oi])) else: # print('Load (binned) kernels!') self.Bisp.load_kernels_shell_average() else: tri_unique = self.Bisp.tri_unique Pdw = self.Pdw(tri_unique, params, de_model=de_model, ell_for_recon=ell_for_recon) if self.real_space: neff = None else: neff = tri_unique * \ self.Pdw_spline.derivative(n=1)(tri_unique)/Pdw if binning and self.RSD_model == 'VDG_infty': if cnloB_mapping is not None: coeff = cnloB_mapping([self.params['avirB'], self.params['sv'].squeeze()]) self.params['cnloB'] = \ - (coeff[0]*self.params['avirB']**1.75 \ + 0.5*self.params['sv']**1.75) Bell = self.Bisp.Bell(Pdw, neff, self.params, ell[oi], W_damping[oi]) if self.data[oi].cov_is_block_diagonal: diff = {} for i,l in enumerate(Bell.keys()): n1 = sum(self.data[oi].nbins[:i]) n2 = sum(self.data[oi].nbins[:i+1]) diff[l] = Bell[l] - self.data[oi].signal_kmax[n1:n2] Ldiff = np.zeros(sum(self.data[oi].nbins)) for i,l1 in enumerate(Bell.keys()): n1 = sum(self.data[oi].nbins[:i]) n2 = sum(self.data[oi].nbins[:i+1]) for j,l2 in enumerate(list(Bell.keys())[i:]): ids_i = self.data[oi].tri_id_ell2_in_ell1[l1+l2] ids_j = self.data[oi].tri_id_ell1_in_ell2[l1+l2] Ldiff[n1:n2][ids_i] += \ self.data[oi].cholesky_diag[l1+l2] * \ diff[l2][ids_j] else: Bell_list = np.hstack([Bell[m] for m in Bell.keys()]) diff = Bell_list - self.data[oi].signal_kmax Ldiff = self.data[oi].inverse_cov_kmax_cholesky @ diff chi2 += np.sum(Ldiff**2) else: chi2 = 0.0 # check if cosmological + RSD parameters have changed, if so, # re-evaluate chi2 decomposition if de_model is None and self.use_Mpc: check_params = self.params_list + self.RSD_params_list elif de_model is None and not self.use_Mpc: check_params = self.params_list + ['h'] + \ self.RSD_params_list else: check_params = self.params_shape_list \ + self.de_model_params_list[de_model] \ + self.RSD_params_list if 'Ok' not in params: check_params.remove('Ok') for p in self.RSD_params_list: if p not in params: check_params.remove(p) if binning != self.X_binning: self.chi2_decomposition = None self.X_binning = binning params_changed = True if \ any(params[p] != self.params[p] for p in check_params) \ else False compute_chi2_decomposition = True if params_changed \ or self.chi2_decomposition is None else False compute_Bisp_chi2_decomposition = True if params_changed \ or self.Bisp_chi2_decomposition is None else False for oi in obs_id: if self.data[oi].stat == 'powerspectrum': if compute_chi2_decomposition: convolve_oi = oi if convolve_window else None PX_ell_list = np.zeros([sum(self.data[oi].nbins), len(self.diagrams_all)]) for i, X in enumerate(self.diagrams_all): PX_ell = self.PX_ell(self.data[oi].bins_kmax, params, ell[oi], X, binning=binning, obs_id=convolve_oi, de_model=de_model, q_tr_lo=q_tr_lo, W_damping=W_damping[oi], ell_for_recon=ell_for_recon) PX_ell_list[:, i] = np.hstack([PX_ell[m] for m in PX_ell.keys()]) self.chi2_decomposition = {} self.chi2_decomposition['DD'] = self.data[oi].SN_kmax self.chi2_decomposition['XD'] = PX_ell_list.T \ @ self.data[oi].inverse_cov_kmax \ @ self.data[oi].signal_kmax self.chi2_decomposition['XX'] = PX_ell_list.T \ @ self.data[oi].inverse_cov_kmax @ PX_ell_list elif self.data[oi].stat == 'bispectrum': if compute_Bisp_chi2_decomposition: Pdw = self.Pdw(self.Bisp.tri_unique, params, de_model=de_model, ell_for_recon=ell_for_recon) if self.real_space: neff = None else: neff = self.Bisp.tri_unique * \ self.Pdw_spline.derivative(n=1)( self.Bisp.tri_unique) / Pdw BX_ell = self.Bisp.BX_ell(Pdw, neff, self.params, ell=ell[oi], W_damping=W_damping[oi]) BX_ell_list = np.zeros([sum(self.data[oi].nbins), len(self.Bisp_diagrams_all)]) for i, X in enumerate(self.Bisp_diagrams_all): BX_ell_list[:, i] = np.hstack([BX_ell[m][X] for m in BX_ell.keys()]) self.Bisp_chi2_decomposition = {} self.Bisp_chi2_decomposition['DD'] = \ self.data[oi].SN_kmax self.Bisp_chi2_decomposition['XD'] = BX_ell_list.T \ @ self.data[oi].inverse_cov_kmax \ @ self.data[oi].signal_kmax self.Bisp_chi2_decomposition['XX'] = BX_ell_list.T \ @ self.data[oi].inverse_cov_kmax @ BX_ell_list self._update_bias_params(params) self.splines_up_to_date = False self.dw_spline_up_to_date = False for oi in obs_id: if self.data[oi].stat == 'powerspectrum': bX = self._get_bias_coeff_for_chi2_decomposition() chi2 += (bX @ self.chi2_decomposition['XX'] @ bX - 2*bX @ self.chi2_decomposition['XD'] + self.chi2_decomposition['DD']) elif self.data[oi].stat == 'bispectrum': bX = self._get_bias_coeff_for_Bisp_chi2_decomposition() chi2 += (bX @ self.Bisp_chi2_decomposition['XX'] @ bX - 2*bX @ self.Bisp_chi2_decomposition['XD'] + self.Bisp_chi2_decomposition['DD']) return chi2