"""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