pybird.resum module

class pybird.resum.Resum(LambdaIR=0.1, NFFT=192, fft=False, co=<pybird.common.Common object>)

Bases: object

A class for IR-resummation of the power spectrum and correlation function.

The Resum class performs the IR-resummation of the power spectrum by computing the bulk flow effects on the BAO feature. Two resummation schemes are available:

1. fullresum (default): FFTLog transforms are performed on the full integrands from s = 0.1 to s = 10000 Mpc/h. This is the more complete treatment.

2. optiresum: FFTLog transforms are performed only on the extracted BAO peak (after removing the broadband). The peak is padded with zeros and transforms run from s = 0.1 to s = 1000 Mpc/h. This is computationally faster.

co

Common parameters shared across calculations.

Type:

Common

LambdaIR

Integral cutoff for IR-filters X and Y. Default is 0.2 for fullresum, but 1.0 works for either scheme.

Type:

float

# Correlation function arrays

sr

Separation array for resummation.

Type:

ndarray

sbao

Separation array for BAO peak (optiresum).

Type:

ndarray

snobao

Separation array for broadband (optiresum).

Type:

ndarray

# Power spectrum arrays

kr

Wavenumber array for resummation.

Type:

ndarray

k2p

Powers of k^2 for IR corrections.

Type:

ndarray

# FFTLog settings and objects

fftsettings

Settings for IR correction FFTLog.

Type:

dict

fft

FFTLog engine for IR corrections.

Type:

FFTLog

M

Spherical Bessel transform matrices for IR corrections.

Type:

ndarray

kPow

k-dependent power terms for IR corrections.

Type:

ndarray

Xfftsettings

Settings for IR-filter FFTLog.

Type:

dict

Xfft

FFTLog engine for IR-filters.

Type:

FFTLog

XM

Spherical Bessel transform matrices for IR-filters.

Type:

ndarray

XsPow

s-dependent power terms for IR-filters.

Type:

ndarray

Cfftsettings

Settings for correlation function FFTLog.

Type:

dict

Cfft

FFTLog engine for correlation functions.

Type:

FFTLog

Ml

Spherical Bessel transform matrices for correlation functions.

Type:

ndarray

sPow

s-dependent power terms for correlation functions.

Type:

ndarray

# Damping windows

dampPs

Damping windows for power spectrum.

Type:

ndarray

dampCf

Damping window for correlation function.

Type:

ndarray

# Optimization paths

optipath_cf

Optimized einsum path for correlation function.

Type:

list

optipath_XpYpC

Optimized path for XpYp * correlation function.

Type:

list

optipath_IRPs

Optimized path for IR power spectrum.

Type:

list

optipath_k2IRPs

Optimized path for k^2 * IR power spectrum.

Type:

list

setXsPow()

Compute s-dependent power terms for IR-filters.

setXM()

Compute transform matrices for IR-filters.

IRFilters()

Compute the IR-filters X and Y.

setkPow()

Compute k-dependent power terms for IR corrections.

setM()

Compute transform matrices for IR corrections.

IRn()

Compute spherical Bessel transform for IR correction order n.

extractBAO()

Extract BAO feature from correlation function.

setXpYp()

Compute powers of IR-filters X and Y.

makeQ()

Compute bulk flow coefficients Q.

setMl()

Compute transform matrices for correlation functions.

setsPow()

Compute s-dependent power terms for correlation functions.

Ps2Cf()

Transform power spectrum to correlation function.

IRCf()

Compute IR corrections in configuration space.

IRPs()

Compute IR corrections in Fourier space.

PsCf()

Compute both power spectrum and correlation function with IR-resummation.

Ps()

Compute power spectrum with IR-resummation.

Initialize the Resum engine for IR-resummation calculations.

Parameters:

• LambdaIR (float, optional) – Integral cutoff for IR-filters X and Y in Mpc/h, by default 0.1

• NFFT (int, optional) – Number of FFT points for transforms, by default 192

• fft (bool, optional) – Whether to use O(NFFT logNFFT) FFT instead of O(NFFT x Nk) sum, by default False

• co (Common, optional) – Common parameters object, by default co

Notes

The choice of LambdaIR depends on the resummation scheme: - fullresum: LambdaIR = 0.2 (default for complete treatment) - optiresum: LambdaIR = 1.0 (faster, works for either scheme)

setXsPow()

Multiply the coefficients with the s’s to the powers of the FFTLog to evaluate the IR-filters X and Y.

setXM()

Compute the matrices to evaluate the IR-filters X and Y. Called at instantiation.

IRFilters(bird, soffset=1.0, LambdaIR=None, RescaleIR=1.0)

Compute the IR-filters X and Y.

setkPow()

Multiply the coefficients with the k’s to the powers of the FFTLog to evaluate the IR-corrections.

setM(Nl=3)

Compute the matrices to evaluate the IR-corrections. Called at instantiation.

IRn(XpYpC)

Compute the spherical Bessel transform in the IR correction of order n given [XY]^n

extractBAO(cf)

Given a correlation function cf, - if fullresum, return cf - if optiresum, extract the BAO peak

setXpYp(bird)

makeQ(f)

Compute the bulk coefficients Q^{ll’}_{||N-j}(n, lpha, f)

setMl()

Compute the power spectrum to correlation function spherical Bessel transform matrices. Called at the instantiation.

setsPow()

Multiply the coefficients with the s’s to the powers of the FFTLog to evaluate the IR corrections in configuration space.

Ps2Cf(P, l=0)

IRCf(bird)

Compute the IR corrections in configuration space by spherical Bessel transforming the IR corrections in Fourier space.

PsCf(bird, makeIR=True, makeQ=True, setIR=True, setPs=True, setCf=True)

Perform IR-resummation for both power spectrum and correlation function.

This is the main method that applies IR-resummation to both the power spectrum and correlation function, handling the bulk flow effects on the BAO feature.

Parameters:

• bird (Bird) – Bird object containing the power spectrum and correlation function

• makeIR (bool, optional) – Whether to compute IR-resummed power spectrum, by default True

• makeQ (bool, optional) – Whether to compute the Q factors, by default True

• setIR (bool, optional) – Whether to set IR-resummed components, by default True

• setPs (bool, optional) – Whether to set power spectrum components, by default True

• setCf (bool, optional) – Whether to set correlation function components, by default True

Notes

This method orchestrates the complete IR-resummation procedure, including computing Q factors, IR filters, and applying resummation to both Fourier and configuration space quantities.

Ps(bird, makeIR=True, makeQ=True, setIR=True, setPs=True)

Apply IR-resummation to the power spectrum.

Computes the IR-resummed power spectrum by applying bulk flow corrections to the BAO feature using the IR-resummation formalism.

Parameters:

• bird (Bird) – Bird object containing the power spectrum to be resummed

• makeIR (bool, optional) – Whether to compute IR-resummed components, by default True

• makeQ (bool, optional) – Whether to compute Q factors for resummation, by default True

• setIR (bool, optional) – Whether to set IR components in the bird object, by default True

• setPs (bool, optional) – Whether to set final power spectrum components, by default True

Notes

The IR-resummation process involves: 1. Computing Q factors from the growth rate 2. Computing IR-resummed power spectrum components 3. Setting the resummed components in the bird object

getIRPs(cf, XpYp, optipath_cf=False, optipath_XpYpC=False, optipath_IRPs=False, optipath_k2IRPs=False)

IRPs(bird)

This is the main method of the class. Compute the IR corrections in Fourier space.