PLENSLIKE
=========

This library contains Python and C code associated with the Planck lensing likelihood.

Multiple likelihoods are available, based on different data cuts and band combinations. The likelihood data files are human readable.

Each likelihood file describes (at least) a choice of bins (l_{min}^{i}, l_{max}^{i}), a weight function for accumulating signal into the bins (C_l^{pp, fid.} V_l^{-1}), measured amplitudes for each bin, and an associated covariance matrix.

The likelihood for a potential power spectrum C_l^{pp} is calculated as

lnL[C_l^{pp}] = -1/2 \sum_{ij} ( D^{i}[C_l^{pp}] - D^{i}[\hat{C}_l^{pp}] ) \sigma^{-1}_{ij} \sum_{ij} ( D^{j}[C_l^{pp}] - D^{j}[\hat{C}_l^{pp}] ),

where D^{i}[C_l] is a binning function given by

D^{i}[C_l] = (\sum_{l_{min}^{i}}^{l_{max}^{i}} C_l C_l^{pp, fid} V_l^{-1}) / (\sum_{l_{min}^{i}}^{l_{max}^{i}} (C_l^{pp, fid})^2 V_l^{-1}).

D^{i}[\hat{C}_l^{pp}] are the measured bin values.

The bin covariance \sigma_{ij} is determined from simulations based on a fiducial bestfit cosmology C_l^{TT, fid} and beam transfer function(s) B_l^{fid}. It includes the uncertainty due to CMB+EFG+Noise power, and the point source shot-noise correction. Cosmological and beam uncertainties on the binned estimate may be accounted for (if desired) in a sampling approach. Given an underlying theoretical lensing power spectrum C_l^{pp, th} and revised estimates of C_l^{TT} and the beam transfer function(s) B_l, this is accomplished by rescaling the theoretical power spectrum to account for the difference between the fiducial estimator normalization and that expected given the revised cosmology/beam description. Code to apply this renormalization when calculating the likelihood is provided.

There are multiple formats for the likelihood files, depending on how many effective beams and effective filter functions are needed to describe the lensing measurement:

* "mono"
      This format is for likelihoods based on temperature-only lens reconstruction from a single map with a single effective beam. The likelihood file contains the associated filter function F_l and beam B_l^{fid}, as well as the estimator normalization A_l.

* "quad"
      This format describes a more general (temperature only) lensing likelihood in which the four multiples of the trispectrum used to probe C_l^{pp} may each be sourced by a different map with a different effective beam. This format also allows the use of non-standard quadratic lensing estimators.

* "qecl"
      This format describes a very general temperature+polarization based lens reconstruction, built from cross- and auto-spectra of a set of quadratic estimators. The estimators are specified explicitly, and can be standard, bias-hardened, etc. The filter functions are included in the estimator weights, and so not specified explicitly for this format.

* "full"
      This format is for temperature+poliarzation based lens reconstrution, similar to "qecl", but also including a pre-computed estimate of the dependence of the N1 bias on C_l^{pp}, and information on the point source correction.