# Copyright (c) 2003-2024 by Mike Jarvis
#
# TreeCorr is free software: redistribution and use in source and binary forms,
# with or without modification, are permitted provided that the following
# conditions are met:
#
# 1. Redistributions of source code must retain the above copyright notice, this
# list of conditions, and the disclaimer given in the accompanying LICENSE
# file.
# 2. Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions, and the disclaimer given in the documentation
# and/or other materials provided with the distribution.
"""
.. module:: nkcorrelation
"""
import numpy as np
from . import _treecorr
from .catalog import calculateVarK
from .corr2base import Corr2
from .util import make_writer
from .config import make_minimal_config
[docs]class NKCorrelation(Corr2):
r"""This class handles the calculation and storage of a 2-point count-scalar correlation
function.
.. note::
While we use the term kappa (:math:`\kappa`) here and the letter K in various places,
in fact any scalar field will work here. For example, you can use this to compute
correlations of non-shear quantities, e.g. the sizes or concentrations of galaxies, around
a set of lenses, where "kappa" would be the measurements of these quantities.
Ojects of this class holds the following attributes:
Attributes:
nbins: The number of bins in logr
bin_size: The size of the bins in logr
min_sep: The minimum separation being considered
max_sep: The maximum separation being considered
In addition, the following attributes are numpy arrays of length (nbins):
Attributes:
logr: The nominal center of the bin in log(r) (the natural logarithm of r).
rnom: The nominal center of the bin converted to regular distance.
i.e. r = exp(logr).
meanr: The (weighted) mean value of r for the pairs in each bin.
If there are no pairs in a bin, then exp(logr) will be used instead.
meanlogr: The (weighted) mean value of log(r) for the pairs in each bin.
If there are no pairs in a bin, then logr will be used instead.
xi: The correlation function, :math:`\xi(r) = \langle \kappa\rangle`.
varxi: An estimate of the variance of :math:`\xi`
weight: The total weight in each bin.
npairs: The number of pairs going into each bin (including pairs where one or
both objects have w=0).
cov: An estimate of the full covariance matrix.
raw_xi: The raw value of xi, uncorrected by an RK calculation. cf. `calculateXi`
raw_varxi: The raw value of varxi, uncorrected by an RK calculation. cf. `calculateXi`
.. note::
The default method for estimating the variance and covariance attributes (``varxi``,
and ``cov``) is 'shot', which only includes the shape noise propagated into
the final correlation. This does not include sample variance, so it is always an
underestimate of the actual variance. To get better estimates, you need to set
``var_method`` to something else and use patches in the input catalog(s).
cf. `Covariance Estimates`.
If ``sep_units`` are given (either in the config dict or as a named kwarg) then the distances
will all be in these units.
.. note::
If you separate out the steps of the `Corr2.process` command and use `Corr2.process_cross`,
then the units will not be applied to ``meanr`` or ``meanlogr`` until the `finalize`
function is called.
The typical usage pattern is as follows:
>>> nk = treecorr.NKCorrelation(config)
>>> nk.process(cat1,cat2) # Compute the cross-correlation function.
>>> nk.write(file_name) # Write out to a file.
>>> xi = nk.xi # Or access the correlation function directly.
Parameters:
config (dict): A configuration dict that can be used to pass in kwargs if desired.
This dict is allowed to have addition entries besides those listed
in `Corr2`, which are ignored here. (default: None)
logger: If desired, a logger object for logging. (default: None, in which case
one will be built according to the config dict's verbose level.)
Keyword Arguments:
**kwargs: See the documentation for `Corr2` for the list of allowed keyword
arguments, which may be passed either directly or in the config dict.
"""
_cls = 'NKCorrelation'
_letter1 = 'N'
_letter2 = 'K'
_letters = 'NK'
_builder = _treecorr.NKCorr
_calculateVar1 = lambda *args, **kwargs: None
_calculateVar2 = staticmethod(calculateVarK)
_sig1 = None
_sig2 = 'sig_k'
# The angles are not important for accuracy of NK correlations.
_default_angle_slop = 1
[docs] def __init__(self, config=None, *, logger=None, **kwargs):
"""Initialize `NKCorrelation`. See class doc for details.
"""
super().__init__(config, logger=logger, **kwargs)
self._xi1 = np.zeros_like(self.rnom, dtype=float)
self._xi2 = self._xi3 = self._xi4 = np.array([])
self.xi = self.raw_xi
self._rk = None
self._varxi = None
self._raw_varxi = None
self.logger.debug('Finished building NKCorr')
@property
def raw_xi(self):
return self._xi1
[docs] def copy(self):
"""Make a copy"""
ret = super().copy()
if self.xi is self.raw_xi:
ret.xi = ret.raw_xi
if self._rk is not None:
ret._rk = self._rk.copy()
return ret
[docs] def finalize(self, vark):
"""Finalize the calculation of the correlation function.
The `Corr2.process_cross` command accumulates values in each bin, so it can be called
multiple times if appropriate. Afterwards, this command finishes the calculation
by dividing each column by the total weight.
Parameters:
vark: The variance of the scalar field.
"""
self._finalize()
self._var_num = vark
self.xi = self.raw_xi
@property
def raw_varxi(self):
if self._raw_varxi is None:
self._raw_varxi = np.zeros_like(self.rnom, dtype=float)
if self._var_num != 0:
self._raw_varxi.ravel()[:] = self.cov_diag
return self._raw_varxi
@property
def varxi(self):
if self._varxi is None:
self._varxi = self.raw_varxi
return self._varxi
def _clear(self):
"""Clear the data vectors
"""
super()._clear()
self.xi = self.raw_xi
self._rk = None
self._raw_varxi = None
self._varxi = None
def _sum(self, others):
# Equivalent to the operation of:
# self._clear()
# for other in others:
# self += other
# but no sanity checks and use numpy.sum for faster calculation.
np.sum([c._xi1 for c in others], axis=0, out=self._xi1)
np.sum([c.meanr for c in others], axis=0, out=self.meanr)
np.sum([c.meanlogr for c in others], axis=0, out=self.meanlogr)
np.sum([c.weight for c in others], axis=0, out=self.weight)
np.sum([c.npairs for c in others], axis=0, out=self.npairs)
self.xi = self.raw_xi
self._raw_varxi = None
self._varxi = None
self._cov = None
[docs] def calculateXi(self, *, rk=None):
r"""Calculate the correlation function possibly given another correlation function
that uses random points for the foreground objects.
- If rk is None, the simple correlation function :math:`\langle \kappa \rangle` is
returned.
- If rk is not None, then a compensated calculation is done:
:math:`\langle \kappa \rangle = (DK - RK)`, where DK represents the mean kappa
around the lenses and RK represents the mean kappa around random points.
After calling this function, the attributes ``xi``, ``varxi`` and ``cov`` will correspond
to the compensated values (if rk is provided). The raw, uncompensated values are
available as ``rawxi`` and ``raw_varxi``.
Parameters:
rk (NKCorrelation): The cross-correlation using random locations as the lenses (RK),
if desired. (default: None)
Returns:
Tuple containing
- xi = array of :math:`\xi(r)`
- varxi = array of variance estimates of :math:`\xi(r)`
"""
if rk is not None:
self.xi = self.raw_xi - rk.xi
self._rk = rk
if rk.npatch1 not in (1,self.npatch1) or rk.npatch2 != self.npatch2:
raise RuntimeError("RK must be run with the same patches as DK")
if len(self.results) > 0:
# If there are any rk patch pairs that aren't in results (e.g. due to different
# edge effects among the various pairs in consideration), then we need to add
# some dummy results to make sure all the right pairs are computed when we make
# the vectors for the covariance matrix.
template = next(iter(self.results.values())) # Just need something to copy.
for ij in rk.results:
if ij in self.results: continue
new_cij = template.copy()
new_cij.xi.ravel()[:] = 0
new_cij.weight.ravel()[:] = 0
self.results[ij] = new_cij
self._cov = self.estimate_cov(self.var_method)
self._varxi = np.zeros_like(self.rnom, dtype=float)
self._varxi.ravel()[:] = self.cov_diag
else:
self._varxi = self.raw_varxi + rk.varxi
else:
self.xi = self.raw_xi
self._varxi = self.raw_varxi
return self.xi, self.varxi
def _calculate_xi_from_pairs(self, pairs):
self._sum([self.results[ij] for ij in pairs])
self._finalize()
if self._rk is not None:
# If rk has npatch1 = 1, adjust pairs appropriately
if self._rk.npatch1 == 1 and not all([p[0] == 0 for p in pairs]):
pairs = [(0,ij[1]) for ij in pairs if ij[0] == ij[1]]
# Make sure all ij are in the rk results (some might be missing, which is ok)
pairs = [ij for ij in pairs if self._rk._ok[ij[0],ij[1]]]
self._rk._calculate_xi_from_pairs(pairs)
self.xi -= self._rk.xi
[docs] def write(self, file_name, * ,rk=None, file_type=None, precision=None,
write_patch_results=False, write_cov=False):
r"""Write the correlation function to the file, file_name.
- If rk is None, the simple correlation function :math:`\langle \kappa \rangle(R)` is
used.
- If rk is not None, then a compensated calculation is done:
:math:`\langle \kappa \rangle = (DK - RK)`, where DK represents the mean kappa
around the lenses and RK represents the mean kappa around random points.
The output file will include the following columns:
========== =========================================================
Column Description
========== =========================================================
r_nom The nominal center of the bin in r
meanr The mean value :math:`\langle r\rangle` of pairs that
fell into each bin
meanlogr The mean value :math:`\langle \log(r)\rangle` of pairs
that fell into each bin
kappa The mean value :math:`\langle \kappa\rangle(r)`
sigma The sqrt of the variance estimate of
:math:`\langle \kappa\rangle`
weight The total weight contributing to each bin
npairs The total number of pairs in each bin
========== =========================================================
If ``sep_units`` was given at construction, then the distances will all be in these units.
Otherwise, they will be in either the same units as x,y,z (for flat or 3d coordinates) or
radians (for spherical coordinates).
Parameters:
file_name (str): The name of the file to write to.
rk (NKCorrelation): The cross-correlation using random locations as the lenses (RK),
if desired. (default: None)
file_type (str): The type of file to write ('ASCII' or 'FITS'). (default: determine
the type automatically from the extension of file_name.)
precision (int): For ASCII output catalogs, the desired precision. (default: 4;
this value can also be given in the constructor in the config dict.)
write_patch_results (bool): Whether to write the patch-based results as well.
(default: False)
write_cov (bool): Whether to write the covariance matrix as well. (default: False)
"""
self.logger.info('Writing NK correlations to %s',file_name)
self.calculateXi(rk=rk)
precision = self.config.get('precision', 4) if precision is None else precision
with make_writer(file_name, precision, file_type, self.logger) as writer:
self._write(writer, None, write_patch_results, write_cov=write_cov)
@property
def _write_col_names(self):
return ['r_nom','meanr','meanlogr','kappa','sigma','weight','npairs']
@property
def _write_data(self):
data = [ self.rnom, self.meanr, self.meanlogr,
self.xi, np.sqrt(self.varxi), self.weight, self.npairs ]
data = [ col.flatten() for col in data ]
return data
def _read_from_data(self, data, params):
super()._read_from_data(data, params)
s = self.logr.shape
self._xi1 = data['kappa'].reshape(s)
self._varxi = data['sigma'].reshape(s)**2
self.xi = self.raw_xi
self._raw_varxi = self._varxi