KKKCorrelation: Scalar-scalar-scalar correlations

class treecorr.KKKCorrelation(config=None, *, logger=None, **kwargs)[source]

Bases: Corr3

This class handles the calculation and storage of a 3-point scalar-scalar-scalar correlation function.

Note

While we use the term kappa (\(\kappa\)) 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 the CMB temperature fluctuations, where “kappa” would really be \(\Delta T\).

See the doc string of Corr3 for a description of how the triangles are binned.

Ojects of this class holds the following attributes:

Attributes:

nbins – The number of bins in logr where r = d2.
bin_size – The size of the bins in logr.
min_sep – The minimum separation being considered.
max_sep – The maximum separation being considered.
logr1d – The nominal centers of the nbins bins in log(r).

If the bin_type is LogRUV, then it will have these attributes:

Attributes:

nubins – The number of bins in u where u = d3/d2.
ubin_size – The size of the bins in u.
min_u – The minimum u being considered.
max_u – The maximum u being considered.
nvbins – The number of bins in v where v = +-(d1-d2)/d3.
vbin_size – The size of the bins in v.
min_v – The minimum v being considered.
max_v – The maximum v being considered.
u1d – The nominal centers of the nubins bins in u.
v1d – The nominal centers of the nvbins bins in v.

If the bin_type is LogSAS, then it will have these attributes:

Attributes:

nphi_bins – The number of bins in phi.
phi_bin_size – The size of the bins in phi.
min_phi – The minimum phi being considered.
max_phi – The maximum phi being considered.
phi1d – The nominal centers of the nphi_bins bins in phi.

If the bin_type is LogMultipole, then it will have these attributes:

Attributes:

max_n – The maximum multipole index n being stored.
n1d – The multipole index n in the 2*max_n+1 bins of the third bin direction.

In addition, the following attributes are numpy arrays whose shape is:

(nbins, nubins, nvbins) if bin_type is LogRUV

(nbins, nbins, nphi_bins) if bin_type is LogSAS

(nbins, nbins, 2*max_n+1) if bin_type is LogMultipole

If bin_type is LogRUV:

Attributes:

logr – The nominal center of each bin in log(r).
rnom – The nominal center of each bin converted to regular distance. i.e. r = exp(logr).
u – The nominal center of each bin in u.
v – The nominal center of each bin in v.
meanu – The (weighted) mean value of u for the triangles in each bin.
meanv – The (weighted) mean value of v for the triangles in each bin.

If bin_type is LogSAS:

Attributes:

logd2 – The nominal center of each bin in log(d2).
d2nom – The nominal center of each bin converted to regular d2 distance. i.e. d2 = exp(logd2).
logd3 – The nominal center of each bin in log(d3).
d3nom – The nominal center of each bin converted to regular d3 distance. i.e. d3 = exp(logd3).
phi – The nominal center of each angular bin.
meanphi – The (weighted) mean value of phi for the triangles in each bin.

If bin_type is LogMultipole:

Attributes:

logd2 – The nominal center of each bin in log(d2).
d2nom – The nominal center of each bin converted to regular d2 distance. i.e. d2 = exp(logd2).
logd3 – The nominal center of each bin in log(d3).
d3nom – The nominal center of each bin converted to regular d3 distance. i.e. d3 = exp(logd3).
n – The multipole index n for each bin.

For any bin_type:

Attributes:

zeta – The correlation function, \(\zeta\).
varzeta – The variance of \(\zeta\), only including the shot noise propagated into the final correlation. This does not include sample variance, so it is always an underestimate of the actual variance.
meand1 – The (weighted) mean value of d1 for the triangles in each bin.
meanlogd1 – The (weighted) mean value of log(d1) for the triangles in each bin.
meand2 – The (weighted) mean value of d2 (aka r) for the triangles in each bin.
meanlogd2 – The (weighted) mean value of log(d2) for the triangles in each bin.
meand3 – The (weighted) mean value of d3 for the triangles in each bin.
meanlogd3 – The (weighted) mean value of log(d3) for the triangles in each bin.
weight – The total weight in each bin.
ntri – The number of triangles going into each bin (including those where one or more objects have w=0).

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 Corr3.process command and use process_auto and/or Corr3.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:

>>> kkk = treecorr.KKKCorrelation(config)
>>> kkk.process(cat)              # For auto-correlation.
>>> kkk.process(cat1,cat2,cat3)   # For cross-correlation.
>>> kkk.write(file_name)          # Write out to a file.
>>> zeta = kkk.zeta               # To access zeta 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 Corr3, 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 Corr3 for the list of allowed keyword arguments, which may be passed either directly or in the config dict.

__init__(config=None, *, logger=None, **kwargs)[source]: Initialize KKKCorrelation. See class doc for details.

finalize(vark1, vark2, vark3)[source]

Finalize the calculation of the correlation function.

The process_auto, process_cross12 and Corr3.process_cross commands accumulate values in each bin, so they can be called multiple times if appropriate. Afterwards, this command finishes the calculation by dividing by the total weight.

Parameters:

vark1 (float) – The variance of the first scalar field.
vark2 (float) – The variance of the second scalar field.
vark3 (float) – The variance of the third scalar field.

process_auto(cat, *, metric=None, num_threads=None)[source]

Process a single catalog, accumulating the auto-correlation.

This accumulates the auto-correlation for the given catalog. After calling this function as often as desired, the finalize command will finish the calculation of meand1, meanlogd1, etc.

Parameters:

cat (Catalog) – The catalog to process
metric (str) – Which metric to use. See Metrics for details. (default: ‘Euclidean’; this value can also be given in the constructor in the config dict.)
num_threads (int) – How many OpenMP threads to use during the calculation. (default: use the number of cpu cores; this value can also be given in the constructor in the config dict.)

process_cross12(cat1, cat2, *, metric=None, ordered=True, num_threads=None)[source]

Process two catalogs, accumulating the 3pt cross-correlation, where one of the points in each triangle come from the first catalog, and two come from the second.

This accumulates the cross-correlation for the given catalogs as part of a larger auto- or cross-correlation calculation. E.g. when splitting up a large catalog into patches, this is appropriate to use for the cross correlation between different patches as part of the complete auto-correlation of the full catalog.

Parameters:

cat1 (Catalog) – The first catalog to process. (1 point in each triangle will come from this catalog.)
cat2 (Catalog) – The second catalog to process. (2 points in each triangle will come from this catalog.)
metric (str) – Which metric to use. See Metrics for details. (default: ‘Euclidean’; this value can also be given in the constructor in the config dict.)
ordered (bool) – Whether to fix the order of the triangle vertices to match the catalogs. (default: True)
num_threads (int) – How many OpenMP threads to use during the calculation. (default: use the number of cpu cores; this value can also be given in the constructor in the config dict.)

toSAS(*, target=None, **kwargs)[source]

Convert a multipole-binned correlation to the corresponding SAS binning.

This is only valid for bin_type == LogMultipole.

Keyword Arguments:

target – A target KKKCorrelation object with LogSAS binning to write to. If this is not given, a new object will be created based on the configuration paramters of the current object. (default: None)
**kwargs – Any kwargs that you want to use to configure the returned object. Typically, might include min_phi, max_phi, nphi_bins, phi_bin_size. The default phi binning is [0,pi] with nphi_bins = self.max_n.

Returns:

A KKKCorrelation object with bin_type=LogSAS containing the same information as this object, but with the SAS binning.

write(file_name, *, file_type=None, precision=None, write_patch_results=False, write_cov=False)[source]

Write the correlation function to the file, file_name.

For bin_type = LogRUV, the output file will include the following columns:

Column	Description
r_nom	The nominal center of the bin in r = d2 where d1 > d2 > d3
u_nom	The nominal center of the bin in u = d3/d2
v_nom	The nominal center of the bin in v = +-(d1-d2)/d3
meanu	The mean value \(\langle u\rangle\) of triangles that fell into each bin
meanv	The mean value \(\langle v\rangle\) of triangles that fell into each bin

For bin_type = LogSAS, the output file will include the following columns:

Column	Description
d2_nom	The nominal center of the bin in d2
d3_nom	The nominal center of the bin in d3
phi_nom	The nominal center of the bin in phi, the opening angle between d2 and d3 in the counter-clockwise direction
meanphi	The mean value \(\langle phi\rangle\) of triangles that fell into each bin

For bin_type = LogMultipole, the output file will include the following columns:

Column	Description
d2_nom	The nominal center of the bin in d2
d3_nom	The nominal center of the bin in d3
n	The multipole index n (from -max_n .. max_n)

In addition, all bin types include the following columns:

Column	Description
meand1	The mean value \(\langle d1\rangle\) of triangles that fell into each bin
meanlogd1	The mean value \(\langle \log(d1)\rangle\) of triangles that fell into each bin
meand2	The mean value \(\langle d2\rangle\) of triangles that fell into each bin
meanlogd2	The mean value \(\langle \log(d2)\rangle\) of triangles that fell into each bin
meand3	The mean value \(\langle d3\rangle\) of triangles that fell into each bin
meanlogd3	The mean value \(\langle \log(d3)\rangle\) of triangles that fell into each bin
zeta	The estimator of \(\zeta\) (For LogMultipole, this is split into real and imaginary parts, zeta_re and zeta_im.)
sigma_zeta	The sqrt of the variance estimate of \(\zeta\) (if rrr is given)
weight	The total weight of triangles contributing to each bin. (For LogMultipole, this is split into real and imaginary parts, weight_re and weight_im.)
ntri	The number of triangles contributing to 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.
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)