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 along with the attributes related to the different binning options.

In addition to the attributes common to all Corr3 subclasses, objects of this class hold the following attributes:

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.

The typical usage pattern is as follows:

>>> kkk = treecorr.KKKCorrelation(config)
>>> kkk.process(cat)              # Compute auto-correlation.
>>> kkk.process(cat1, cat2, cat3) # Compute cross-correlation.
>>> kkk.write(file_name)          # Write out to a file.
>>> zeta = kkk.zeta               # 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]
finalize(vark1, vark2, vark3)[source]

Finalize the calculation of the correlation function.

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.

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

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, zetar and zetai.)

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, weightr and weighti.)

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)