QQCorrelation: Quatrefoil-quatrefoil correlations

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

Bases: BaseZZCorrelation

This class handles the calculation and storage of a 2-point quatrefoil-quatrefoil correlation function, where a quatrefoil is any field with spin-4 rotational properties.

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.

  • xip – The correlation function, \(\xi_+(r)\).

  • xim – The correlation function, \(\xi_-(r)\).

  • xip_im – The imaginary part of \(\xi_+(r)\).

  • xim_im – The imaginary part of \(\xi_-(r)\).

  • varxip – An estimate of the variance of \(\xi_+(r)\)

  • varxim – An estimate of the variance of \(\xi_-(r)\)

  • 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 for the data vector with \(\xi_+\) first and then \(\xi_-\).

Note

The default method for estimating the variance and covariance attributes (varxip, varxim, 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 BaseZZCorrelation.process_auto and/or 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:

>>> qq = treecorr.QQCorrelation(config)
>>> qq.process(cat)         # For auto-correlation.
>>> qq.process(cat1,cat2)   # For cross-correlation.
>>> qq.write(file_name)     # Write out to a file.
>>> xip = qq.xip            # 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.

__init__(config=None, *, logger=None, **kwargs)[source]

Initialize QQCorrelation. See class doc for details.

finalize(varq1, varq2)[source]

Finalize the calculation of the correlation function.

The BaseZZCorrelation.process_auto and Corr2.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 each column by the total weight.

Parameters:

  • varq1 (float) – The variance per component of the first quatrefoil field.

  • varq2 (float) – The variance per component of the second quatrefoil field.