NKKCorrelation: Count-scalar-scalar correlations

class treecorr.NKKCorrelation(config=None, *, logger=None, **kwargs)

Bases: Corr3

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

With this class, point 1 of the triangle (i.e. the vertex opposite d1) is the one with the scalar value. Use KNKCorrelation and KKNCorrelation for classes with the scalar in the other two positions.

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 estimate, only including the shot noise propagated into the final correlation.

The typical usage pattern is as follows:

>>> nkk = treecorr.NKKCorrelation(config)
>>> nkk.process(cat1, cat2)        # Compute cross-correlation of two fields.
>>> nkk.process(cat1, cat2, cat3)  # Compute cross-correlation of three fields.
>>> nkk.write(file_name)           # Write out to a file.
>>> rkk.process(rand, cat2)        # Compute cross-correlation with randoms.
>>> nkk.calculateZeta(rkk=rkk)     # Calculate zeta using randoms
>>> zeta = nkk.zeta                # Access correlation function
>>> zetar = nkk.zetar              # Or access real and imaginary parts separately
>>> zetai = nkk.zetai

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)

calculateZeta(*, rkk=None)

Calculate the correlation function possibly given another correlation function that uses random points for the foreground objects.

• If rkk is None, the simple correlation function (self.zeta) is returned.

• If rkk is not None, then a compensated calculation is done: \(\zeta = (DKK - RKK)\), where DKK represents the correlation of the kappa field with the data points and RKK represents the correlation with random points.

After calling this function, the attributes zeta, varzeta and cov will correspond to the compensated values (if rkk is provided). The raw, uncompensated values are available as rawxi and raw_varxi.

Parameters:

rkk (NKKCorrelation) – The cross-correlation using random locations as the lenses (RKK), if desired. (default: None)

Returns:

Tuple containing

• zeta = array of \(\zeta\)

• varzeta = array of variance estimates of \(\zeta\)

copy()

Make a copy

finalize(vark1, vark2)

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.

write(file_name, *, file_type=None, precision=None, write_patch_results=False, write_cov=False)

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 \(\zeta\).
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)

KNKCorrelation: Scalar-count-scalar correlations

class treecorr.KNKCorrelation(config=None, *, logger=None, **kwargs)

Bases: Corr3

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

With this class, point 2 of the triangle (i.e. the vertex opposite d2) is the one with the scalar value. Use NKKCorrelation and KKNCorrelation for classes with the scalar in the other two positions.

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 estimate, only including the shot noise propagated into the final correlation.

The typical usage pattern is as follows:

>>> knk = treecorr.NKKCorrelation(config)
>>> knk.process(cat1, cat2, cat1)  # Compute cross-correlation of two fields.
>>> knk.process(cat1, cat2, cat3)  # Compute cross-correlation of three fields.
>>> knk.write(file_name)           # Write out to a file.
>>> krk.process(cat1, rand, cat1)  # Compute cross-correlation with randoms.
>>> knk.calculateZeta(krk=krk)     # Calculate zeta using randoms
>>> zeta = knk.zeta                # Access correlation function
>>> zetar = knk.zetar              # Or access real and imaginary parts separately
>>> zetai = knk.zetai

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)

calculateZeta(*, krk=None)

Calculate the correlation function possibly given another correlation function that uses random points for the foreground objects.

• If krk is None, the simple correlation function (self.zeta) is returned.

• If krk is not None, then a compensated calculation is done: \(\zeta = (KDK - KRK)\), where KDK represents the correlation of the kappa field with the data points and KRK represents the correlation with random points.

After calling this function, the attributes zeta, varzeta and cov will correspond to the compensated values (if krk is provided). The raw, uncompensated values are available as rawxi and raw_varxi.

Parameters:

krk (KNKCorrelation) – The cross-correlation using random locations as the lenses (RKK), if desired. (default: None)

Returns:

Tuple containing

• zeta = array of \(\zeta\)

• varzeta = array of variance estimates of \(\zeta\)

copy()

Make a copy

finalize(vark1, vark2)

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.

write(file_name, *, file_type=None, precision=None, write_patch_results=False, write_cov=False)

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 \(\zeta\).
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)

KKNCorrelation: Scalar-scalar-count correlations

class treecorr.KKNCorrelation(config=None, *, logger=None, **kwargs)

Bases: Corr3

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

With this class, point 3 of the triangle (i.e. the vertex opposite d3) is the one with the scalar value. Use NKKCorrelation and KNKCorrelation for classes with the scalar in the other two positions.

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 estimate, only including the shot noise propagated into the final correlation.

The typical usage pattern is as follows:

>>> kkn = treecorr.KKNCorrelation(config)
>>> kkn.process(cat1, cat2)        # Compute cross-correlation of two fields.
>>> kkn.process(cat1, cat2, cat3)  # Compute cross-correlation of three fields.
>>> kkn.write(file_name)           # Write out to a file.
>>> kkr.process(cat1, rand)        # Compute cross-correlation with randoms.
>>> kkn.calculateZeta(kkr=kkr)     # Calculate zeta using randoms
>>> zeta = kkn.zeta                # Access correlation function
>>> zetar = kkn.zetar              # Or access real and imaginary parts separately
>>> zetai = kkn.zetai

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)

calculateZeta(*, kkr=None)

Calculate the correlation function possibly given another correlation function that uses random points for the foreground objects.

• If kkr is None, the simple correlation function (self.zeta) is returned.

• If kkr is not None, then a compensated calculation is done: \(\zeta = (DKK - RKK)\), where DKK represents the correlation of the kappa field with the data points and RKK represents the correlation with random points.

After calling this function, the attributes zeta, varzeta and cov will correspond to the compensated values (if kkr is provided). The raw, uncompensated values are available as rawxi and raw_varxi.

Parameters:

kkr (KKNCorrelation) – The cross-correlation using random locations as the lenses (RKK), if desired. (default: None)

Returns:

Tuple containing

• zeta = array of \(\zeta\)

• varzeta = array of variance estimates of \(\zeta\)

copy()

Make a copy

finalize(vark1, vark2)

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.

write(file_name, *, file_type=None, precision=None, write_patch_results=False, write_cov=False)

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 \(\zeta\).
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)