# Maths#

Mathematics.

## `Binning`#

clusterking.maths.binning.bin_function(fct, binning: numpy.array, normalize=False) numpy.array[source]#

Bin function, i.e. calculate the integrals of a function for each bin.

Parameters
• fct – Function to be integrated per bin

• binning – Array of bin edge points.

• normalize – If true, we will normalize the distribution, i.e. divide by the sum of all bins in the end.

Returns

Array of bin contents

## `Metric`#

clusterking.maths.metric.chi2(n1: numpy.ndarray, n2: numpy.ndarray, cov1: numpy.ndarray, cov2: numpy.ndarray, normalize=False) [source]#
Parameters
• n1 – n_obs x n_bins

• n2 – Either n_obs x n_bins or just nbins if we’re testing against a constant histogram

• cov1 – Either n_obs x n_bins x n_bins or n_bins x n_bins

• cov2 – Either n_obs x n_bins x n_bins or n_bins x n_bins

• normalize

Returns

n_obs vector of chi2 test results (degrees of freedom not yet divided out)

clusterking.maths.metric.chi2_metric(dwe: clusterking.data.dwe.DataWithErrors, output='condensed')[source]#

Returns the chi2/ndf values of the comparison of a datasets.

Parameters
• output – ‘condensed’ (condensed distance matrix) or ‘full’ (full distance matrix)

Returns

Condensed distance matrix or full distance matrix

## `Statistics`#

clusterking.maths.statistics.cov2err(cov)[source]#

Convert covariance matrix (or array of covariance matrices of equal shape) to error array (or array thereof).

Parameters

cov – [n x ] nbins x nbins array

Returns

[n x ] nbins array

clusterking.maths.statistics.cov2corr(cov)[source]#

Convert covariance matrix (or array of covariance matrices of equal shape) to correlation matrix (or array thereof).

Parameters

cov – [n x ] nbins x nbins array

Returns

[n x ] nbins x nbins array

clusterking.maths.statistics.corr2cov(corr, err)[source]#

Convert correlation matrix (or array of covariance matrices of equal shape) together with error array (or array thereof) to covariance matrix (or array thereof).

Parameters
• corr – [n x ] nbins x nbins array

• err – [n x ] nbins array

Returns

[n x ] nbins x nbins array

clusterking.maths.statistics.rel2abs_cov(cov, data)[source]#

Convert relative covariance matrix to absolute covariance matrix

Parameters
• cov – n x nbins x nbins array

• data – n x nbins array

Returns

n x nbins x nbins array

clusterking.maths.statistics.abs2rel_cov(cov, data)[source]#

Convert covariance matrix to relative covariance matrix

Parameters
• cov – n x nbins x nbins array

• data – n x nbins array

Returns

n x nbins x nbins array