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asymmetry

analysis_helpers.asymmetry

get_asymmetry_array(arr1, arr2, sumw2_arr1=None, sumw2_arr2=None, correlation=0.0)

Calculates the asymmetry between two arrays

  • \(a = \frac{n_1- n_2}{n_1 + n_2}\)
  • \(\sigma_a^2 = 4\frac{n_2^2 \sigma_1^2 + n_1^2\sigma_2^2 - 2n_1 n_2 \rho \sigma_1\sigma_2}{ \left(n_1 + n_2\right)^4}\)

Parameters:

Name Type Description Default
arr1 array

array with the first set of values

 required
arr2 array

array with the second set of values

 required
sumw2_arr1 array

array with the squared sum of weights for first set of values. Defaults to None.

 None
sumw2_arr2 array

array with the squared sum of weights for second set of values. Defaults to None.

 None
correlation float

correlation between the two data sets. Defaults to 0.

 0.0

Returns:

Name Type Description
_type_

description
Source code in src/analysis_helpers/asymmetry.py 
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def get_asymmetry_array(arr1, arr2,
                        sumw2_arr1=None, sumw2_arr2=None,
                        correlation=0.):
    r"""Calculates the asymmetry between two arrays

    - $a = \frac{n_1- n_2}{n_1 + n_2}$
    - $\sigma_a^2 = 4\frac{n_2^2 \sigma_1^2 + n_1^2\sigma_2^2 - 2n_1 n_2 \rho \sigma_1\sigma_2}{ \left(n_1 + n_2\right)^4}$

    Args:
        arr1 (array): array with the first set of values
        arr2 (array): array with the second set of values
        sumw2_arr1 (array, optional): array with the squared sum of weights for first set of values. Defaults to None.
        sumw2_arr2 (array, optional): array with the squared sum of weights for second set of values. Defaults to None.
        correlation (float, optional): correlation between the two data sets. Defaults to 0.

    Returns:
        _type_: _description_
    """    
    # Asymmetry calculation
    den = np.where(arr1 + arr2, arr1 + arr2, 1)
    num =  arr1 - arr2
    asym = np.divide(num, den)
    # Uncertainty calculation
    arr1_err = np.sqrt(sumw2_arr1) if sumw2_arr1 is not None else np.sqrt(arr1)
    arr2_err = np.sqrt(sumw2_arr2) if sumw2_arr2 is not None else np.sqrt(arr2)
    err2_num = 4.*( arr2**2 * arr1_err**2 + arr1**2 * arr2_err**2 \
                   - 2*correlation*arr1*arr2*arr1_err*arr2_err )
    err2_den = den**4
    asym_err = np.sqrt( np.divide( err2_num, err2_den ) )
    return asym, asym_err