logistic_completeness_function

skypy.utils.photometry.logistic_completeness_function(magnitude, magnitude_95, magnitude_50)

Logistic completeness function.

This function calculates the logistic completeness function (based on eq. (7) in López-Sanjuan, C. et al. (2017) [1].

\[p(m) = \frac{1}{1 + \exp[\kappa (m - m_{50})]}\;,\]

which describes the probability \(p(m)\) that an object of magnitude \(m\) is detected in a specific band and with

\[\kappa = \frac{\ln(\frac{1}{19})}{m_{95} - m_{50}}\;.\]

Here, \(m_{95}\) and \(m_{50}\) are the 95% and 50% completeness magnitudes, respectively.

Parameters:

magnitudearray_like

Magnitudes. Can be multidimensional for computing with multiple filter bands.

magnitude_95scalar or 1-D array_like

95% completeness magnitude. If magnitude_50 is 1-D array it has to be scalar or 1-D array of the same shape.

magnitude_50scalar or 1-D array_like

50% completeness magnitude. If magnitude_95 is 1-D array it has to be scalar or 1-D array of the same shape.

Returns:

probabilityscalar or array_like

Probability of detecting an object with magnitude \(m\). Returns array_like of the same shape as magnitude. Exemption: If magnitude is scalar and magnitude_95 or magnitude_50 is array_like of shape (nb, ) it returns array_like of shape (nb, ).

References

[1]

López-Sanjuan, C. et al., 2017A&A…599A..62L