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Module « scipy.special »

Fonction xlog1py - module scipy.special

Signature de la fonction xlog1py

def xlog1py(*args, **kwargs) 

Description

help(scipy.special.xlog1py)

xlog1py(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

xlog1py(x, y, out=None)

Compute ``x*log1p(y)`` so that the result is 0 if ``x = 0``.

Parameters
----------
x : array_like
    Multiplier
y : array_like
    Argument
out : ndarray, optional
    Optional output array for the function results

Returns
-------
z : scalar or ndarray
    Computed x*log1p(y)

Notes
-----

.. versionadded:: 0.13.0

Examples
--------
This example shows how the function can be used to calculate the log of
the probability mass function for a geometric discrete random variable.
The probability mass function of the geometric distribution is defined
as follows:

.. math:: f(k) = (1-p)^{k-1} p

where :math:`p` is the probability of a single success
and :math:`1-p` is the probability of a single failure
and :math:`k` is the number of trials to get the first success.

>>> import numpy as np
>>> from scipy.special import xlog1py
>>> p = 0.5
>>> k = 100
>>> _pmf = np.power(1 - p, k - 1) * p
>>> _pmf
7.888609052210118e-31

If we take k as a relatively large number the value of the probability
mass function can become very low. In such cases taking the log of the
pmf would be more suitable as the log function can change the values
to a scale that is more appropriate to work with.

>>> _log_pmf = xlog1py(k - 1, -p) + np.log(p)
>>> _log_pmf
-69.31471805599453

We can confirm that we get a value close to the original pmf value by
taking the exponential of the log pmf.

>>> _orig_pmf = np.exp(_log_pmf)
>>> np.isclose(_pmf, _orig_pmf)
True

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