scipy.special.

logsumexp#

scipy.special.logsumexp(a, axis=None, b=None, keepdims=False, return_sign=False)[source]#

Compute the log of the sum of exponentials of input elements.

Parameters:

aarray_like: Input array.
axisNone or int or tuple of ints, optional: Axis or axes over which the sum is taken. By default axis is None, and all elements are summed.

Added in version 0.11.0.
barray-like, optional: Scaling factor for exp(a) must be of the same shape as a or broadcastable to a. These values may be negative in order to implement subtraction.

Added in version 0.12.0.
keepdimsbool, optional: If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original array.

Added in version 0.15.0.
return_signbool, optional: If this is set to True, the result will be a pair containing sign information; if False, results that are negative will be returned as NaN. Default is False (no sign information).

Added in version 0.16.0.

Returns:

resndarray: The result, np.log(np.sum(np.exp(a))) calculated in a numerically more stable way. If b is given then np.log(np.sum(b*np.exp(a))) is returned. If return_sign is True, res contains the log of the absolute value of the argument.
sgnndarray: If return_sign is True, this will be an array of floating-point numbers matching res containing +1, 0, -1 (for real-valued inputs) or a complex phase (for complex inputs). This gives the sign of the argument of the logarithm in res. If return_sign is False, only one result is returned.

See also

numpy.logaddexp, numpy.logaddexp2

Notes

NumPy has a logaddexp function which is very similar to logsumexp, but only handles two arguments. logaddexp.reduce is similar to this function, but may be less stable.

The logarithm is a multivalued function: for each \(x\) there is an infinite number of \(z\) such that \(exp(z) = x\). The convention is to return the \(z\) whose imaginary part lies in \((-pi, pi]\).

Examples

>>> import numpy as np
>>> from scipy.special import logsumexp
>>> a = np.arange(10)
>>> logsumexp(a)
9.4586297444267107
>>> np.log(np.sum(np.exp(a)))
9.4586297444267107

With weights

>>> a = np.arange(10)
>>> b = np.arange(10, 0, -1)
>>> logsumexp(a, b=b)
9.9170178533034665
>>> np.log(np.sum(b*np.exp(a)))
9.9170178533034647

Returning a sign flag

>>> logsumexp([1,2],b=[1,-1],return_sign=True)
(1.5413248546129181, -1.0)

Notice that logsumexp does not directly support masked arrays. To use it on a masked array, convert the mask into zero weights:

>>> a = np.ma.array([np.log(2), 2, np.log(3)],
...                  mask=[False, True, False])
>>> b = (~a.mask).astype(int)
>>> logsumexp(a.data, b=b), np.log(5)
1.6094379124341005, 1.6094379124341005