ath::

    h(X) = - \int_{\chi} f(x) \log f(x) dx

`logentropy` computes the logarithm of the differential entropy
("log-entropy"), :math:`log(h(X))`, but it may be numerically favorable
compared to the naive implementation (computing :math:`h(X)` then
taking the logarithm).

Parameters
----------
method : {None, 'formula', 'logexp', 'quadrature}
    The strategy used to evaluate the log-entropy. By default
    (``None``), the infrastructure chooses between the following options,
    listed in order of precedence.

    - ``'formula'``: use a formula for the log-entropy itself
    - ``'logexp'``: evaluate the entropy and take the logarithm
    - ``'quadrature'``: numerically log-integrate the logarithm of the
      entropy integrand

    Not all `method` options are available for all distributions.
    If the selected `method` is not available, a ``NotImplementedError``
    will be raised.

Returns
-------
out : array
    The log-entropy.

See Also
--------
entropy
logpdf

Notes
-----
If the entropy of a distribution is negative, then the log-entropy
is complex with imaginary part :math:`\pi`. For
consistency, the result of this function always has complex dtype,
regardless of the value of the imaginary part.

References
----------
.. [1] Differential entropy, *Wikipedia*,
       https://en.wikipedia.org/wiki/Differential_entropy

Examples
--------
Instantiate a distribution with the desired parameters:

>>> import numpy as np
>>> from scipy import stats
>>> X = stats.Uniform(a=-1., b=1.)

Evaluate the log-entropy:

>>> X.logentropy()
(-0.3665129205816642+0j)
>>> np.allclose(np.exp(X.logentropy()), X.entropy())
True

For a random variable with negative entropy, the log-entropy has an
imaginary part equal to `np.pi`.

>>> X = stats.Uniform(a=-.1, b=.1)
>>> X.entropy(), X.logentropy()
(-1.6094379124341007, (0.4758849953271105+3.141592653589793j))

r