|
"""Compute the log of the sum of exponentials of input elements.
Parameters ---------- a : array_like Input array. axis : None 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.
.. versionadded:: 0.11.0 keepdims : bool, 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.
.. versionadded:: 0.15.0 b : array-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.
.. versionadded:: 0.12.0 return_sign : bool, 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).
.. versionadded:: 0.16.0
Returns ------- res : ndarray 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. sgn : ndarray If return_sign is True, this will be an array of floating-point numbers matching res and +1, 0, or -1 depending on the sign of the result. If 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.
Examples -------- >>> from scipy.special import logsumexp >>> a = np.arange(10) >>> np.log(np.sum(np.exp(a))) 9.4586297444267107 >>> logsumexp(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
""" a = _asarray_validated(a, check_finite=False) if b is not None: a, b = np.broadcast_arrays(a, b) if np.any(b == 0): a = a + 0. # promote to at least float a[b == 0] = -np.inf
a_max = np.amax(a, axis=axis, keepdims=True)
if a_max.ndim > 0: a_max[~np.isfinite(a_max)] = 0 elif not np.isfinite(a_max): a_max = 0
if b is not None: b = np.asarray(b) tmp = b * np.exp(a - a_max) else: tmp = np.exp(a - a_max)
# suppress warnings about log of zero with np.errstate(divide='ignore'): s = np.sum(tmp, axis=axis, keepdims=keepdims) if return_sign: sgn = np.sign(s) s *= sgn # /= makes more sense but we need zero -> zero out = np.log(s)
if not keepdims: a_max = np.squeeze(a_max, axis=axis) out += a_max
if return_sign: return out, sgn else: return out |