def logsumexp(arr, axis=0):
"""Computes the sum of arr assuming arr is in the log domain.
Returns log(sum(exp(arr))) while minimizing the possibility of
over/underflow.
Examples
--------
>>> import numpy as np
>>> from sklearn.utils.extmath import logsumexp
>>> a = np.arange(10)
>>> np.log(np.sum(np.exp(a)))
9.4586297444267107
>>> logsumexp(a)
9.4586297444267107
"""
return scipy_logsumexp(arr, axis)
def logsumexp(arr, axis=0):
"""Computes the sum of arr assuming arr is in the log domain.
Returns log(sum(exp(arr))) while minimizing the possibility of
over/underflow.
Examples
--------
>>> import numpy as np
>>> from sklearn.utils.extmath import logsumexp
>>> a = np.arange(10)
>>> np.log(np.sum(np.exp(a)))
9.4586297444267107
>>> logsumexp(a)
9.4586297444267107
"""
return scipy_logsumexp(arr, axis)
def logsumexp(x, axis=None, keepdims=False):
"""Computes log(sum(exp(elements across dimensions of a tensor))).
This function is more numerically stable than log(sum(exp(x))).
It avoids overflows caused by taking the exp of large inputs and
underflows caused by taking the log of small inputs.
# Arguments
x: A tensor or variable.
axis: An integer, the axis to reduce over.
keepdims: A boolean, whether to keep the dimensions or not.
If `keepdims` is `False`, the rank of the tensor is reduced
by 1. If `keepdims` is `True`, the reduced dimension is
retained with length 1.
# Returns
The reduced tensor.
"""
return scipy_logsumexp(x, axis=axis, keepdims=keepdims)
def log_sum_exp(x, axis=None, keepdims=False):
"""
Compute log(sum(exp(x))) in a numerically stable way.
Examples
--------
>>> x = np.arange(10)
>>> np.log(np.sum(np.exp(x))) #doctest: +ELLIPSIS
9.4586297444267...
>>> log_sum_exp(x) #doctest: +ELLIPSIS
9.4586297444267...
>>> log_sum_exp(x + 1000.) - 1000. #doctest: +ELLIPSIS
9.4586297444267...
>>> log_sum_exp(x - 1000.) + 1000. #doctest: +ELLIPSIS
9.4586297444267...
>>> log_sum_exp(np.random.rand(10, 5), axis=1).shape
(10,)
>>> log_sum_exp(np.random.rand(10, 5), axis=1, keepdims=True).shape
(10, 1)
"""
return scipy_logsumexp(x, axis=axis, keepdims=keepdims)
def get_union_bound_factor(n, d):
""" Compute the natural logarithm of the number of itemsets """
binoms = []
for i in range(1, d + 1):
binoms.append(log_binomial(n, i))
return scipy_logsumexp(binoms)
def get_union_bound_factor(n, d):
""" Compute the natural logarithm of the number of itemsets """
binoms = []
for i in range(1,d+1):
binoms.append(log_binomial(n, i))
return scipy_logsumexp(binoms)
def logsumexp(a):
return float(scipy_logsumexp(a))
def logsumexp(v): """ Logsumexp - our own version wraps the scipy to handle -infs """ if max(v) > -Infinity: return scipy_logsumexp(v) else: return -Infinity