def log_sum(
log_x: np.ndarray,
offset: Optional[Union[Iterable[float], float]] = None
) -> Union[np.ndarray, float]:
r"""
Calculates the sum of a log vector or matrix.
If the input array is a matrix, the sum is taken along the columns.
Notes
-----
Given a vector, :math:`V`,
.. math::
V = [x_1, x_2, \dots, x_n]
where :math:`x_i` is the log value at row :math:`i`, the function will calculate the sum of this vector. If data
is a matrix, it will calculate the sum of the column vectors.
Parameters
----------
log_x
a vector or matrix of log values
offset
the offset to subtract and re-add. This is done to avoid corner cases where the log values are extremely large
Returns
-------
ndarray or float
sum of log values
"""
log_x = as_array(log_x)
if log_x.ndim == 1:
log_x = log_x.reshape(-1, 1)
elif log_x.ndim > 2:
raise ValueError("Input must be a vector or matrix.")
if offset is None:
offset = log_x.max(0) # maximum from each column
elif hasattr(offset, "__iter__"):
offset = np.asarray(offset)
assert len(
offset) == log_x.shape[1], "Offset must match data dimensions"
res = offset + np.log(np.exp(log_x - offset).sum(0))
return res if len(res) > 1 else res[0]
def debye2(x):
"""
Custom debye order 2 that takes care of negative numbers or non-finite numbers
Parameters
----------
x: array_like
Numeric vector
Returns
-------
ndarray or scalar
Debye order 2 numbers
See Also
--------
:code:`copulae.special.debye.debye_2`: The debye order 2 function
"""
x = as_array(x)
fin = np.isfinite(x)
d = np.ravel(np.abs(x))
with np.errstate(invalid='ignore'):
if np.all(fin):
d = debye_2(d)
else:
d[fin] = debye_2(d[fin])
d = np.ravel(d)
pinf = np.isposinf(x)
if np.any(pinf):
d[pinf] = 0 # set positive infinity to 0 (but not na, thus can't use ~fin)
d = np.ravel(d)
d[x < 0] -= 2 / 3 * x[x < 0]
return d.item(0) if d.size == 1 else d