arctanh function¶
(Shortest import: from brian2 import arctanh)
-
brian2.units.unitsafefunctions.
arctanh
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶ Inverse hyperbolic tangent element-wise.
Parameters: x : array_like
Input array.
out : ndarray, None, or tuple of ndarray and None, optional
A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or
None
, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.where : array_like, optional
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
**kwargs :
For other keyword-only arguments, see the ufunc docs.
Returns: out : ndarray
Array of the same shape as
x
.See also
emath.arctanh
Notes
arctanh()
is a multivalued function: for eachx
there are infinitely many numbersz
such thattanh(z) = x
. The convention is to return thez
whose imaginary part lies in[-pi/2, pi/2]
.For real-valued input data types,
arctanh()
always returns real output. For each value that cannot be expressed as a real number or infinity, it yieldsnan
and sets theinvalid
floating point error flag.For complex-valued input,
arctanh()
is a complex analytical function that has branch cuts[-1, -inf]
and[1, inf]
and is continuous from above on the former and from below on the latter.The inverse hyperbolic tangent is also known as
atanh
ortanh^-1
.References
[R17] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/ [R18] Wikipedia, “Inverse hyperbolic function”, http://en.wikipedia.org/wiki/Arctanh Examples
>>> np.arctanh([0, -0.5]) array([ 0. , -0.54930614])