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
This condition is broadcast over the input. At locations where the condition is True, the
out
array will be set to the ufunc result. Elsewhere, theout
array will retain its original value. Note that if an uninitializedout
array is created via the defaultout=None
, locations within it where the condition is False will remain uninitialized.**kwargs :
For other keyword-only arguments, see the ufunc docs.
- Returns
out : ndarray or scalar
Array of the same shape as
x
. This is a scalar ifx
is a scalar.
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”, https://en.wikipedia.org/wiki/Arctanh
Examples
>>> np.arctanh([0, -0.5]) array([ 0. , -0.54930614])