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 or scalar

Array of the same shape as x. This is a scalar if x is a scalar.

See also

emath.arctanh

Notes

arctanh() is a multivalued function: for each x there are infinitely many numbers z such that tanh(z) = x. The convention is to return the z 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 yields nan and sets the invalid 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 or tanh^-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])