arctanh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'arctanh'>¶
Inverse hyperbolic tangent element-wise.
x : array_like
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.
For other keyword-only arguments, see the ufunc docs.
out : ndarray
Array of the same shape as x.
arctanhis 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,
arctanhalways returns real output. For each value that cannot be expressed as a real number or infinity, it yields
nanand sets the invalid floating point error flag.
For complex-valued input,
arctanhis 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
[R8] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/ [R9] Wikipedia, “Inverse hyperbolic function”, http://en.wikipedia.org/wiki/Arctanh
>>> np.arctanh([0, -0.5]) array([ 0. , -0.54930614])