Inverse hyperbolic tangent element-wise.
LAX-backend implementation of
arctanh(). Original docstring below.
arctanh(x, /, out=None, *, where=True, casting=’same_kind’, order=’K’, dtype=None, subok=True[, signature, extobj])
x (array_like) – Input array.
out – Array of the same shape as x. This is a scalar if x is a scalar.
- Return type
ndarray or scalar
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
nanand 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
M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/
Wikipedia, “Inverse hyperbolic function”, https://en.wikipedia.org/wiki/Arctanh
>>> np.arctanh([0, -0.5]) array([ 0. , -0.54930614])