# jax.numpy.arctanh¶

jax.numpy.arctanh(x)

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])

Parameters

x (array_like) – Input array.

Returns

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

Return type

ndarray or scalar

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

1

M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/

2

Wikipedia, “Inverse hyperbolic function”, https://en.wikipedia.org/wiki/Arctanh

Examples

>>> np.arctanh([0, -0.5])
array([ 0.        , -0.54930614])