numpy.arctanh(x[, out])

Inverse hyperbolic tangent elementwise.

Parameters :

x : array_like

Input array.

Returns :

out : ndarray

Array of the same shape as x.

See also



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.


[R7]M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86.
[R8]Wikipedia, “Inverse hyperbolic function”,


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

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