mars.tensor.arctanh

mars.tensor.arctanh(x, out=None, where=None, **kwargs)[source]

Inverse hyperbolic tangent element-wise.

x : array_like
Input tensor.
out : Tensor, None, or tuple of Tensor 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 tensor 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

out : Tensor
Array of the same shape as x.

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.

[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”, http://en.wikipedia.org/wiki/Arctanh
>>> import mars.tensor as mt
>>> mt.arctanh([0, -0.5]).execute()
array([ 0.        , -0.54930614])