numpy.arctanh()

numpy.arctanh(x[, out]) =

Inverse hyperbolic tangent element-wise.

Parameters:

x : array_like

Input array.

Returns:

out : ndarray

Array of the same shape as x.

See also

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

[R7] M. Abramowitz and I.A. Stegun, ?Handbook of Mathematical Functions?, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/
[R8] Wikipedia, ?Inverse hyperbolic function?, http://en.wikipedia.org/wiki/Arctanh

Examples

>>> np.arctanh([0, -0.5])
array([ 0.        , -0.54930614])
doc_NumPy
2017-01-10 18:12:43
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