numpy.arctanh¶
- numpy.arctanh(x[, out]) = <ufunc 'arctanh'>¶
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])