numpy.arctanh¶

numpy.
arctanh
(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'arctanh'>¶ Inverse hyperbolic tangent elementwise.
Parameters: x : array_like
Input array.
out : ndarray, None, or tuple of ndarray 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 freshlyallocated array 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
For other keywordonly arguments, see the ufunc docs.
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 realvalued input data types,
arctanh
always returns real output. For each value that cannot be expressed as a real number or infinity, it yieldsnan
and sets the invalid floating point error flag.For complexvalued 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])