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
 xarray_like
Input array.
 outndarray, 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.
 wherearray_like, optional
This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default
out=None
, locations within it where the condition is False will remain uninitialized. **kwargs
For other keywordonly arguments, see the ufunc docs.
 Returns
 outndarray or scalar
Array of the same shape as x. This is a scalar if x is a scalar.
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
 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”, https://en.wikipedia.org/wiki/Arctanh
Examples
>>> np.arctanh([0, 0.5]) array([ 0. , 0.54930614])