# xarray.ufuncs.arctanh¶

xarray.ufuncs.arctanh = <xarray.ufuncs._UFuncDispatcher object>

xarray specific variant of numpy.arctanh. Handles xarray.Dataset, xarray.DataArray, xarray.Variable, numpy.ndarray and dask.array.Array objects with automatic dispatching.

Documentation from numpy:

arctanh(x[, out])

Inverse hyperbolic tangent element-wise.

Parameters: x : array_like Input array. out : ndarray Array of the same shape as x.

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

 [R35] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/
 [R36] Wikipedia, “Inverse hyperbolic function”, http://en.wikipedia.org/wiki/Arctanh

Examples

>>> np.arctanh([0, -0.5])
array([ 0.        , -0.54930614])