# 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=None, *, where=True, casting=’same_kind’, order=’K’, dtype=None, subok=True[, signature, extobj])

  Inverse hyperbolic tangent element-wise.

  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 freshly-allocated 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 keyword-only 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 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

  [R84] | M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/

  [R85] | Wikipedia, “Inverse hyperbolic function”, http://en.wikipedia.org/wiki/Arctanh

  Examples

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