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
[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”, http://en.wikipedia.org/wiki/Arctanh Examples
>>> np.arctanh([0, -0.5]) array([ 0. , -0.54930614])