dpnp.atanh

dpnp.atanh(x, out=None, where=True, order='K', dtype=None, subok=True, **kwargs)

Computes hyperbolic inverse tangent for each element x_i for input array x.

The inverse of dpnp.tanh, so that if y = tanh(x) then x = arctanh(y). Note that dpnp.atanh is an alias of dpnp.arctanh.

For full documentation refer to numpy.arctanh.

Parameters:

x ({dpnp.ndarray, usm_ndarray}) -- Input array, expected to have numeric data type.
out ({None, dpnp.ndarray, usm_ndarray}, optional) -- Output array to populate. Array must have the correct shape and the expected data type. Default: None.
order ({"C", "F", "A", "K"}, optional) -- Memory layout of the newly output array, if parameter out is None. Default: "K".

Returns:

out -- An array containing the element-wise hyperbolic inverse tangent. The data type of the returned array is determined by the Type Promotion Rules.

Return type:

dpnp.ndarray

Limitations

Parameters where and subok are supported with their default values. Keyword argument kwargs is currently unsupported. Otherwise NotImplementedError exception will be raised.

See also

dpnp.tanh: Hyperbolic tangent, element-wise.
dpnp.arcsinh: Hyperbolic inverse sine, element-wise.
dpnp.arccosh: Hyperbolic inverse cosine, element-wise.
dpnp.arctan: Trigonometric inverse tangent, element-wise.

Notes

dpnp.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 angle z whose real part lies in [-pi/2, pi/2].

For real-valued input data types, dpnp.arctanh always returns real output. For each value that cannot be expressed as a real number or infinity, it yields nan.

For complex-valued input, dpnp.arctanh is a complex analytic function that has, by convention, the branch cuts [-1, -inf] and [1, inf] and is is continuous from above on the former and from below on the latter.

The inverse hyperbolic tan is also known as \(atanh\) or \(tanh^{-1}\).

Examples

>>> import dpnp as np
>>> x = np.array([0, -0.5])
>>> np.arctanh(x)
array([0.0, -0.54930614])