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 \(x = atanh(y)\). Note that dpnp.arctanh is an alias of dpnp.atanh.

For full documentation refer to numpy.atanh.

Parameters:

  • x ({dpnp.ndarray, usm_ndarray}) -- Input array, expected to have a floating-point 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 ({None, "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 inverse hyperbolic tangent, in radians. 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.asinh

Hyperbolic inverse sine, element-wise.

dpnp.acosh

Hyperbolic inverse cosine, element-wise.

dpnp.atan

Trigonometric inverse tangent, element-wise.

Notes

dpnp.atanh 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 the imaginary part lies in the interval \([-\pi/2, \pi/2]\).

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

For complex floating-point input data types, dpnp.atanh is a complex analytic function that has, by convention, the branch cuts \((-\infty, -1]\) and \([1, \infty)\) and is continuous from above on the former and from below on the latter.

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

Examples

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