dpnp.arctanh

dpnp.arctanh = <DPNPUnaryFunc 'atanh'>

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, tuple of ndarray}, optional

Output array to populate. Array must have the correct shape and the expected data type. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.

Default: None.

order{None, "C", "F", "A", "K"}, optional

Memory layout of the newly output array, if parameter out is None.

Default: "K".

Returns:

outdpnp.ndarray

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.

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])