dpnp.acosh

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

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

The inverse of dpnp.cosh so that, if y = cosh(x), then x = arccosh(y). Note that dpnp.acosh is an alias of dpnp.arccosh.

For full documentation refer to numpy.arccosh.

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 inverse hyperbolic cosine, in radians and in the half-closed interval [0, inf). 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.cosh

Hyperbolic cosine, element-wise.

dpnp.arcsinh

Hyperbolic inverse sine, element-wise.

dpnp.sinh

Hyperbolic sine, element-wise.

dpnp.arctanh

Hyperbolic inverse tangent, element-wise.

dpnp.tanh

Hyperbolic tangent, element-wise.

dpnp.arccos

Trigonometric inverse cosine, element-wise.

Notes

dpnp.arccosh is a multivalued function: for each x there are infinitely many numbers z such that cosh(z) = x. The convention is to return the angle z whose real part lies in [0, inf].

For real-valued input data types, dpnp.arccosh 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.arccosh is a complex analytic function that has, by convention, the branch cuts [-inf, 1] and is continuous from above.

The inverse hyperbolic cos is also known as \(acosh\) or \(cosh^{-1}\).

Examples

>>> import dpnp as np
>>> x = np.array([1.0, np.e, 10.0])
>>> np.arccosh(x)
array([0.0, 1.65745445, 2.99322285])