dpnp.arccosh

dpnp.arccosh(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 \(x = acosh(y)\). Note that dpnp.arccosh is an alias of dpnp.acosh.

For full documentation refer to numpy.acosh.

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 cosine, in radians and in the half-closed interval \([0, \infty)\). 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.asinh

Hyperbolic inverse sine, element-wise.

dpnp.sinh

Hyperbolic sine, element-wise.

dpnp.atanh

Hyperbolic inverse tangent, element-wise.

dpnp.tanh

Hyperbolic tangent, element-wise.

dpnp.acos

Trigonometric inverse cosine, element-wise.

Notes

dpnp.acosh 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 the real part lies in the interval \([0, \infty)\) and the imaginary part in the interval \([-\pi, \pi]\).

For real-valued floating-point input data types, dpnp.acosh 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.acosh is a complex analytic function that has, by convention, the branch cuts \((-\infty, 1)\) and is continuous from above on it.

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

Examples

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