dpnp.arccosh¶

dpnp.arccosh = <DPNPUnaryFunc 'acosh'>¶

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, 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 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.

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])