# numpy.arccosh#

numpy.arccosh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature]) = <ufunc 'arccosh'>#

Inverse hyperbolic cosine, element-wise.

Parameters:
xarray_like

Input array.

outndarray, None, or tuple of ndarray and None, optional

A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.

wherearray_like, optional

This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default `out=None`, locations within it where the condition is False will remain uninitialized.

**kwargs

For other keyword-only arguments, see the ufunc docs.

Returns:
arccoshndarray

Array of the same shape as x. This is a scalar if x is a scalar.

Notes

`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 z whose imaginary part lies in `[-pi, pi]` and the real part in `[0, inf]`.

For real-valued input data types, `arccosh` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields `nan` and sets the invalid floating point error flag.

For complex-valued input, `arccosh` is a complex analytical function that has a branch cut [-inf, 1] and is continuous from above on it.

References

[1]

M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. https://personal.math.ubc.ca/~cbm/aands/page_86.htm

[2]

Wikipedia, “Inverse hyperbolic function”, https://en.wikipedia.org/wiki/Arccosh

Examples

```>>> import numpy as np
>>> np.arccosh([np.e, 10.0])
array([ 1.65745445,  2.99322285])
>>> np.arccosh(1)
0.0
```