jax.numpy.arccosh

jax.numpy.arccosh(x)[source]

Inverse hyperbolic cosine, element-wise.

LAX-backend implementation of arccosh(). Original docstring below.

arccosh(x, /, out=None, *, where=True, casting=’same_kind’, order=’K’, dtype=None, subok=True[, signature, extobj])

Parameters
  • x (array_like) – Input array.

  • out (ndarray, 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.

Returns

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

Return type

ndarray

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. http://www.math.sfu.ca/~cbm/aands/

2

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

Examples

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