arccosh function

(Shortest import: from brian2 import arccosh)

brian2.units.unitsafefunctions.arccosh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

Inverse hyperbolic cosine, element-wise.

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.

where : array_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

arccosh : ndarray

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

See also

cosh(), arcsinh(), sinh(), arctanh(), tanh()

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

R13

M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/

R14

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