arccosh function¶
(Shortest import: from brian2 import arccosh)
-
brian2.units.unitsafefunctions.
arccosh
(x[, out])¶ Inverse hyperbolic cosine, element-wise.
Parameters: x : array_like
Input array.
out : ndarray, optional
Array of the same shape as
x
, to store results in. Seedoc.ufuncs
(Section “Output arguments”) for details.Returns: arccosh : ndarray
Array of the same shape as
x
.Notes
arccosh()
is a multivalued function: for eachx
there are infinitely many numbersz
such thatcosh(z) = x
. The convention is to return thez
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 yieldsnan
and sets theinvalid
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”, http://en.wikipedia.org/wiki/Arccosh Examples
>>> np.arccosh([np.e, 10.0]) array([ 1.65745445, 2.99322285]) >>> np.arccosh(1) 0.0