numpy.arccosh¶
- numpy.arccosh(x[, out]) = <ufunc 'arccosh'>¶
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. See doc.ufuncs (Section “Output arguments”) for details.
Returns: arccosh : ndarray
Array of the same shape as x.
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
[R2] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/ [R3] 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