numpy.arccosh — NumPy v1.11 Manual (original) (raw)
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. |
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| 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/ |
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| [R3] | Wikipedia, “Inverse hyperbolic function”,http://en.wikipedia.org/wiki/Arccosh |
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Examples
np.arccosh([np.e, 10.0]) array([ 1.65745445, 2.99322285]) np.arccosh(1) 0.0