numpy.arcsinh — NumPy v1.11 Manual (original) (raw)
numpy.arcsinh(_x_[, _out_]) = <ufunc 'arcsinh'>¶
Inverse hyperbolic sine element-wise.
| Parameters: | x : array_like Input array. out : ndarray, optional Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See doc.ufuncs. |
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| Returns: | out : ndarray Array of of the same shape as x. |
Notes
arcsinh is a multivalued function: for each x there are infinitely many numbers z such that sinh(z) = x. The convention is to return the_z_ whose imaginary part lies in [-pi/2, pi/2].
For real-valued input data types, arcsinh always returns real output. For each value that cannot be expressed as a real number or infinity, it returns nan and sets the invalid floating point error flag.
For complex-valued input, arccos is a complex analytical function that has branch cuts [1j, infj] and [-1j, -infj] and is continuous from the right on the former and from the left on the latter.
The inverse hyperbolic sine is also known as asinh or sinh^-1.
References
| [R4] | 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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| [R5] | Wikipedia, “Inverse hyperbolic function”,http://en.wikipedia.org/wiki/Arcsinh |
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Examples
np.arcsinh(np.array([np.e, 10.0])) array([ 1.72538256, 2.99822295])