numpy.arctanh — NumPy v1.11 Manual (original) (raw)
numpy.arctanh(_x_[, _out_]) = <ufunc 'arctanh'>¶
Inverse hyperbolic tangent element-wise.
| Parameters: | x : array_like Input array. |
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| Returns: | out : ndarray Array of the same shape as x. |
Notes
arctanh is a multivalued function: for each x there are infinitely many numbers z such that tanh(z) = x. The convention is to return the z whose imaginary part lies in [-pi/2, pi/2].
For real-valued input data types, arctanh 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, arctanh is a complex analytical function that has branch cuts [-1, -inf] and [1, inf] and is continuous from above on the former and from below on the latter.
The inverse hyperbolic tangent is also known as atanh or tanh^-1.
References
| [R7] | 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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| [R8] | Wikipedia, “Inverse hyperbolic function”,http://en.wikipedia.org/wiki/Arctanh |
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Examples
np.arctanh([0, -0.5]) array([ 0. , -0.54930614])