numpy.atanh#

numpy.atanh(x,/,out=None,*,where=True,casting='same_kind',order='K',dtype=None,subok=True[,signature])=<ufunc'arctanh'>#

Inverse hyperbolic tangent, element-wise.

Parameters:
xarray_like

Input array.

outndarray, None, or tuple of ndarray and None, optional

A location into which the result is stored. If provided, it must havea shape that the inputs broadcast to. If not provided or None,a freshly-allocated array is returned. A tuple (possible only as akeyword argument) must have length equal to the number of outputs.

wherearray_like, optional

This condition is broadcast over the input. At locations where thecondition is True, theout array will be set to the ufunc result.Elsewhere, theout array will retain its original value.Note that if an uninitializedout array is created via the defaultout=None, locations within it where the condition is False willremain uninitialized.

**kwargs

For other keyword-only arguments, see theufunc docs.

Returns:
outndarray or scalar

Array of the same shape asx.This is a scalar ifx is a scalar.

Notes

arctanh is a multivalued function: for eachx there are infinitelymany numbersz such thattanh(z)=x. The convention is to returnthez 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 yieldsnan and sets theinvalid floating point error flag.

For complex-valued input,arctanh is a complex analytical functionthat has branch cuts[-1, -inf] and[1, inf] and is continuous fromabove on the former and from below on the latter.

The inverse hyperbolic tangent is also known asatanh ortanh^-1.

References

[1]

M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”,10th printing, 1964, pp. 86.https://personal.math.ubc.ca/~cbm/aands/page_86.htm

[2]

Wikipedia, “Inverse hyperbolic function”,https://en.wikipedia.org/wiki/Arctanh

Examples

>>>importnumpyasnp>>>np.arctanh([0,-0.5])array([ 0.        , -0.54930614])
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