nums.numpy.arctanh

nums.numpy.arctanh(x, out=None, where=True, **kwargs)[source]

Inverse hyperbolic tangent element-wise.

This docstring was copied from numpy.arctanh.

Some inconsistencies with the NumS version may exist.

Parameters

  • x (BlockArray) – Input array.

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

  • where (BlockArray, optional) – This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized.

  • **kwargs – For other keyword-only arguments, see the ufunc docs.

Returns

out – Array of the same shape as x.

Return type

BlockArray or scalar

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

1

M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/

2

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

Examples

The doctests shown below are copied from NumPy. They won’t show the correct result until you operate get().

>>> nps.arctanh(nps.array([0, -0.5])).get()  
array([ 0.        , -0.54930614])

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