numpy.arcsinh#

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

Inverse hyperbolic sine 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 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.

wherearray_like, 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:
outndarray or scalar

Array of the same shape as x. This is a scalar if x is a scalar.

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, arcsinh 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

[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/Arcsinh

Examples

>>> import numpy as np
>>> np.arcsinh(np.array([np.e, 10.0]))
array([ 1.72538256,  2.99822295])
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