# jax.numpy.arcsinh¶

jax.numpy.arcsinh(x)

Inverse hyperbolic sine element-wise.

LAX-backend implementation of arcsinh(). Original docstring below.

arcsinh(x, /, out=None, *, where=True, casting=’same_kind’, order=’K’, dtype=None, subok=True[, signature, extobj])

Parameters

x (array_like) – Input array.

Returns

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

Return type

ndarray or 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, 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

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/Arcsinh

Examples

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