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])