# arcsinh function¶

(Shortest import: from brian2 import arcsinh)

brian2.units.unitsafefunctions.arcsinh(x[, out])

Inverse hyperbolic sine element-wise.

Parameters: x : array_like Input array. out : ndarray, optional Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. See doc.ufuncs. out : ndarray Array of of the same shape as x.

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

 [R15] M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 86. http://www.math.sfu.ca/~cbm/aands/
 [R16] Wikipedia, “Inverse hyperbolic function”, http://en.wikipedia.org/wiki/Arcsinh

Examples

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