# nlcpy.arcsinh

nlcpy.arcsinh = <ufunc 'nlcpy_arcsinh'>

Computes the element-wise inverse hyperbolic sine.

Parameters
xarray_like

Input an array or a scalar.

outndarray or 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 section Optional Keyword Arguments.

Returns
yndarray

The inverse hyperbolic sine values for each element of x. If x is a scalar, this function returns the result as a 0-dimension ndarray.

`sinh`

Computes the element-wise hyperbolic sine.

`arccosh`

Computes the element-wise inverse hyperbolic cosine.

`arctanh`

Computes the element-wise inverse hyperbolic tangent.

• `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.

Examples

```>>> import nlcpy as vp
>>> vp.arcsinh(vp.array([vp.e, 10.0]))
array([1.72538256, 2.99822295])
```