# asinh#

ivy.asinh(x, /, *, out=None)[source]#

Calculate an implementation-dependent approximation to the inverse hyperbolic sine, having domain `[-infinity, +infinity]` and codomain `[-infinity, +infinity]`, for each element `x_i` in the input array `x`.

Special cases

For floating-point operands,

• If `x_i` is `NaN`, the result is `NaN`.

• If `x_i` is `+0`, the result is `+0`.

• If `x_i` is `-0`, the result is `-0`.

• If `x_i` is `+infinity`, the result is `+infinity`.

• If `x_i` is `-infinity`, the result is `-infinity`.

Parameters:
• x (`Union`[`Array`, `NativeArray`]) – input array whose elements each represent the area of a hyperbolic sector. Should have a floating-point data type.

• out (`Optional`[`Array`]) – optional output array, for writing the result to. It must have a shape that the (default: `None`) inputs broadcast to.

Return type:

`Array`

Returns:

ret – an array containing the inverse hyperbolic sine of each element in `x`. The returned array must have a floating-point data type determined by type-promotion.

This function conforms to the Array API Standard. This docstring is an extension of the docstring # noqa in the standard.

Both the description and the type hints above assumes an array input for simplicity, but this function is nestable, and therefore also accepts `ivy.Container` instances in place of any of the arguments.

Examples

With `ivy.Array` input:

```>>> x = ivy.array([-3.5, -0, +0, 1.3, float('nan')])
>>> y = ivy.asinh(x)
>>> print(y)
ivy.array([-1.97, 0., 0., 1.08, nan])
```
```>>> x = ivy.array([-2, -0.75, 0.9, 1])
>>> y = ivy.zeros(4)
>>> ivy.asinh(x, out=y)
>>> print(y)
ivy.array([-1.44, -0.693, 0.809, 0.881])
```
```>>> x = ivy.array([[0.2, 0.4, 0.6],[-0.8, -1, -2]])
>>> ivy.asinh(x, out=x)
>>> print(x)
ivy.array([[ 0.199, 0.39, 0.569],
[-0.733, -0.881, -1.44]])
```

With `ivy.Container` input:

```>>> x = ivy.Container(a=ivy.array([0., 1, 2]),
...                   b=ivy.array([4.2, -5.3, -0, -2.3]))
>>> y = ivy.asinh(x)
>>> print(y)
{
a: ivy.array([0., 0.881, 1.44]),
b: ivy.array([2.14, -2.37, 0., -1.57])
}
```
Array.asinh(self, *, out=None)#

ivy.Array instance method variant of ivy.asinh. This method simply wraps the function, and so the docstring for ivy.asinh also applies to this method with minimal changes.

Parameters:
• self (`Array`) – input array whose elements each represent the area of a hyperbolic sector. Should have a floating-point data type.

• out (`Optional`[`Array`]) – optional output array, for writing the result to. It must have a shape that (default: `None`) the inputs broadcast to.

Return type:

`Array`

Returns:

ret – an array containing the inverse hyperbolic sine of each element in `self`. The returned array must have a floating-point data type determined by type-promotion.

Examples

```>>> x = ivy.array([-1., 0., 3.])
>>> y = x.asinh()
>>> print(y)
ivy.array([-0.881,  0.   ,  1.82 ])
```
Container.asinh(self, *, key_chains=None, to_apply=True, prune_unapplied=False, map_sequences=False, out=None)#

ivy.Container instance method variant of ivy.asinh. This method simply wraps the function, and so the docstring for ivy.asinh also applies to this method with minimal changes.

Parameters:
• self (`Container`) – input container whose elements each represent the area of a hyperbolic sector. Should have a floating-point data type.

• key_chains (`Optional`[`Union`[`List`[`str`], `Dict`[`str`, `str`]]]) – The key-chains to apply or not apply the method to. Default is `None`. (default: `None`)

• to_apply (`bool`) – If True, the method will be applied to key_chains, otherwise key_chains (default: `True`) will be skipped. Default is `True`.

• prune_unapplied (`bool`) – Whether to prune key_chains for which the function was not applied. (default: `False`) Default is `False`.

• map_sequences (`bool`) – Whether to also map method to sequences (lists, tuples). (default: `False`) Default is `False`.

• out (`Optional`[`Container`]) – optional output container, for writing the result to. It must have a shape (default: `None`) that the inputs broadcast to.

Return type:

`Container`

Returns:

ret – a container containing the inverse hyperbolic sine of each element in `self`. The returned container must have a floating-point data type determined by type-promotion.

Examples

```>>> x = ivy.Container(a=ivy.array([-1, 3.7, -5.1]),
...                   b=ivy.array([4.5, -2.4, -1.5]))
>>> y = x.asinh()
>>> print(y)
{
a: ivy.array([-0.881, 2.02, -2.33]),
b: ivy.array([2.21, -1.61, -1.19])
}
```