Calculate the logarithm of the sum of exponentiations ```log(exp(x1) + exp(x2))``` for each element `x1_i` of the input array `x1` with the respective element `x2_i` of the input array `x2`.

Special cases

For floating-point operands,

• If either `x1_i` or `x2_i` is `NaN`, the result is `NaN`.

• If `x1_i` is `+infinity` and `x2_i` is not `NaN`, the result is `+infinity`.

• If `x1_i` is not `NaN` and `x2_i` is `+infinity`, the result is `+infinity`.

Parameters:
• x1 (`Union`[`Array`, `NativeArray`]) – first input array. Should have a floating-point data type.

• x2 (`Union`[`Array`, `NativeArray`]) – second input array. Must be compatible with `x1` (see broadcasting). Should have a floating-point data type.

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

Return type:

`Array`

Returns:

ret – an array containing the element-wise results. 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 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([2., 5., 15.])
>>> y = ivy.array([3., 2., 4.])
>>> print(z)
ivy.array([ 3.31,  5.05, 15.  ])
```
```>>> x = ivy.array([[[1.1], [3.2], [-6.3]]])
>>> y = ivy.array([[8.4], [2.5], [1.6]])
>>> print(x)
ivy.array([[[8.4], [3.6], [1.6]]])
```

With one `ivy.Container` input:

```>>> x = ivy.array([[5.1, 2.3, -3.6]])
>>> y = ivy.Container(a=ivy.array([[4.], [5.], [6.]]),
...                   b=ivy.array([[5.], [6.], [7.]]))
>>> print(z)
{
a: ivy.array([[5.39, 4.17, 4.],
[5.74, 5.07, 5.],
[6.34, 6.02, 6.]]),
b: ivy.array([[5.74, 5.07, 5.],
[6.34, 6.02, 6.],
[7.14, 7.01, 7.]])
}
```

With multiple `ivy.Container` inputs:

```>>> x = ivy.Container(a=ivy.array([4., 5., 6.]),b=ivy.array([2., 3., 4.]))
>>> y = ivy.Container(a=ivy.array([1., 2., 3.]),b=ivy.array([5., 6., 7.]))
>>> print(z)
{
a: ivy.array([4.05, 5.05, 6.05]),
b: ivy.array([5.05, 6.05, 7.05])
}
```

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

Parameters:
• self (`Array`) – first input array. Should have a real-valued data type.

• x2 (`Union`[`Array`, `NativeArray`]) – second input array. Must be compatible with `self` (see broadcasting). Should have a real-valued data type.

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

Return type:

`Array`

Returns:

ret – an array containing the element-wise results. The returned array must have a real-valued floating-point data type determined by type-promotion.

Examples

```>>> x = ivy.array([2., 5., 15.])
>>> y = ivy.array([3., 2., 4.])
>>> print(z)
ivy.array([ 3.31,  5.05, 15.  ])
```
Container.logaddexp(self, x2, /, *, key_chains=None, to_apply=True, prune_unapplied=False, map_sequences=False, out=None)[source]#

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

Parameters:
• self (`Container`) – input array or container. Should have a real-valued data type.

• x2 (`Union`[`Container`, `Array`, `NativeArray`]) – input array or container. Must be compatible with `self` (see broadcasting). Should have a real-valued data type.

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

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

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

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

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

Return type:

`Container`

Returns:

ret – a container containing the element-wise results. The returned container must have a real-valued floating-point data type determined by type-promotion.

Examples

Using `ivy.Container` input:

```>>> x = ivy.Container(a=ivy.array([4., 5., 6.]),
...                   b=ivy.array([2., 3., 4.]))
>>> y = ivy.Container(a=ivy.array([1., 2., 3.]),
...                   b=ivy.array([5., 6., 7.]))