# Example for using a custom BoTorch test function in a continuous searchspace

This example shows how an arbitrary python function can be used as lookup.

This example assumes some basic familiarity with using BayBE.
We thus refer to [`campaign`](./../Basics/campaign.md) for a basic example.

## Necessary imports


```python
from baybe import Campaign
from baybe.objectives import SingleTargetObjective
from baybe.parameters import NumericalContinuousParameter
from baybe.searchspace import SearchSpace
from baybe.targets import NumericalTarget
```

## Defining the custom test function

The function should accept an arbitrary or fixed amount of floats as input.
It needs to return either a single float or a tuple of floats.
It is assumed that the analytical test function does only perform a single calculation.
That is, it is assumed to work in a non-batched-way!

In this example, we implement a simple sum of squares function with a single output.


```python
def sum_of_squares(*x: float) -> float:
    """Calculate the sum of squares."""
    res = 0
    for y in x:
        res += y**2
    return res
```


```python
TEST_FUNCTION = sum_of_squares
```

For our actual experiment, we need to specify the number of dimension that we want to
use.
This is necessary to know for the creation of the parameters.
Similarly, it is necessary to state the bounds of the parameters.
These should be provided as a list of two-dimensional tuples.


```python
DIMENSION = 4
BOUNDS = [(-2, 2), (-2, 2), (-2, 2), (-2, 2)]
```

## Creating the searchspace and the objective


```python
parameters = [
    NumericalContinuousParameter(
        name=f"x_{k+1}",
        bounds=BOUNDS[k],
    )
    for k in range(DIMENSION)
]
```


```python
searchspace = SearchSpace.from_product(parameters=parameters)
```


```python
objective = SingleTargetObjective(target=NumericalTarget(name="Target", mode="MIN"))
```

## Constructing the campaign and performing a recommendation


```python
campaign = Campaign(
    searchspace=searchspace,
    objective=objective,
)
```


```python
# Get a recommendation for a fixed batch size.
BATCH_SIZE = 3
recommendation = campaign.recommend(batch_size=BATCH_SIZE)
```

Evaluate the test function.
Note that we need iterate through the rows of the recommendation.
Furthermore, we need to interpret the row as a list.


```python
target_values = []
for index, row in recommendation.iterrows():
    target_values.append(TEST_FUNCTION(*row.to_list()))
```

We add an additional column with the calculated target values.


```python
recommendation["Target"] = target_values
```

Here, we inform the campaign about our measurement.


```python
campaign.add_measurements(recommendation)
print("\n\nRecommended experiments with measured values: ")
print(recommendation)
```

    
    
    Recommended experiments with measured values: 
            x_1       x_2       x_3       x_4    Target
    0 -1.017128 -0.645944 -1.372829 -1.632060  6.000075
    1  0.630527 -0.442172  1.592231  1.351824  4.955705
    2 -1.211391  1.836804  0.287272  1.522062  7.240516