# Creating Continuous Search Spaces

This example illustrates several ways to create continuous spaces space.

## Imports


```python
import numpy as np
```


```python
from baybe.parameters import NumericalContinuousParameter
from baybe.searchspace import SearchSpace, SubspaceContinuous
```

## Settings

We begin by defining the continuous parameters that span our space:


```python
DIMENSION = 4
BOUNDS = (-1, 1)
```


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

From these parameter objects, we can now construct a continuous subspace.
Let us draw some samples from it and verify that they are within the bounds:


```python
subspace = SubspaceContinuous(parameters)
samples = subspace.sample_uniform(10)
print(samples)
assert np.all(samples >= BOUNDS[0]) and np.all(samples <= BOUNDS[1])
```

            x_1       x_2       x_3       x_4
    0 -0.184832  0.005348 -0.706812  0.186633
    1  0.790052  0.792900 -0.720528  0.824114
    2 -0.551268 -0.943288 -0.340380  0.447687
    3 -0.888001 -0.261984  0.808173  0.060061
    4 -0.506423  0.868892 -0.495761 -0.939145
    5 -0.925973 -0.111182  0.792783 -0.734339
    6  0.485637 -0.809896 -0.859195 -0.218443
    7  0.363565  0.440093 -0.440328 -0.535968
    8 -0.580427 -0.734504 -0.364797  0.783661
    9  0.975841 -0.722036  0.432780 -0.941887


There are several ways we can turn the above objects into a search space.
This provides a lot of flexibility depending on the context:


```python
# Using conversion:
searchspace1 = SubspaceContinuous(parameters).to_searchspace()
```


```python
# Explicit attribute assignment via the regular search space constructor:
searchspace2 = SearchSpace(continuous=SubspaceContinuous(parameters))
```


```python
# Using an alternative search space constructor:
searchspace3 = SearchSpace.from_product(parameters=parameters)
```

No matter which version we choose, we can be sure that the resulting search space
objects are equivalent:


```python
assert searchspace1 == searchspace2 == searchspace3
```