# 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 -0.657925 -0.449926  0.644716  0.666811
    1 -0.305675 -0.133885 -0.415179 -0.144869
    2  0.117462  0.044651 -0.456064  0.598598
    3 -0.303347 -0.938454  0.692164 -0.916760
    4 -0.297150 -0.709411  0.465011  0.404464
    5  0.956274  0.362860 -0.011565  0.602300
    6  0.370266 -0.110847  0.646062 -0.537952
    7 -0.192416 -0.937654 -0.732442 -0.948462
    8 -0.841857  0.082312 -0.408335 -0.187503
    9  0.633939  0.288728  0.001924 -0.643819


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
```