# 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  0.893413 -0.356334  0.833179  0.839585
    1  0.820896 -0.151804  0.743704  0.134664
    2 -0.977255  0.137418  0.349572 -0.162359
    3 -0.276872  0.795354 -0.460301  0.435170
    4 -0.552397  0.539102  0.477156 -0.831487
    5 -0.439010 -0.961025 -0.871273  0.905627
    6 -0.166370 -0.024044 -0.241759 -0.832785
    7  0.731557  0.411581  0.662045 -0.845442
    8  0.579161 -0.395107  0.009426 -0.217006
    9 -0.129863 -0.244680 -0.463913  0.596830


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
```