# 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  0.601695 -0.934194  0.653773 -0.205518
    1 -0.774099 -0.043234  0.849342  0.071294
    2 -0.615049 -0.179733 -0.646783 -0.608451
    3 -0.884077  0.826561 -0.534024  0.370063
    4 -0.130680 -0.513415  0.302674  0.230553
    5 -0.562261  0.349272  0.635123 -0.584136
    6 -0.833806 -0.753765  0.506007 -0.599539
    7  0.032850 -0.399415  0.727299  0.103442
    8  0.944060 -0.804807 -0.472628  0.035451
    9 -0.128686  0.094946  0.352237  0.166231


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
```