Parameter space

In this example, we will see the basics of ParameterSpace.

from __future__ import absolute_import, division, print_function, unicode_literals

from future import standard_library

from gemseo.algos.parameter_space import ParameterSpace
from gemseo.api import configure_logger, create_discipline, create_scenario

configure_logger()

standard_library.install_aliases()

Firstly, a ParameterSpace does not require any mandatory argument.

Create a parameter space

parameter_space = ParameterSpace()

Then, we can add either deterministic variables from their lower and upper bounds (use DesignSpace.add_variable()) or uncertain variables from their distribution names and parameters (use add_random_variable())

parameter_space.add_variable("x", l_b=-2.0, u_b=2.0)
parameter_space.add_random_variable("y", "SPNormalDistribution", mu=0.0, sigma=1.0)
print(parameter_space)

Out:

+-------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|                                                                          Parameter space                                                                          |
+------+-------------+-------+-------------+-------+-------------------------+----------------+-------------+------+--------------------+---------------------------+
| name | lower_bound | value | upper_bound | type  |   Initial distribution  | Transformation |   Support   | Mean | Standard deviation |           Range           |
+------+-------------+-------+-------------+-------+-------------------------+----------------+-------------+------+--------------------+---------------------------+
| x    |      -2     |  None |      2      | float |                         |                |             |      |                    |                           |
| y    |     -inf    |   0   |     inf     | float | norm(mu=0.0, sigma=1.0) |       y        | [-inf  inf] | 0.0  |        1.0         | [-7.03448383  7.03448691] |
+------+-------------+-------+-------------+-------+-------------------------+----------------+-------------+------+--------------------+---------------------------+

We can check that the deterministic and uncertain variables are implemented as deterministic and deterministic variables respectively:

print("x is deterministic: ", parameter_space.is_deterministic("x"))
print("y is deterministic: ", parameter_space.is_deterministic("y"))
print("x is uncertain: ", parameter_space.is_uncertain("x"))
print("y is uncertain: ", parameter_space.is_uncertain("y"))

Out:

x is deterministic:  True
y is deterministic:  False
x is uncertain:  False
y is uncertain:  True

Sample from the parameter space

We can sample the uncertain variables from the ParameterSpace and get values either as an array (default value) or as a dictionary:

sample = parameter_space.get_sample(n_samples=2, as_dict=True)
print(sample)
sample = parameter_space.get_sample(n_samples=4)
print(sample)

Out:

[{'y': array([1.62434536])}, {'y': array([-0.61175641])}]
[[-0.52817175]
 [-1.07296862]
 [ 0.86540763]
 [-2.3015387 ]]

Sample a discipline over the parameter space

We can also sample a discipline over the parameter space. For simplicity, we instantiate an AnalyticDiscipline from a dictionary of expressions and update the cache policy # so as to cache all data in memory.

discipline = create_discipline("AnalyticDiscipline", expressions_dict={"z": "x+y"})
discipline.set_cache_policy(discipline.MEMORY_FULL_CACHE)

From these parameter space and discipline, we build a DOEScenario and execute it with a Latin Hypercube Sampling algorithm and 100 samples.

Warning

A Scenario deals with all variables available in the DesignSpace. By inheritance, a DOEScenario deals with all variables available in the ParameterSpace. Thus, if we do not filter the uncertain variables, the DOEScenario will consider all variables. In particular, the deterministic variables will be consider as uniformly distributed.

scenario = create_scenario(
    [discipline], "DisciplinaryOpt", "z", parameter_space, scenario_type="DOE"
)
scenario.execute({"algo": "lhs", "n_samples": 100})

Out:

{'eval_jac': False, 'algo': 'lhs', 'n_samples': 100}

We can visualize the result by encapsulating the disciplinary cache in a Dataset:

dataset = discipline.cache.export_to_dataset()

This visualization can be tabular for example:

print(dataset.export_to_dataframe())

Out:

      inputs             outputs
           x         y         z
           0         0         0
0   1.299635 -0.989742  0.309892
1  -1.735541 -0.775826 -2.511367
2  -1.970047 -1.937612 -3.907659
3   1.069838  0.119366  1.189204
4   0.941424  1.992783  2.934207
..       ...       ...       ...
95 -0.209952 -1.634437 -1.844389
96  0.192194 -1.225602 -1.033407
97  0.672494  0.361084  1.033578
98  1.132283  0.913791  2.046074
99 -0.764176  0.263038 -0.501139

[100 rows x 3 columns]

or graphical by means of a scatter plot matrix for example:

dataset.plot("ScatterMatrix")

Out:

<gemseo.post.dataset.scatter_plot_matrix.ScatterMatrix object at 0x7fc29e072bb0>

Sample a discipline over the uncertain space

If we want to sample a discipline over the uncertain space, we need to filter the uncertain variables:

parameter_space.filter(parameter_space.uncertain_variables)

Out:

<gemseo.algos.parameter_space.ParameterSpace object at 0x7fc29b2718b0>

Then, we clear the cache, create a new scenario from this parameter space containing only the uncertain variables and execute it.

discipline.cache.clear()
scenario = create_scenario(
    [discipline], "DisciplinaryOpt", "z", parameter_space, scenario_type="DOE"
)
scenario.execute({"algo": "lhs", "n_samples": 100})

Out:

{'eval_jac': False, 'algo': 'lhs', 'n_samples': 100}

Finally, we build a dataset from the disciplinary cache and visualize it. We can see that the deterministic variable ‘x’ is set to its default value for all evaluations, contrary to the previous case where we were considering the whole parameter space.

dataset = discipline.cache.export_to_dataset()
print(dataset.export_to_dataframe())

Out:

   inputs             outputs
        x         y         z
        0         0         0
0     0.0  0.415113  0.415113
1     0.0  0.055256  0.055256
2     0.0  0.489919  0.489919
3     0.0 -0.523228 -0.523228
4     0.0  1.138853  1.138853
..    ...       ...       ...
95    0.0  0.607114  0.607114
96    0.0  0.550599  0.550599
97    0.0  0.114359  0.114359
98    0.0 -0.382169 -0.382169
99    0.0  0.011416  0.011416

[100 rows x 3 columns]