Note
Go to the end to download the full example code.
Parameter space#
In this example, we will see the basics of ParameterSpace.
from __future__ import annotations
from gemseo import configure_logger
from gemseo import create_discipline
from gemseo import sample_disciplines
from gemseo.algos.parameter_space import ParameterSpace
from gemseo.post.dataset.scatter_plot_matrix import ScatterMatrix
configure_logger()
<RootLogger root (INFO)>
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 ParameterSpace.add_variable()):
parameter_space.add_variable("x", lower_bound=-2.0, upper_bound=2.0)
or uncertain variables from their distribution names and parameters
(use ParameterSpace.add_random_variable()):
parameter_space.add_random_variable("y", "SPNormalDistribution", mu=0.0, sigma=1.0)
parameter_space
Warning
We cannot mix probability distributions from different families,
e.g. an OTDistribution and a SPDistribution.
We can check that the variables x and y are implemented as deterministic and uncertain variables respectively:
parameter_space.is_deterministic("x"), parameter_space.is_uncertain("y")
(True, True)
Note that when GEMSEO does not offer a class for the SciPy distribution,
we can use the generic GEMSEO class SPDistribution
to create any SciPy distribution
by setting interfaced_distribution to its SciPy name
and parameters as a dictionary of SciPy parameter names and values
(see the documentation of SciPy).
# parameter_space.add_random_variable(
# "y",
# "SPDistribution",
# interfaced_distribution="norm",
# parameters={"loc": 1.0, "scale": 2.0},
# )
A similar procedure can be followed
for OpenTURNS distributions for which
GEMSEO does not offer a class directly.
We can use the generic GEMSEO class OTDistribution
to create any OpenTURNS distribution
by setting interfaced_distribution to its OpenTURNS name
and parameters as a tuple of OpenTURNS parameter values
(see the documentation of OpenTURNS).
# parameter_space.add_random_variable(
# "y",
# "OTDistribution",
# interfaced_distribution="Normal",
# parameters=(1.0, 2.0),
# )
Sample from the parameter space#
We can sample the uncertain variables from the ParameterSpace and
get values either as an array (default value):
sample = parameter_space.compute_samples(n_samples=2, as_dict=True)
sample
[{'y': array([1.40864186])}, {'y': array([-0.34049952])}]
or as a dictionary:
sample = parameter_space.compute_samples(n_samples=4)
sample
array([[-1.06729486],
[ 1.09949007],
[-0.67016986],
[ 0.30104017]])
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.
discipline = create_discipline("AnalyticDiscipline", expressions={"z": "x+y"})
Then,
we use the sample_disciplines() function
with an LHS algorithm
to generate 100 samples of the discipline
over the whole parameter space:
dataset = sample_disciplines(
[discipline], parameter_space, "z", algo_name="PYDOE_LHS", n_samples=100
)
WARNING - 11:24:57: No coupling in MDA, switching chain_linearize to True.
INFO - 11:24:57:
INFO - 11:24:57: *** Start Sampling execution ***
INFO - 11:24:57: Sampling
INFO - 11:24:57: Disciplines: AnalyticDiscipline
INFO - 11:24:57: MDO formulation: MDF
INFO - 11:24:57: Running the algorithm PYDOE_LHS:
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INFO - 11:24:57: *** End Sampling execution (time: 0:00:00.043557) ***
and visualize it in a tabular way:
dataset
or graphical by means of a scatter plot matrix for example:
ScatterMatrix(dataset).execute(save=False, show=True)
[<Figure size 640x480 with 9 Axes>]
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)
# If we want to sample a discipline over the uncertain space only,
# we need to extract it:
uncertain_space = parameter_space.extract_uncertain_space()
Then, we sample the discipline over this uncertain space:
dataset = sample_disciplines(
[discipline], uncertain_space, "z", algo_name="PYDOE_LHS", n_samples=100
)
dataset
WARNING - 11:24:58: No coupling in MDA, switching chain_linearize to True.
INFO - 11:24:58:
INFO - 11:24:58: *** Start Sampling execution ***
INFO - 11:24:58: Sampling
INFO - 11:24:58: Disciplines: AnalyticDiscipline
INFO - 11:24:58: MDO formulation: MDF
INFO - 11:24:58: Running the algorithm PYDOE_LHS:
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INFO - 11:24:58: 100%|██████████| 100/100 [00:00<00:00, 3209.48 it/sec]
INFO - 11:24:58: *** End Sampling execution (time: 0:00:00.042539) ***
Total running time of the script: (0 minutes 0.455 seconds)