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)>
Create a parameter space#
Firstly,
the creation of a ParameterSpace does not require any mandatory argument:
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 a NumPy array (by default)
sample = parameter_space.compute_samples(n_samples=2, as_dict=True)
sample
[{'y': array([0.34864772])}, {'y': array([3.32304444])}]
or as a dictionary of NumPy arrays indexed by the names of the variables:
sample = parameter_space.compute_samples(n_samples=4)
sample
array([[-0.0897349 ],
[ 0.47029186],
[-0.28020125],
[ 0.86069996]])
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 - 02:42:54: No coupling in MDA, switching chain_linearize to True.
INFO - 02:42:54: *** Start Sampling execution ***
INFO - 02:42:54: Sampling
INFO - 02:42:54: Disciplines: AnalyticDiscipline
INFO - 02:42:54: MDO formulation: MDF
INFO - 02:42:54: Running the algorithm PYDOE_LHS:
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INFO - 02:42:54: *** End Sampling execution (time: 0:00:00.046381) ***
and visualize it in a tabular way:
dataset
or with a graphical post-processing, e.g. a scatter plot matrix:
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 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 - 02:42:55: No coupling in MDA, switching chain_linearize to True.
INFO - 02:42:55: *** Start Sampling execution ***
INFO - 02:42:55: Sampling
INFO - 02:42:55: Disciplines: AnalyticDiscipline
INFO - 02:42:55: MDO formulation: MDF
INFO - 02:42:55: Running the algorithm PYDOE_LHS:
INFO - 02:42:55: 1%| | 1/100 [00:00<00:00, 1943.61 it/sec]
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INFO - 02:42:55: 100%|██████████| 100/100 [00:00<00:00, 3004.17 it/sec]
INFO - 02:42:55: *** End Sampling execution (time: 0:00:00.044720) ***
Total running time of the script: (0 minutes 0.470 seconds)