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 create_discipline
from gemseo import sample_disciplines
from gemseo.algos.parameter_space import ParameterSpace
from gemseo.post.dataset.scatter_plot_matrix import ScatterMatrix
from gemseo.settings.probability_distributions import SPNormalDistribution_Settings
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_Settings(mu=0.0, sigma=1.0)
)
parameter_space
or without Pydantic model:
parameter_space.add_random_variable("y", "SPNormalDistribution", mu=0.0, sigma=1.0)
Warning
We cannot mix probability distributions from different families,
e.g. an OTDistribution and a SPDistribution.
Note
This page
lists the available probability distributions.
The names prefixed with SP correspond to distributions based on SciPy.
while those prefixed with OT correspond to distributions based on OpenTURNS.
The settings class DistributionClassName_Settings
associated with the distribution DistributionClassName can be imported
from gemseo.settings.probability_distributions.
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_Settings(interface_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_Settings(interface_distribution="Normal", parameters=(1.0, 2.0)),
)
Sample from the parameter space#
We can sample the uncertain variables from the ParameterSpace
and return the result either as a dictionary of NumPy arrays
indexed by the names of these variables:
samples = parameter_space.compute_samples(n_samples=4)
samples
array([[ 0.12431805],
[-0.43733539],
[-1.26062742],
[-0.06811378]])
or a unique NumPy array concatenating the values of these variables
according to the order in which they were added to the ParameterSpace:
samples = parameter_space.compute_samples(n_samples=2, as_dict=True)
samples
[{'y': array([0.16919772])}, {'y': array([-0.16398223])}]
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
)
INFO - 16:22:28: *** Start Sampling execution ***
INFO - 16:22:28: Sampling
INFO - 16:22:28: Disciplines: AnalyticDiscipline
INFO - 16:22:28: MDO formulation: MDF
INFO - 16:22:28: Running the algorithm PYDOE_LHS:
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INFO - 16:22:28: *** End Sampling execution ***
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, 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
INFO - 16:22:28: *** Start Sampling execution ***
INFO - 16:22:28: Sampling
INFO - 16:22:28: Disciplines: AnalyticDiscipline
INFO - 16:22:28: MDO formulation: MDF
INFO - 16:22:28: Running the algorithm PYDOE_LHS:
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INFO - 16:22:28: 77%|███████▋ | 77/100 [00:00<00:00, 3903.09 it/sec]
INFO - 16:22:28: 78%|███████▊ | 78/100 [00:00<00:00, 3906.99 it/sec]
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INFO - 16:22:28: 80%|████████ | 80/100 [00:00<00:00, 3906.86 it/sec]
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INFO - 16:22:28: 83%|████████▎ | 83/100 [00:00<00:00, 3912.38 it/sec]
INFO - 16:22:28: 84%|████████▍ | 84/100 [00:00<00:00, 3915.03 it/sec]
INFO - 16:22:28: 85%|████████▌ | 85/100 [00:00<00:00, 3918.36 it/sec]
INFO - 16:22:28: 86%|████████▌ | 86/100 [00:00<00:00, 3918.76 it/sec]
INFO - 16:22:28: 87%|████████▋ | 87/100 [00:00<00:00, 3918.61 it/sec]
INFO - 16:22:28: 88%|████████▊ | 88/100 [00:00<00:00, 3921.33 it/sec]
INFO - 16:22:28: 89%|████████▉ | 89/100 [00:00<00:00, 3924.73 it/sec]
INFO - 16:22:28: 90%|█████████ | 90/100 [00:00<00:00, 3928.07 it/sec]
INFO - 16:22:28: 91%|█████████ | 91/100 [00:00<00:00, 3931.17 it/sec]
INFO - 16:22:28: 92%|█████████▏| 92/100 [00:00<00:00, 3930.09 it/sec]
INFO - 16:22:28: 93%|█████████▎| 93/100 [00:00<00:00, 3925.79 it/sec]
INFO - 16:22:28: 94%|█████████▍| 94/100 [00:00<00:00, 3925.61 it/sec]
INFO - 16:22:28: 95%|█████████▌| 95/100 [00:00<00:00, 3925.74 it/sec]
INFO - 16:22:28: 96%|█████████▌| 96/100 [00:00<00:00, 3925.91 it/sec]
INFO - 16:22:28: 97%|█████████▋| 97/100 [00:00<00:00, 3927.82 it/sec]
INFO - 16:22:28: 98%|█████████▊| 98/100 [00:00<00:00, 3930.52 it/sec]
INFO - 16:22:28: 99%|█████████▉| 99/100 [00:00<00:00, 3930.67 it/sec]
INFO - 16:22:28: 100%|██████████| 100/100 [00:00<00:00, 3887.93 it/sec]
INFO - 16:22:28: *** End Sampling execution ***
Total running time of the script: (0 minutes 0.317 seconds)