# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com # # This work is licensed under a BSD 0-Clause License. # # Permission to use, copy, modify, and/or distribute this software # for any purpose with or without fee is hereby granted. # # THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL # WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED # WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL # THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT, # OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING # FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, # NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION # WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. # Contributors: # INITIAL AUTHORS - initial API and implementation and/or initial # documentation # :author: Matthias De Lozzo # OTHER AUTHORS - MACROSCOPIC CHANGES """ Parameter space =============== In this example, we will see the basics of :class:`.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 from gemseo.settings.probability_distributions import SPNormalDistribution_Settings configure_logger() # %% # Create a parameter space # ------------------------ # Firstly, # the creation of a :class:`.ParameterSpace` does not require any mandatory argument: parameter_space = ParameterSpace() # %% # Then, we can add either deterministic variables # from their lower and upper bounds # (use :meth:`.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 :meth:`.ParameterSpace.add_random_variable`): parameter_space.add_random_variable( "y", SPNormalDistribution_Settings(mu=0.0, sigma=1.0) ) parameter_space # %% # or without Pydantic model: # # .. code-block:: python # # 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 :class:`.OTDistribution` and a :class:`.SPDistribution`. # # .. note:: # :ref:`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") # %% # Note that when GEMSEO does not offer a class for the SciPy distribution, # we can use the generic GEMSEO class :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 # `__). # # .. code-block:: python # # 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 :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 # `__). # # .. code-block:: python # # 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 :class:`.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 # %% # or a unique NumPy array concatenating the values of these variables # according to the order in which they were added to the :class:`.ParameterSpace`: samples = parameter_space.compute_samples(n_samples=2, as_dict=True) samples # %% # Sample a discipline over the parameter space # -------------------------------------------- # We can also sample a discipline over the parameter space. # For simplicity, # we instantiate an :class:`.AnalyticDiscipline` from a dictionary of expressions: discipline = create_discipline("AnalyticDiscipline", expressions={"z": "x+y"}) # %% # Then, # we use the :func:`.sample_disciplines` function # with an :term:`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 ) # %% # 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) # %% # 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