From 6108de0baf59f7282712bad3546b05e2738475f4 Mon Sep 17 00:00:00 2001 From: Jean-Philippe ARGAUD Date: Sun, 26 May 2024 21:25:59 +0200 Subject: [PATCH] Documentation examples corrections and update --- ...orithm_InterpolationByReducedModelTest.rst | 11 +- ...thm_MeasurementsOptimalPositioningTask.rst | 27 +++++ doc/en/ref_observations_requirements.rst | 36 ++++--- ...ple_MeasurementsOptimalPositioningTask3.py | 90 ++++++++++++++++ ...le_MeasurementsOptimalPositioningTask3.res | 8 ++ ...le_MeasurementsOptimalPositioningTask3.rst | 30 ++++++ ...e_MeasurementsOptimalPositioningTask31.png | Bin 0 -> 131117 bytes ...e_MeasurementsOptimalPositioningTask32.png | Bin 0 -> 33766 bytes ...e_MeasurementsOptimalPositioningTask33.png | Bin 0 -> 31698 bytes ...orithm_InterpolationByReducedModelTest.rst | 9 +- ...thm_MeasurementsOptimalPositioningTask.rst | 27 +++++ doc/fr/ref_observations_requirements.rst | 36 ++++--- ...ple_MeasurementsOptimalPositioningTask3.py | 90 ++++++++++++++++ ...le_MeasurementsOptimalPositioningTask3.res | 8 ++ ...le_MeasurementsOptimalPositioningTask3.rst | 33 ++++++ ...e_MeasurementsOptimalPositioningTask31.png | Bin 0 -> 130672 bytes ...e_MeasurementsOptimalPositioningTask32.png | Bin 0 -> 36554 bytes ...e_MeasurementsOptimalPositioningTask33.png | Bin 0 -> 32605 bytes .../TwoDimensionalInverseDistanceCS2010.py | 102 ++++++++++++++++++ src/daComposant/daNumerics/Models/__init__.py | 21 ++++ 20 files changed, 485 insertions(+), 43 deletions(-) create mode 100644 doc/en/scripts/simple_MeasurementsOptimalPositioningTask3.py create mode 100644 doc/en/scripts/simple_MeasurementsOptimalPositioningTask3.res create mode 100644 doc/en/scripts/simple_MeasurementsOptimalPositioningTask3.rst create mode 100644 doc/en/scripts/simple_MeasurementsOptimalPositioningTask31.png create mode 100644 doc/en/scripts/simple_MeasurementsOptimalPositioningTask32.png create mode 100644 doc/en/scripts/simple_MeasurementsOptimalPositioningTask33.png create mode 100644 doc/fr/scripts/simple_MeasurementsOptimalPositioningTask3.py create mode 100644 doc/fr/scripts/simple_MeasurementsOptimalPositioningTask3.res create mode 100644 doc/fr/scripts/simple_MeasurementsOptimalPositioningTask3.rst create mode 100644 doc/fr/scripts/simple_MeasurementsOptimalPositioningTask31.png create mode 100644 doc/fr/scripts/simple_MeasurementsOptimalPositioningTask32.png create mode 100644 doc/fr/scripts/simple_MeasurementsOptimalPositioningTask33.png create mode 100644 src/daComposant/daNumerics/Models/TwoDimensionalInverseDistanceCS2010.py create mode 100644 src/daComposant/daNumerics/Models/__init__.py diff --git a/doc/en/ref_algorithm_InterpolationByReducedModelTest.rst b/doc/en/ref_algorithm_InterpolationByReducedModelTest.rst index f6c55eb..d122878 100644 --- a/doc/en/ref_algorithm_InterpolationByReducedModelTest.rst +++ b/doc/en/ref_algorithm_InterpolationByReducedModelTest.rst @@ -31,13 +31,14 @@ Checking algorithm "*InterpolationByReducedModelTest*" .. include:: snippets/Header2Algo01.rst This algorithm provides a simple way of analyzing the quality of the empirical -state interpolation obtained using a reduced basis, using measurements at -specific points. +interpolation obtained by a reduced basis for complete states, using +measurements at precise points. The results displayed by default are simple statistics related to the -normalized errors of interpolation with a reduced basis. The test uses a -reduced base and a set of optimal measurement positions, and uses -pseudo-measurements from each complete state (“*snapshot*”) included in the +normalized errors between the interpolation with a reduced basis and the +complete states we seek to represent on the reduced basis. The test requires a +reduced basis and a set of optimal measurement positions, and uses +pseudo-measurements from each complete state ("*snapshot*") included in the given test set. Please note: to be consistent, this test must use the same mathematical norm as diff --git a/doc/en/ref_algorithm_MeasurementsOptimalPositioningTask.rst b/doc/en/ref_algorithm_MeasurementsOptimalPositioningTask.rst index 7e260eb..a61ccd3 100644 --- a/doc/en/ref_algorithm_MeasurementsOptimalPositioningTask.rst +++ b/doc/en/ref_algorithm_MeasurementsOptimalPositioningTask.rst @@ -220,6 +220,33 @@ StoreSupplementaryCalculations .. literalinclude:: scripts/simple_MeasurementsOptimalPositioningTask2.res :language: none +.. --------- .. +.. include:: scripts/simple_MeasurementsOptimalPositioningTask3.rst + +.. literalinclude:: scripts/simple_MeasurementsOptimalPositioningTask3.py + +.. include:: snippets/Header2Algo10.rst + +.. literalinclude:: scripts/simple_MeasurementsOptimalPositioningTask3.res + :language: none + +.. include:: snippets/Header2Algo11.rst + +.. _simple_MeasurementsOptimalPositioningTask31: +.. image:: scripts/simple_MeasurementsOptimalPositioningTask31.png + :align: center + :width: 60% + +.. _simple_MeasurementsOptimalPositioningTask32: +.. image:: scripts/simple_MeasurementsOptimalPositioningTask32.png + :align: center + :width: 60% + +.. _simple_MeasurementsOptimalPositioningTask33: +.. image:: scripts/simple_MeasurementsOptimalPositioningTask33.png + :align: center + :width: 60% + .. ------------------------------------ .. .. include:: snippets/Header2Algo06.rst diff --git a/doc/en/ref_observations_requirements.rst b/doc/en/ref_observations_requirements.rst index 81f896d..3ec2454 100644 --- a/doc/en/ref_observations_requirements.rst +++ b/doc/en/ref_observations_requirements.rst @@ -91,14 +91,15 @@ of measurements, or several fields physically homogeneous or not. - data text file (TXT, CSV, TSV, DAT), with variable pointer by name in column or row, indicated by the keyword "*DataFile*" with the condition ``Vector=True`` - binary data file (NPY, NPZ), with variable pointer by name, indicated by the keyword "*DataFile*" with the condition ``Vector=True`` -- Examples of statements in TUI interface: +Examples of statements in TUI interface: +:: - - ``case.setObservation( Vector = [1, 2, 3] )`` - - ``case.setObservation( Vector = numpy.array([1, 2, 3]) )`` - - ``case.setObservation( Vector = '1 2 3' )`` - - ``case.setObservation( Vector=True, Script = 'script.py' )``` - - ``case.setObservation( Vector=True, DataFile = 'data.csv' )``` - - ``case.setObservation( Vector=True, DataFile = 'data.npy' )``` + case.setObservation( Vector = [1, 2, 3] ) + case.setObservation( Vector = numpy.array([1, 2, 3]) ) + case.setObservation( Vector = '1 2 3' ) + case.setObservation( Vector=True, Script = 'script.py' ) + case.setObservation( Vector=True, DataFile = 'data.csv' ) + case.setObservation( Vector=True, DataFile = 'data.npy' ) Use note: in a given study, only the last record (whether a single vector or a series of vectors) can be used, as only one observation concept exists per ADAO @@ -139,16 +140,17 @@ of which we consider a history. - data text file (TXT, CSV, TSV), with variable pointer by name in column or row, indicated by the keyword "*DataFile*" with the condition ``VectorSerie=True`` - binary data file (NPY, NPZ), with variable pointer by name, indicated by the keyword "*DataFile*" with the condition ``VectorSerie=True`` -- Examples of statements in TUI interface: - - - ``case.setObservation( VectorSerie = [[1,2,3], [1,2,3]] )`` - - ``case.setObservation( VectorSerie = [numpy.array([1,2,3]), numpy.array([1,2,3])] )`` - - ``case.setObservation( VectorSerie = ['1 2 3', '1 2 3'] )`` - - ``case.setObservation( VectorSerie = '[[1,2,3], [1,2,3]]' )`` - - ``case.setObservation( VectorSerie = '1 2 3 ; 1 2 3' )`` - - ``case.setObservation( VectorSerie=True, Script = 'script.py' )``` - - ``case.setObservation( VectorSerie=True, DataFile = 'data.csv' )``` - - ``case.setObservation( VectorSerie=True, DataFile = 'data.npy' )``` +Examples of statements in TUI interface: +:: + + case.setObservation( VectorSerie = [[1,2,3], [1,2,3]] ) + case.setObservation( VectorSerie = [numpy.array([1,2,3]), numpy.array([1,2,3])] ) + case.setObservation( VectorSerie = ['1 2 3', '1 2 3'] ) + case.setObservation( VectorSerie = '[[1,2,3], [1,2,3]]' ) + case.setObservation( VectorSerie = '1 2 3 ; 1 2 3' ) + case.setObservation( VectorSerie=True, Script = 'script.py' ) + case.setObservation( VectorSerie=True, DataFile = 'data.csv' ) + case.setObservation( VectorSerie=True, DataFile = 'data.npy' ) Use note: in a given study, only the last record (whether a single vector or a series of vectors) can be used, as only one observation concept exists per ADAO diff --git a/doc/en/scripts/simple_MeasurementsOptimalPositioningTask3.py b/doc/en/scripts/simple_MeasurementsOptimalPositioningTask3.py new file mode 100644 index 0000000..8878d12 --- /dev/null +++ b/doc/en/scripts/simple_MeasurementsOptimalPositioningTask3.py @@ -0,0 +1,90 @@ +# -*- coding: utf-8 -*- +# +import numpy as np +import matplotlib.pyplot as plt +np.random.seed(123456789) +# +dimension = 20 +# +print("Defining a set of artificial physical fields") +from Models.TwoDimensionalInverseDistanceCS2010 \ + import TwoDimensionalInverseDistanceCS2010 as Equation +Eq = Equation(dimension, dimension) +print() +# +print("Search for optimal measurement positions") +from adao import adaoBuilder +case = adaoBuilder.New() +case.setAlgorithmParameters( + Algorithm = 'MeasurementsOptimalPositioningTask', + Parameters = { + "Variant":"DEIM", + "SampleAsnUplet":Eq.get_sample_of_mu(15, 15), + "MaximumNumberOfLocations":50, + "ErrorNorm":"Linf", + "ErrorNormTolerance":0., + "StoreSupplementaryCalculations":[ + "SingularValues", + "OptimalPoints", + "EnsembleOfSimulations", + ], + } + ) +case.setBackground(Vector = [1,1] ) +case.setObservationOperator(OneFunction = Eq.OneRealisation) +case.execute() +# +print() +print("Graphical display of the results") +# +sp = case.get("EnsembleOfSimulations")[-1] +x1, x2 = Eq.get_x() +x1, x2 = np.meshgrid(x1, x2) +name = "Representation of a few snapshots of G out of a total of %i"%sp.shape[1] +print(" -", name) +fig, ax = plt.subplots(subplot_kw={"projection": "3d"}, figsize=(6, 6)) +fig.suptitle(name) +ax.set_xlabel("Position x1", fontweight='bold', color='red') +ax.set_ylabel("Position x2", fontweight='bold', color='red') +ax.set_zlabel("Magnitude of G", fontweight='bold', color='red') +for i in range(sp.shape[1]): + if i % 44 != 0: continue + ax.plot_surface(x1, x2, sp[:,i].reshape((dimension, dimension)), cmap='coolwarm') +fig.savefig("simple_MeasurementsOptimalPositioningTask31.png") +plt.close() +# +sv = case.get("SingularValues")[-1] +name = "Singular values of the set of G simulations" +print(" -", name) +fig, ax = plt.subplots(figsize=(6, 6)) +fig.suptitle(name) +ax.set_xlabel("Index of singular values, numbered from 1") +ax.set_ylabel("Magnitude of singular values") +ax.set_xlim(1, len(sv)) +ax.set_yscale("log") +ax.grid(True) +ax.plot(range(1, 1 + len(sv)), sv) +fig.savefig("simple_MeasurementsOptimalPositioningTask32.png") +plt.tight_layout() +plt.close() +# +nbmax = 15 +op = case.get("OptimalPoints")[-1] +posx1 = [x1.reshape((-1,))[ip] for ip in op[:nbmax]] +posx2 = [x2.reshape((-1,))[ip] for ip in op[:nbmax]] +name = "Set of %i first optimal points of measurement"%nbmax +Omega = Eq.get_bounds_on_space() +print(" -", name) +fig, ax = plt.subplots(figsize=(6, 6)) +fig.suptitle(name) +ax.set_xlabel("Position x1", fontweight='bold', color='red') +ax.set_ylabel("Position x2", fontweight='bold', color='red') +ax.set_xlim(Omega[0][0] - 0.05, Omega[0][1] + 0.05) +ax.set_ylim(Omega[1][0] - 0.05, Omega[1][1] + 0.05) +ax.grid(True, which='both', linestyle=(0, (1, 5)), linewidth=0.5) +ax.plot(posx1, posx2, markersize=6, marker="o", linestyle='') +for i in range(len(posx1)): + ax.text(posx1[i] + 0.005, posx2[i] + 0.01, str(i + 1), fontweight='bold') +fig.savefig("simple_MeasurementsOptimalPositioningTask33.png") +plt.tight_layout() +plt.close() diff --git a/doc/en/scripts/simple_MeasurementsOptimalPositioningTask3.res b/doc/en/scripts/simple_MeasurementsOptimalPositioningTask3.res new file mode 100644 index 0000000..455a3d3 --- /dev/null +++ b/doc/en/scripts/simple_MeasurementsOptimalPositioningTask3.res @@ -0,0 +1,8 @@ +Defining a set of artificial physical fields + +Search for optimal measurement positions + +Graphical display of the results + - Representation of a few snapshots of G out of a total of 225 + - Singular values of the set of G simulations + - Set of 15 first optimal points of measurement diff --git a/doc/en/scripts/simple_MeasurementsOptimalPositioningTask3.rst b/doc/en/scripts/simple_MeasurementsOptimalPositioningTask3.rst new file mode 100644 index 0000000..9445285 --- /dev/null +++ b/doc/en/scripts/simple_MeasurementsOptimalPositioningTask3.rst @@ -0,0 +1,30 @@ +.. index:: single: MeasurementsOptimalPositioningTask (example) + +Third example +............. + +This more complete example describes the optimal positioning of measurements +associated with a reduced DEIM-type decomposition on a classical parametric +non-linear function, as proposed in reference [Chaturantabut10]_. This +particular function has the notable advantage of being dependent only on a +position :math:`x` in 2D and a parameter :math:`\mu` in 2D too. It therefore +enables a pedagogical illustration of optimal measurement points. + +This function depends on the position :math:`x=(x_1,x_2)\in\Omega=[0.1,0.9]^2` +in the 2D plane, and on the parameter +:math:`\mu=(\mu_1,\mu_2)\in\mathcal{D}=[-1,-0.01]^2` of dimension 2 : + +.. math:: G(x;\mu) = \frac{1}{\sqrt{(x_1 - \mu_1)^2 + (x_2 - \mu_2)^2 + 0.1^2}} + +The function is represented on a regular :math:`\Omega_G` spatial grid of size +20x20 points. It is available in ADAO built-in test models under the name +`TwoDimensionalInverseDistanceCS2010`. So here we first build a set of +simulations of :math:`G`, then apply the DEIM-type decomposition algorithm to +it, and derive some simple illustrations. + +It can be seen that the singular values decrease steadily down to numerical +noise, indicating that around a hundred basis elements are needed to fully +represent the information contained in the set of :math:`G` simulations. +Furthermore, the optimal measurement points in the :math:`\Omega_G` domain are +inhomogeneously distributed, favoring the spatial zone near the +:math:`(0.1,0.1)` corner in which the :math:`G` function varies more. diff --git a/doc/en/scripts/simple_MeasurementsOptimalPositioningTask31.png b/doc/en/scripts/simple_MeasurementsOptimalPositioningTask31.png new file mode 100644 index 0000000000000000000000000000000000000000..128980dee497796b23ae54bf9a36bbd85362f503 GIT binary patch literal 131117 zcmeFZWmHye7cG2?poG#T-7O^`AR$PXfQX1Rh;+AfOP7Qa5()?isC1Wr2#9pIl$3xp 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znLO_*FG#-k-3qx&+8jsL1M;yZPI7Yc=}xttssb6-CEM~!St?84;7~SLElz9KZ7`J( z&6XY*?y^fd<$v9ZyWMuy3X-A>Q<47~XZatlaG%=qe{(tf@BVYz$5}2{&Z{itXAWb& PHf8%(ZS|DR<|qFLIJ~W& literal 0 HcmV?d00001 diff --git a/doc/fr/ref_algorithm_InterpolationByReducedModelTest.rst b/doc/fr/ref_algorithm_InterpolationByReducedModelTest.rst index 1b4831e..a0f4651 100644 --- a/doc/fr/ref_algorithm_InterpolationByReducedModelTest.rst +++ b/doc/fr/ref_algorithm_InterpolationByReducedModelTest.rst @@ -31,14 +31,15 @@ Algorithme de vérification "*InterpolationByReducedModelTest*" .. include:: snippets/Header2Algo01.rst Cet algorithme permet d'analyser de manière simple la qualité de -l'interpolation empirique des états obtenue par une base réduite, en utilisant -des mesures en des points précis. +l'interpolation empirique obtenue par une base réduite pour des états complets, +en utilisant des mesures en des points précis. Les résultats affichés par défaut sont des statistiques simples liées aux -erreurs normalisées de l'interpolation avec une base réduite. Le test utilise +erreurs normalisées entre l'interpolation avec une base réduite et les états +complets que l'on cherche à représenter sur la base réduite. Le test requiert une base réduite et un ensemble de positions de mesures optimales, et utilise des pseudo-mesures provenant de chaque état complet ("*snapshot*") inclus dans -l'ensemble de test donné. +l'ensemble donné de test. Attention : pour être cohérent, ce test doit utiliser la même norme mathématique que celle utilisée pour construire la base réduite. La norme étant diff --git a/doc/fr/ref_algorithm_MeasurementsOptimalPositioningTask.rst b/doc/fr/ref_algorithm_MeasurementsOptimalPositioningTask.rst index 26e45ee..a4adb23 100644 --- a/doc/fr/ref_algorithm_MeasurementsOptimalPositioningTask.rst +++ b/doc/fr/ref_algorithm_MeasurementsOptimalPositioningTask.rst @@ -223,6 +223,33 @@ StoreSupplementaryCalculations .. literalinclude:: scripts/simple_MeasurementsOptimalPositioningTask2.res :language: none +.. --------- .. +.. include:: scripts/simple_MeasurementsOptimalPositioningTask3.rst + +.. literalinclude:: scripts/simple_MeasurementsOptimalPositioningTask3.py + +.. include:: snippets/Header2Algo10.rst + +.. literalinclude:: scripts/simple_MeasurementsOptimalPositioningTask3.res + :language: none + +.. include:: snippets/Header2Algo11.rst + +.. _simple_MeasurementsOptimalPositioningTask31: +.. image:: scripts/simple_MeasurementsOptimalPositioningTask31.png + :align: center + :width: 60% + +.. _simple_MeasurementsOptimalPositioningTask32: +.. image:: scripts/simple_MeasurementsOptimalPositioningTask32.png + :align: center + :width: 60% + +.. _simple_MeasurementsOptimalPositioningTask33: +.. image:: scripts/simple_MeasurementsOptimalPositioningTask33.png + :align: center + :width: 60% + .. ------------------------------------ .. .. include:: snippets/Header2Algo06.rst diff --git a/doc/fr/ref_observations_requirements.rst b/doc/fr/ref_observations_requirements.rst index 327084e..dd04765 100644 --- a/doc/fr/ref_observations_requirements.rst +++ b/doc/fr/ref_observations_requirements.rst @@ -94,14 +94,15 @@ physiquement homogènes ou pas. - fichier texte de données (TXT, CSV, TSV, DAT), avec pointeur de variable par nom en colonne ou en ligne, indiqué par le mot-clé "*DataFile*" avec la condition ``Vector=True`` - fichier binaire de données (NPY, NPZ), avec pointeur de variable par nom, indiqué par le mot-clé "*DataFile*" avec la condition ``Vector=True`` -- Exemples de déclaration en interface TUI : +Exemples de déclaration en interface TUI : +:: - - ``case.setObservation( Vector = [1, 2, 3] )`` - - ``case.setObservation( Vector = numpy.array([1, 2, 3]) )`` - - ``case.setObservation( Vector = '1 2 3' )`` - - ``case.setObservation( Vector=True, Script = 'script.py' )``` - - ``case.setObservation( Vector=True, DataFile = 'data.csv' )``` - - ``case.setObservation( Vector=True, DataFile = 'data.npy' )``` + case.setObservation( Vector = [1, 2, 3] ) + case.setObservation( Vector = numpy.array([1, 2, 3]) ) + case.setObservation( Vector = '1 2 3' ) + case.setObservation( Vector=True, Script = 'script.py' ) + case.setObservation( Vector=True, DataFile = 'data.csv' ) + case.setObservation( Vector=True, DataFile = 'data.npy' ) Remarque d'utilisation : dans une étude donnée, seul le dernier enregistrement (que ce soit un vecteur unique ou une série de vecteurs) est utilisable, car un @@ -142,16 +143,17 @@ physiquement homogènes ou pas, dont on considère un historique. - fichier texte de données (TXT, CSV, TSV, DAT), avec pointeur de variable par nom en colonne ou en ligne, indiqué par le mot-clé "*DataFile*" avec la condition ``VectorSerie=True`` - fichier binaire de données (NPY, NPZ), avec pointeur de variable par nom, indiqué par le mot-clé "*DataFile*" avec la condition ``VectorSerie=True`` -- Exemples de déclaration en interface TUI : - - - ``case.setObservation( VectorSerie = [[1,2,3], [1,2,3]] )`` - - ``case.setObservation( VectorSerie = [numpy.array([1,2,3]), numpy.array([1,2,3])] )`` - - ``case.setObservation( VectorSerie = ['1 2 3', '1 2 3'] )`` - - ``case.setObservation( VectorSerie = '[[1,2,3], [1,2,3]]' )`` - - ``case.setObservation( VectorSerie = '1 2 3 ; 1 2 3' )`` - - ``case.setObservation( VectorSerie=True, Script = 'script.py' )``` - - ``case.setObservation( VectorSerie=True, DataFile = 'data.csv' )``` - - ``case.setObservation( VectorSerie=True, DataFile = 'data.npy' )``` +Exemples de déclaration en interface TUI : +:: + + case.setObservation( VectorSerie = [[1,2,3], [1,2,3]] ) + case.setObservation( VectorSerie = [numpy.array([1,2,3]), numpy.array([1,2,3])] ) + case.setObservation( VectorSerie = ['1 2 3', '1 2 3'] ) + case.setObservation( VectorSerie = '[[1,2,3], [1,2,3]]' ) + case.setObservation( VectorSerie = '1 2 3 ; 1 2 3' ) + case.setObservation( VectorSerie=True, Script = 'script.py' ) + case.setObservation( VectorSerie=True, DataFile = 'data.csv' ) + case.setObservation( VectorSerie=True, DataFile = 'data.npy' ) Remarque d'utilisation : dans une étude donnée, seul le dernier enregistrement (que ce soit un vecteur unique ou une série de vecteurs) est utilisable, car un diff --git a/doc/fr/scripts/simple_MeasurementsOptimalPositioningTask3.py b/doc/fr/scripts/simple_MeasurementsOptimalPositioningTask3.py new file mode 100644 index 0000000..d9fca5a --- /dev/null +++ b/doc/fr/scripts/simple_MeasurementsOptimalPositioningTask3.py @@ -0,0 +1,90 @@ +# -*- coding: utf-8 -*- +# +import numpy as np +import matplotlib.pyplot as plt +np.random.seed(123456789) +# +dimension = 20 +# +print("Définition d'un ensemble artificiel de champs physiques") +from Models.TwoDimensionalInverseDistanceCS2010 \ + import TwoDimensionalInverseDistanceCS2010 as Equation +Eq = Equation(dimension, dimension) +print() +# +print("Recherche des positions optimales de mesure") +from adao import adaoBuilder +case = adaoBuilder.New() +case.setAlgorithmParameters( + Algorithm = 'MeasurementsOptimalPositioningTask', + Parameters = { + "Variant":"DEIM", + "SampleAsnUplet":Eq.get_sample_of_mu(15, 15), + "MaximumNumberOfLocations":50, + "ErrorNorm":"Linf", + "ErrorNormTolerance":0., + "StoreSupplementaryCalculations":[ + "SingularValues", + "OptimalPoints", + "EnsembleOfSimulations", + ], + } + ) +case.setBackground(Vector = [1,1] ) +case.setObservationOperator(OneFunction = Eq.OneRealisation) +case.execute() +# +print() +print("Affichage graphique des résultats") +# +sp = case.get("EnsembleOfSimulations")[-1] +x1, x2 = Eq.get_x() +x1, x2 = np.meshgrid(x1, x2) +name = "Représentation de quelques snapshots de G sur un total de %i"%sp.shape[1] +print(" -", name) +fig, ax = plt.subplots(subplot_kw={"projection": "3d"}, figsize=(6, 6)) +fig.suptitle(name) +ax.set_xlabel("Position x1", fontweight='bold', color='red') +ax.set_ylabel("Position x2", fontweight='bold', color='red') +ax.set_zlabel("Amplitude de G", fontweight='bold', color='red') +for i in range(sp.shape[1]): + if i % 44 != 0: continue + ax.plot_surface(x1, x2, sp[:,i].reshape((dimension, dimension)), cmap='coolwarm') +fig.savefig("simple_MeasurementsOptimalPositioningTask31.png") +plt.close() +# +sv = case.get("SingularValues")[-1] +name = "Valeurs singulières de l'ensemble des simulations de G" +print(" -", name) +fig, ax = plt.subplots(figsize=(6, 6)) +fig.suptitle(name) +ax.set_xlabel("Index des valeurs singulières, numérotées à partir de 1") +ax.set_ylabel("Amplitude des valeurs singulières") +ax.set_xlim(1, len(sv)) +ax.set_yscale("log") +ax.grid(True) +ax.plot(range(1, 1 + len(sv)), sv) +fig.savefig("simple_MeasurementsOptimalPositioningTask32.png") +plt.tight_layout() +plt.close() +# +nbmax = 15 +op = case.get("OptimalPoints")[-1] +posx1 = [x1.reshape((-1,))[ip] for ip in op[:nbmax]] +posx2 = [x2.reshape((-1,))[ip] for ip in op[:nbmax]] +name = "Ensemble des %i premiers points optimaux de mesure"%nbmax +Omega = Eq.get_bounds_on_space() +print(" -", name) +fig, ax = plt.subplots(figsize=(6, 6)) +fig.suptitle(name) +ax.set_xlabel("Position x1", fontweight='bold', color='red') +ax.set_ylabel("Position x2", fontweight='bold', color='red') +ax.set_xlim(Omega[0][0] - 0.05, Omega[0][1] + 0.05) +ax.set_ylim(Omega[1][0] - 0.05, Omega[1][1] + 0.05) +ax.grid(True, which='both', linestyle=(0, (1, 5)), linewidth=0.5) +ax.plot(posx1, posx2, markersize=6, marker="o", linestyle='') +for i in range(len(posx1)): + ax.text(posx1[i] + 0.005, posx2[i] + 0.01, str(i + 1), fontweight='bold') +fig.savefig("simple_MeasurementsOptimalPositioningTask33.png") +plt.tight_layout() +plt.close() diff --git a/doc/fr/scripts/simple_MeasurementsOptimalPositioningTask3.res b/doc/fr/scripts/simple_MeasurementsOptimalPositioningTask3.res new file mode 100644 index 0000000..756b5bf --- /dev/null +++ b/doc/fr/scripts/simple_MeasurementsOptimalPositioningTask3.res @@ -0,0 +1,8 @@ +Définition d'un ensemble artificiel de champs physiques + +Recherche des positions optimales de mesure + +Affichage graphique des résultats + - Représentation de quelques snapshots de G sur un total de 225 + - Valeurs singulières de l'ensemble des simulations de G + - Ensemble des 15 premiers points optimaux de mesure diff --git a/doc/fr/scripts/simple_MeasurementsOptimalPositioningTask3.rst b/doc/fr/scripts/simple_MeasurementsOptimalPositioningTask3.rst new file mode 100644 index 0000000..8225906 --- /dev/null +++ b/doc/fr/scripts/simple_MeasurementsOptimalPositioningTask3.rst @@ -0,0 +1,33 @@ +.. index:: single: MeasurementsOptimalPositioningTask (exemple) + +Troisième exemple +................. + +Cet exemple plus complet décrit le positionnement optimal de mesures associé à +une décomposition réduite de type DEIM sur une fonction classique paramétrique +non-linéaire, telle que proposée dans la référence [Chaturantabut10]_. Cette +fonction particulière a l'avantage notable de n'être dépendante que d'une +position :math:`x` en 2D et d'un paramètre :math:`\mu` en 2D aussi. Elle permet +donc une illustration pédagogique pour représenter les points optimaux de +mesure. + +Cette fonction dépend de la position :math:`x=(x_1,x_2)\in\Omega=[0.1,0.9]^2` +dans le plan 2D, et du paramètre +:math:`\mu=(\mu_1,\mu_2)\in\mathcal{D}=[-1,-0.01]^2` de dimension 2 : + +.. math:: G(x;\mu) = \frac{1}{\sqrt{(x_1 - \mu_1)^2 + (x_2 - \mu_2)^2 + 0.1^2}} + +La fonction est représenté sur une grille spatiale régulière :math:`\Omega_G` +de taille 20x20 points. Elle est disponible dans les modèles de tests intégrés +pour ADAO sous le nom `TwoDimensionalInverseDistanceCS2010`. On construit donc +ici tout d'abord un ensemble de simulations de :math:`G`, pour lui appliquer +ensuite l'algorithme de décomposition de type DEIM, et en tirer des +illustrations simples. + +On observe ainsi que les valeurs singulières décroissent régulièrement jusqu'au +bruit numérique, indiquant qu'il faut environ une centaine d'éléments de base +pour complètement représenter l'information contenue dans l'ensemble des +simulations de :math:`G`. Par ailleurs, les points de mesure optimaux dans le +domaine :math:`\Omega_G` sont répartis de manière inhomogène, privilégiant la +zone spatiale proche du coin :math:`(0.1,0.1)` dans laquelle la fonction +:math:`G` varie plus. diff --git a/doc/fr/scripts/simple_MeasurementsOptimalPositioningTask31.png b/doc/fr/scripts/simple_MeasurementsOptimalPositioningTask31.png new file mode 100644 index 0000000000000000000000000000000000000000..4e211794d52c23bd0597ae834e88b366cad1c5f5 GIT binary patch literal 130672 zcmeFZWmr~i)GhjebVx`^he!&dAR(wU0@A`GASsA|(%s#SgoM%{t#o%N5(1*qB_JXt z(y-_9{mwr7$N6{uZZEvvSAAHlb>H)zbBr;^Tw!V|^27wR1Sk}W_`ZUS1`36VMt*<(j+!>+jxNUbW~c|oj<(h|j@Hjin4Qh+9iG{|xXCBNC&bLKgt_^_o4P4VJ?N@vu}Bc zm!)X@u6FUvOh(sUbF)x#c|FUt;2_#h%dy5Ar^rV=CFJNv=M8_UEK=_=OQCn~-`kxXuH@w9ndK*Q z*zSH3Hnp(8vuQcJy0EZd?k;+8vO8qg%iv;UZOyyj)pYuIvTiZ@_Q{!{u`vr@{Zf4B z{x#u0Vr##CrLX1n!A0?0e_yUN9mtHd)^!V?F zf~snWT#lr>yO{H@uYMe_J;@Ui65cV|lzpC<2)X^c?!v=|56L#AqmK_5T&6IBq{y~+ 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z%;ig+91itNU$=Jl$cNqIFariND4Ru4+;PqV5&wkN@KRsu7I*5^6Y)y*9ptcsQLC=cz1 zI2xOu&z>Bzy`|siA+E7lMkptGH!o9RvQ3eM6ok7^3svlv<8j_7 zztL-TWcB1^YmnD)uUC6S)$_p6cv?h!!k)>2!DHizDSO%Zw>!oFY;j5wSn*4Qp0}8| r1HpJ|1itx~#PEOe#Q#?>CnUL%g3Y(o=UHOZJw= solution[-1, -1]) + + def tearDown(cls): + print("\n Tests OK\n") + +# ============================================================================== +if __name__ == "__main__": + sys.stderr = sys.stdout + unittest.main(verbosity=0) diff --git a/src/daComposant/daNumerics/Models/__init__.py b/src/daComposant/daNumerics/Models/__init__.py new file mode 100644 index 0000000..a32af42 --- /dev/null +++ b/src/daComposant/daNumerics/Models/__init__.py @@ -0,0 +1,21 @@ +# -*- coding: utf-8 -*- +# +# Copyright (C) 2008-2024 EDF R&D +# +# This library is free software; you can redistribute it and/or +# modify it under the terms of the GNU Lesser General Public +# License as published by the Free Software Foundation; either +# version 2.1 of the License. +# +# This library is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +# Lesser General Public License for more details. +# +# You should have received a copy of the GNU Lesser General Public +# License along with this library; if not, write to the Free Software +# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA +# +# See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com +# +# Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D -- 2.39.2