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Documentation / Manuel utilisateur en C++ : PDF version

User manual for Uranie v4.9.0

User manual for Uranie v4.9.0

C++ version

The Uranie team

CEA DES

Abstract

This documentation presents the features of the Uranie platform (based on Uranie v4.9.0), that is developed at CEA/DES. This platform is designed for uncertainty propagation, sensitivity analysis and computational code qualification, in a single software environment. It is largely based on the ROOT software (http://root.cern.ch/), an oriented-object framework that is designed and maintained by CERN, primarily used by the particle physicist to analyse the very large amount of data recorded at the LHC (Large Hadron Collider).


Table of Contents

I. Overview: Uranie in a nutshell
I.1. Introducing Uranie
I.1.1. Uranie modules organisation
I.1.2. External dependencies
I.2. ROOT Environment
I.2.1. Environment variables
I.2.2. ROOT interpreter and runtime compiler
I.2.3. Standard compilation
I.2.4. Uranie namespace
I.2.5. Important modifications going from ROOT v5 to ROOT v6
I.2.6. References
I.3. The Python Interface
I.3.1. Python version: greater than 3.8
I.3.2. Environment variables
I.3.3. Using PyROOT
I.3.4. The PyURANIE interface
I.3.5. References
II. The DataServer module
II.1. Introduction
II.2. The TAttribute class
II.2.1. Nature of the attribute
II.2.2. List of variable information
II.2.3. Examples of use of the class TAttribute
II.2.4. Adding TAttribute when data are already available
II.2.5. Introducing the TStochasticAttribute classes
II.3. Data handling
II.3.1. Main format of input/output
II.3.2. Import data from an ASCII file
II.3.3. Import data from a TNtuple/TDSNtuple/TTree
II.3.4. Adding attributes to a TDataServer
II.3.5. Merging two DataServer
II.3.6. Pattern selection
II.3.7. Export to an ASCII file
II.4. Statistical treatments and operations
II.4.1. Normalising the variable
II.4.2. Computing the ranking
II.4.3. Computing the elementary statistic
II.4.4. The quantile computation
II.4.5. Correlation matrix
II.5. Visualisation dedicated to uncertainties
II.5.1. Histogram
II.5.2. Box-and-whisker("boxplot")
II.5.3. CDF, CCDF curves
II.5.4. Graph 2D with contour levels
II.5.5. Graph 2D "profile"
II.5.6. Graph 2D "Tufte"
II.5.7. Graph 2D "pairs"
II.5.8. Graph "CobWeb"
II.5.9. QQ plot
II.5.10. PP plot
II.6. Combining these aspects: performing PCA
II.6.1. PCA usage within Uranie
III. The Sampler module
III.1. Introduction
III.2. The Stochastic methods
III.2.1. Introduction
III.2.2. The main sampler classes
III.2.3. Simple example
III.2.4. TConstrLHS example
III.3. Description of a correlation
III.3.1. Imposing the correlation coefficients
III.3.2. The copula classes
III.4. QMC method
III.5. The random fields
III.6. OAT Design
III.6.1. Introduction
III.6.2. OAT design in Uranie
III.6.3. TOATDesign
III.7. The Vectorial Quantification method
IV. The Launcher module
IV.1. Introduction
IV.1.1. Presentation
IV.1.2. Overview of a simple case
IV.2. Analytic function
IV.3. External Code
IV.3.1. Code input and output files
IV.3.2. TCode definition
IV.3.3. Launcher definition
IV.4. Distribution
IV.4.1. Multi-core computer
IV.4.2. Cluster
IV.4.3. Advanced usage of batch systems
IV.4.4. Multi-step launching mechanism
IV.4.5. Multi-step remote launching to clusters
V. The Modeler module
V.1. Introduction
V.2. The TLinearRegression class
V.3. Chaos polynomial expansion
V.3.1. Nisp in a nutshell
V.3.2. Step 1: Specification of the uncertain parameters
V.3.3. Step 2: Building stochastic variables
V.3.4. Step 3: Constitution of the sample
V.3.5. Step 4: Building the polynomial chaos
V.3.6. Step 5: Uncertainty and sensitivity analysis
V.3.7. Other functionalities
V.4. Adaptive development in polynomial chaos: the Anisp method
V.4.1. Step 1: Specification of the uncertain parameters
V.4.2. Step 2: Creation of the TAnisp Object
V.4.3. Step 3: Running the Anisp method
V.4.4. Step 4: Uncertainty and sensitivity analysis
V.5. The artificial neural network
V.5.1. The working principle
V.5.2. Constructor
V.5.3. Training
V.5.4. Export
V.6. The kriging method
V.6.1. Running a kriging
V.6.2. Construction of a kriging model
V.6.3. Usage of a Kriging model
V.6.4. Advanced usage
VI. The Sensitivity module
VI.1. Brief reminder of theoretical aspects
VI.1.1. Content of the TSensitivity class
VI.1.2. List of available methods
VI.2. The finite differences method
VI.2.1. General presentation of finite difference sensitivity indices
VI.2.2. Computation of local sensitivity indices with the finite differences method
VI.3. The regression method
VI.3.1. General presentation of regression's coefficients
VI.3.2. Computation of the coefficients with Uranie
VI.4. The Morris screening method
VI.4.1. Principle of the Morris' method
VI.4.2. The Morris' method in Uranie
VI.5. The Sobol method
VI.5.1. Introduction to Sobol's sensitivity indices
VI.5.2. Computation of Sobol's sensitivity indices
VI.6. Fourier-based methods
VI.6.1. Introducing the method
VI.6.2. Implementation of methods
VI.6.3. Computation of Sobol indices with the FAST method
VI.6.4. Computation of Sobol indices with the method RBD
VI.7. The Johnson relative weight
VI.7.1. General overview
VI.8. Sensitivity Indices based on HSIC
VI.8.1. Introduction to sensitivity measures using HSIC
VII. The Optimizer module
VII.1. Introduction
VII.2. Function optimisation
VII.2.1. Rosenbrock function
VII.2.2. TOptimizer constructors
VII.2.3. Optimisation as minimum of function seeking
VII.2.4. Optimisation as code adjustment
VII.2.5. Performing the optimisation
VII.3. Multicriteria optimisation
VIII. The Relauncher module
VIII.1. Introduction
VIII.2. Relauncher abstraction levels
VIII.3. TEval
VIII.3.1. TCIntEval and TCJitEval
VIII.3.2. TPythonEval
VIII.3.3. TCodeEval
VIII.3.4. Evaluation functions composition
VIII.4. TRun
VIII.4.1. TSequentialRun
VIII.4.2. TThreadedRun
VIII.4.3. TMpiRun
VIII.5. TMaster
VIII.5.1. Dealing with attributes
VIII.5.2. TLauncher2
IX. The Reoptimizer module
IX.1. Introduction
IX.1.1. local optimizer
IX.1.2. global optimizer
IX.1.3. Number of objectives
IX.2. Problem definition
IX.2.1. Objectives and Constraints
IX.2.2. Sizing of a hollow bar example problem
IX.3. Local solver
IX.3.1. TNlopt
IX.3.2. Solvers
IX.4. Global solver
IX.4.1. A step-by-step description of Vizir
IX.4.2. TVizir2 and TVizirIsland
IX.4.3. Solvers
X. The Metamodel Optimization module
X.1. Introduction
X.2. Efficient Global Optimization
X.2.1. Introduction
X.2.2. Problem definition
XI. The Calibration module
XI.1. Introduction
XI.1.1. The distance used to compare observations and model predictions
XI.2. Calibration classes, distance functions, observations and model
XI.2.1. General introduction on data and model definition
XI.2.2. Defining data and distance functions
XI.2.3. The calibration classes common methods
XI.2.4. Use-case for this chapter
XI.3. Using minimisation techniques
XI.3.1. Constructing the instance
XI.3.2. Setting the optimisation properties
XI.4. Analytical linear Bayesian estimation
XI.4.1. Constructing the TLinearBayesian object
XI.4.2. Define the linear model properties
XI.4.3. Look at the results
XI.4.4. Prediction of the variance
XI.5. The Approximation Bayesian Computation techniques (ABC)
XI.5.1. Constructing the RejectionABC object
XI.5.2. Define the TRejectionABC algorithm properties
XI.5.3. Look at the results
XI.6. The Markov-chain approach
XI.6.1. Constructing the TMetropHasting object
XI.6.2. Define the Metropolis-Hasting algorithm properties
XI.6.3. Look at the results
XII. The Uncertainty modeler module
XII.1. Introduction
XII.2. Tests based on the Empirical Distribution Function ("EDF tests")
XII.3. The Circe method
XIII. The Reliability module
XIII.1. Introduction
XIII.2. Form Sorm
XIII.2.1. Study outline
XIII.2.2. TSimpleTransform
XIII.2.3. TFormEval
XIII.2.4. TSorm
XIV. Use-cases in C++
XIV.1. Introduction
XIV.2. Macros DataServer
XIV.2.1. Macro "dataserverAttributes.C"
XIV.2.2. Macro "dataserverMerge.C"
XIV.2.3. Macro "dataserverLoadASCIIFilePasture.C"
XIV.2.4. Macro "dataserverLoadASCIIFile.C"
XIV.2.5. Macro "dataserverLoadASCIIFileYoungsModulus.C"
XIV.2.6. Macro "dataserverLoadASCIIFileIonosphere.C"
XIV.2.7. Macro "dataserverLoadASCIIFileCornell.C"
XIV.2.8. Macro "dataserverComputeQuantile.C"
XIV.2.9. Macro "dataserverGeyserStat.C"
XIV.2.10. Macro "dataserverGeyserRank.C"
XIV.2.11. Macro "dataserverNormaliseVector.C"
XIV.2.12. Macro "dataserverComputeStatVector.C"
XIV.2.13. Macro "dataserverComputeCorrelationMatrixVector.C"
XIV.2.14. Macro "dataserverComputeQuantileVec.C"
XIV.2.15. Macro "dataserverDrawQQPlot.C"
XIV.2.16. Macro "dataserverDrawPPPlot.C"
XIV.2.17. Macro "dataserverPCAExample.C"
XIV.3. Macros Sampler
XIV.3.1. Macro "samplingFlowrate.C"
XIV.3.2. Macro "samplingLHS.C"
XIV.3.3. Macro "samplingLHSCorrelation.C"
XIV.3.4. Macro "samplingQMC.C"
XIV.3.5. Macro "samplingBasicSampling.C"
XIV.3.6. Macro "samplingOATRegular.C"
XIV.3.7. Macro "samplingOATRandom.C"
XIV.3.8. Macro "samplingOATMulti.C"
XIV.3.9. Macro "samplingOATRange.C"
XIV.3.10. Macro "samplingSpaceFilling.C"
XIV.3.11. Macro "samplingMaxiMinLHSFromLHSGrid.C"
XIV.3.12. Macro "samplingConstrLHSLinear.C"
XIV.3.13. Macro "samplingConstrLHSEllipses.C"
XIV.3.14. Macro "samplerSingularCorrelationCase.C"
XIV.4. Macros Launcher
XIV.4.1. Macro "launchFunctionDataBase.C"
XIV.4.2. Macro "launchFunctionSampling.C"
XIV.4.3. Macro "launchFunctionSamplingGraphs.C"
XIV.4.4. Macro "launchCodeFlowrateKeyDataBase.C"
XIV.4.5. Macro "launchCodeFlowrateKeySampling.C"
XIV.4.6. Macro "launchCodeFlowrateXMLSampling.C"
XIV.4.7. Macro "launchCodeFlowrateKeySamplingKey.C"
XIV.4.8. Macro "launchCodeFlowrateKeyRecreateSampling.C"
XIV.4.9. Macro "launchCodeFlowrateKeyRecreateSamplingOutputDataServer.C"
XIV.4.10. Macro "launchCodeFlowrateRowRecreateSamplingOutputDataServer.C"
XIV.4.11. Macro "launchCodeFlowrateFlagSampling.C"
XIV.4.12. Macro "launchCodeFlowrateFlagSamplingKey.C"
XIV.4.13. Macro "launchCodeFlowrateKeyFlagSampling.C"
XIV.4.14. Macro "launchCodeFlowrateKeywithFlagSampling.C"
XIV.4.15. Macro "launchCodeFlowrateKeyFailure.C"
XIV.4.16. Macro "launchCodeFlowrateFlagFailure.C"
XIV.4.17. Macro "launchCodeFlowrateKeyOATMinMax.C"
XIV.4.18. Macro "launchCodeFlowrateFlagOATMinMax.C"
XIV.4.19. Macro "launchCodeLevelEOutputColumn.C"
XIV.4.20. Macro "launchCodeLevelEOutputRow.C"
XIV.4.21. Macro "launchCodeLevelEOutputKey.C"
XIV.4.22. Input/Output with vector and string: introduction to macros with multitype
XIV.4.23. Macro "launchCodeMultiTypeKey.C"
XIV.4.24. Macro "launchCodeMultiTypeKeyCondensate.C"
XIV.4.25. Macro "launchCodeMultiTypeDataServer.C"
XIV.4.26. Macro "launchCodeMultiTypeColumn.C"
XIV.4.27. Macro "launchCodeMultiTypeRow.C"
XIV.4.28. Macro "launchCodeMultiTypeXML.C"
XIV.4.29. Macro "launchCodeReadMultiTypeKey.C"
XIV.4.30. Macro "launchCodeReadMultiTypeDataServer.C"
XIV.4.31. Macro "launchCodeReadMultiTypeColumn.C"
XIV.4.32. Macro "launchCodeReadMultiTypeRow.C"
XIV.4.33. Macro "launchCodeReadMultiTypeXML.C"
XIV.4.34. Macro "launchCodeFilesWithBlank.C"
XIV.5. Macros Sensitivity
XIV.5.1. Macro "sensitivityBrutForceMethodFlowrate.C"
XIV.5.2. Macro "sensitivityFiniteDifferencesFunctionFlowrate.C"
XIV.5.3. Macro "sensitivityDataBaseFlowrate.C"
XIV.5.4. Macro "sensitivityFASTFunctionFlowrate.C"
XIV.5.5. Macro "sensitivityRBDFunctionFlowrate.C"
XIV.5.6. Macro "sensitivityMorrisFunctionFlowrate.C"
XIV.5.7. Macro "sensitivityMorrisFunctionFlowrateRunner.C"
XIV.5.8. Macro "sensitivityRegressionFunctionFlowrate.C"
XIV.5.9. Macro "sensitivitySobolFunctionFlowrate.C"
XIV.5.10. Macro "sensitivitySobolFunctionFlowrateRunner.C"
XIV.5.11. Macro "sensitivityRegressionLeveLE.C"
XIV.5.12. Macro "sensitivitySobolLeveLE.C"
XIV.5.13. Macro "sensitivitySobolRe-estimation.C"
XIV.5.14. Macro "sensitivitySobolWithData.C"
XIV.5.15. Macro "sensitivitySobolLoadFile.C"
XIV.5.16. Macro "sensitivityJohnsonRWFunctionFlowrate.C"
XIV.5.17. Macro "sensitivityJohnsonRWCorrelatedFunctionFlowrate.C"
XIV.5.18. Macro "sensitivityJohnsonRWJustCorrelationFakeFlowrate.C"
XIV.5.19. Macro "sensitivityHSICFunctionFlowrate.C"
XIV.5.20. Macro "sensitivitySobolRankFunctionFlowrate.C"
XIV.6. Macros Modeler
XIV.6.1. Macro "modelerCornellLinearRegression.C"
XIV.6.2. Macro "modelerFlowrateLinearRegression.C"
XIV.6.3. Macro "modelerFlowrateMultiLinearRegression.C"
XIV.6.4. Macro "modelerFlowrateNeuralNetworks.C"
XIV.6.5. Macro "modelerFlowrateNeuralNetworksLoadingPMML.C"
XIV.6.6. Macro "modelerClassificationNeuralNetworks.C"
XIV.6.7. Macro "modelerFlowratePolynChaosRegression.C"
XIV.6.8. Macro "modelerFlowratePolynChaosIntegration.C"
XIV.6.9. Macro "modelerbuildSimpleGP.C"
XIV.6.10. Macro "modelerbuildGPInitPoint.C"
XIV.6.11. Macro "modelerbuildGPWithAPriori.C"
XIV.6.12. Macro "modelerbuildSimpleGPEstim.C"
XIV.6.13. Macro "modelerbuildSimpleGPEstimWithCov.C"
XIV.6.14. Macro "modelerTestKriging.C"
XIV.7. Macros Optimizer
XIV.7.1. Macro "optimizeFunctionRosenbrock.C"
XIV.7.2. Macro "optimizeFunctionRosenbrockNewInputOutput.C"
XIV.7.3. Macro "optimizeCodeRosenbrockKey.C"
XIV.7.4. Macro "optimizeCodeRosenbrockKeyNewInputOutput.C"
XIV.7.5. Macro "optimizeCodeRosenbrockRow.C"
XIV.7.6. Macro "optimizeCodeRosenbrockKeyRowRecreate.C"
XIV.7.7. Macro "optimizeCodeRosenbrockRowRecreate.C"
XIV.7.8. Macro "optimizeCodeRosenbrockRowRecreateOutputDataServer.C"
XIV.7.9. Example of optimisation with a code that can compute several values at each run
XIV.7.10. Macro "optimizeRosenbrockMulti.C"
XIV.7.11. Macro "optimizeRosenbrockError.C"
XIV.8. Macros Relauncher
XIV.8.1. Macro "relauncherFunctionFlowrateCInt.C"
XIV.8.2. Macro "relauncherFunctionFlowrateCJit.C"
XIV.8.3. Macro "relauncherCJitFunctionThreadTest.C"
XIV.8.4. Macro "relauncherCodeFlowrateSequential.C"
XIV.8.5. Macro "relauncherCodeFlowrateSequential_ConstantVar.C"
XIV.8.6. Macro "relauncherCodeFlowrateThreaded.C"
XIV.8.7. Macro "relauncherCodeFlowrateMPI.C"
XIV.8.8. Macro "relauncherCodeFlowrateMpiStandalone.C"
XIV.8.9. Macro "relauncherCodeFlowrateSequentialFailure.C"
XIV.8.10. Macro "relauncherCodeMultiTypeKey.C"
XIV.8.11. Macro "relauncherCodeMultiTypeKeyEmptyVectors.C"
XIV.8.12. Macro "relauncherCodeMultiTypeKeyEmptyVectorsAsFailure.C"
XIV.8.13. Macro "relauncherCodeReadMultiType.C"
XIV.8.14. Macro "relauncherComposeMultitypeAndReadMultiType.C"
XIV.8.15. Macro "relauncherCodeFlowrateSequential_TemporaryVar.C"
XIV.9. Macros Reoptimizer
XIV.9.1. Macro "reoptimizeHollowBarCode.C"
XIV.9.2. Macro "reoptimizeHollowBarCodeMultiStart.C"
XIV.9.3. Macro "reoptimizeHollowBarCodevizir.C"
XIV.9.4. Macro "reoptimizeHollowBarVizirMoead.C"
XIV.9.5. Macro "reoptimizeHollowBarVizirSplitRuns.C"
XIV.9.6. Macro "reoptimizeZoningBiSubMpi.C"
XIV.9.7. Macro "reoptimizeZoneBiFunMpi.C"
XIV.10. Macros MetaModelOptim
XIV.10.1. Macro "metamodoptEgoHimmel.C"
XIV.11. Macros Calibration
XIV.11.1. Macro "calibrationMinimisationFlowrate1D.C"
XIV.11.2. Macro "calibrationLinBayesFlowrate1D.C"
XIV.11.3. Macro "calibrationRejectionABCFlowrate1D.C"
XIV.11.4. Macro "calibrationMetropHastingFlowrate1D.C"
XIV.11.5. Macro "calibrationMetropHastingLinReg.C"
XIV.11.6. Macro "calibrationMinimisationFlowrate2DVizir.C"
XIV.12. Macros UncertModeler
XIV.12.1. Macro "uncertModelerTestsYoungsModulus.C"
XIV.12.2. Macro "uncertModelerCirce.C"
XIV.13. Macros Reliability
XIV.13.1. Macro "reliabilityFormSorm.C"
XIV.13.2. Macro "reliabilityFormSormBis.C"
References

List of Figures

I.1. Organisation of the Uranie-modules (green boxes) in terms of inter-dependencies. The blue boxes represent the external dependencies (discussed later on).
I.2. Histogram produced using PyROOT
II.1. Diagram of the class TDataServer
II.2. Attributes of TAttribute class
II.3. Graph of the variable sdp
II.4. Scatterplot x2 versus x1 for the geyser data with modification of fields title and unit.
II.5. Example of PDF, CDF and inverse CDF for Uniform distribution.
II.6. Example of PDF, CDF and inverse CDF for LogUniform distributions.
II.7. Example of PDF, CDF and inverse CDF for Triangular distributions.
II.8. Example of PDF, CDF and inverse CDF for Logtriangular distributions.
II.9. Example of PDF, CDF and inverse CDF for Normal distributions.
II.10. Example of PDF, CDF and inverse CDF for a Normal truncated distribution.
II.11. Example of PDF, CDF and inverse CDF for LogNormal distributions.
II.12. Example of PDF, CDF and inverse CDF for a LogNormal truncated distribution.
II.13. Example of PDF, CDF and inverse CDF for Trapezium distributions.
II.14. Example of PDF, CDF and inverse CDF for UniformByParts distributions.
II.15. Example of PDF, CDF and inverse CDF for Exponential distributions.
II.16. Example of PDF, CDF and inverse CDF for a Exponential truncated distribution.
II.17. Example of PDF, CDF and inverse CDF for Cauchy distributions.
II.18. Example of PDF, CDF and inverse CDF for a Cauchy truncated distribution.
II.19. Example of PDF, CDF and inverse CDF for GumbelMax distributions.
II.20. Example of PDF, CDF and inverse CDF for a GumbelMax truncated distribution.
II.21. Example of PDF, CDF and inverse CDF for Weibull distributions.
II.22. Example of PDF, CDF and inverse CDF for a Weibull truncated distribution.
II.23. Example of PDF, CDF and inverse CDF for Beta distributions.
II.24. Example of PDF, CDF and inverse CDF for GenPareto distributions.
II.25. Example of PDF, CDF and inverse CDF for a GenPareto truncated distribution.
II.26. Example of PDF, CDF and inverse CDF for Gamma distributions.
II.27. Example of PDF, CDF and inverse CDF for a Gamma truncated distribution.
II.28. Example of PDF, CDF and inverse CDF for InvGamma distributions.
II.29. Example of PDF, CDF and inverse CDF for a InvGamma truncated distribution.
II.30. Example of PDF, CDF and inverse CDF for Student distribution.
II.31. Example of PDF, CDF and inverse CDF for a Student truncated distribution.
II.32. Example of PDF, CDF and inverse CDF for generalized normal distributions.
II.33. Example of PDF, CDF and inverse CDF for a generalized normal truncated distribution.
II.34. Example of PDF, CDF and inverse CDF for a composed distribution made out of three normal distributions with respective weights.
II.35. Example of PDF, CDF and inverse CDF for a truncated composed distribution made out of three normal distributions with respective weights.
II.36. Import data from an ASCII file
II.37. Content of the ntuple tree contained in "hsimple.root" file.
II.38. Data importation from a TNtuple
II.39. Scatterplot of added attributes
II.40. Graph with a selection definition
II.41. Graph with a definition of Cut
II.42. Different histograms of the same attribute xnorm depending on the method for computing bins. The values are respectively 100(root), 8 from sturges, 7 from fd and scoot.
II.43. Boxplot of attribute x2 of the TDataServer geyser
II.44. CDF graph of attribute x2 of the TDataServer geyser
II.45. Graphs CDF+CCDF of the attribute x2 of the TDataServer geyser
II.46. Scatterplot between attributes x1 and x2 of the TDataServer geyser.
II.47. Scatterplot between attributes x1 and x2 of the TDataServer geyser.
II.48. Graphs of "Tufte" type between the attributes x1 and x2 of the TDataServer geyser.
II.49. Graphs of "Tufte" type between the attributes x1 and x2 of the TDataServer geyser.
II.50. Graphs of "drawPairs" type between the 8 uniformly-distributed inputs and the output of a given problem.
II.51. Graphs of "CobWeb" type between the 8 uniformly-distributed inputs and the output of a given problem.
II.52. Plot resulting from the "drawQQPlot" method, comparing "x2" to a normal distribution.
II.53. Plot resulting from the "drawPPPlot" method, comparing "x2" to a normal distribution.
II.54. Representation of some variables of the Notes sample.
II.55. Representation of the eigenvalues (left) their overall contributions in percent (middle) and the sum of the contributions (right) from the PCA analysis.
II.56. Representation of correlation between the original variables and the PC under study.
II.57. Representation of the data points in the PC-defined plane.
III.1. Schematic view of the input/output relation through a code
III.2. Comparison of the two sampling methods SRS (left) and LHS (right) with samples of size 8.
III.3. Comparison of deterministic design-of-experiments obtained using either SRS (left) or LHS (right) algorithm, when having two independent random variables (uniform and normal one)
III.4. Tufte plot of the design-of-experiments created using a normal and uniform distribution, with a LHS method with three correlation coefficient: 0, 0.45 and 0.9
III.5. Tufte plot of the rank of the design-of-experiments created using a normal and uniform distribution, with a LHS method with three correlation coefficient: 0, 0.45 and 0.9
III.6. Example of sampling done with half million points and two uniform attributes (from 0 to 1), using AMH copula and varying the parameter value.
III.7. Example of sampling done with half million points and two uniform attributes (from 0 to 1), using Clayton copula and varying the parameter value.
III.8. Example of sampling done with half million points and two uniform attributes (from 0 to 1), using Frank copula and varying the parameter value.
III.9. Example of sampling done with half million points and two uniform attributes (from 0 to 1), using Plackett copula and varying the parameter value.
III.10. Comparison of both quasi Monte-Carlo sequences with both LHS and SRS sampling when dealing with two uniform attributes.
III.11. Comparison of design-of-experiments made with Petras algorithm, using different level values, when dealing with two uniform attributes.
III.12. Gaussian Random Field
III.13. Gaussian variograms. Several configurations (in terms of scale factor and variance parameters) are shown as well.
III.14. Sine cardinal variograms. Several configurations (in terms of scale factor and variance parameters) are shown as well.
III.15. Random values for OAT design
III.16. Example of a dataset reduction (the geyser one) using the NeuralGas algorithm, to go from 272 points (left) to 50 one (right)
IV.1. Sketch of the flowrate problem and its variables[BoreHole].
IV.2. Inheritance diagram for the class TLauncher
IV.3. Schematic description of the launcher procedure when using an external code. Yellow boxes show instances of class, and green ones are precision about attributes. The design-of-experiments part can be replaced by an already-existing database.
IV.4. Multi-core computer
V.1. Simplified decomposition of the model creation process into a four important-step recipe.
V.2. Schematic view of the Nisp methodology
V.3. Schematic description of the working flow of an artificial neural network as used in Uranie
V.4. Schematic description of the kriging procedure as done within Uranie
V.5. Estimation using a simple Kriging model
V.6. Residual distribution using a validation database with and without prediction covariance correction.
VI.1. SRC coefficients estimated for the flowrate function.
VI.2. SRRC coefficients estimated for the flowrate function.
VI.3. Histogram of SRC coefficients
VI.4. Morris screening indices
VI.5. Histogram of Sobol's indices
VI.6. Pie chart of Sobol's indices
VI.7. Frequency spectrum from the FAST estimation
VI.8. Histogram of FAST's indices
VI.9. Pie chart of FAST's indices
VI.10. Frequency spectrum from the RBD estimation
VI.11. Histogram of RBD's indices
VI.12. Pie chart of RBD's indices
VI.13. Histogram of JohnsonRW's indices
VI.14. Pie chart of JohnsonRW's indices
VII.1. 3D representation of the Rosenbrock function
VIII.1. Schematic description of the needed steps to define a relauncher procedure
VIII.2. Hierarchy of classes and structures for the evaluation part of the Relauncher module.
VIII.3. Hierarchy of classes and structures for the runner part of the Relauncher module.
IX.1. Hollow Bar
IX.2. Schematic description of the requested steps of an optimisation procedure once this one is performed with Vizir
XI.1. Hierarchy of classes and structures out of Doxygen for the Calibration module
XI.2. Trace distributions split between below and above 100 threshold
XII.1. Results of the macro defined previously to produce variety of test of already implemented distributions
XIV.1. Graph of the macro "dataserverLoadASCIIFilePasture.C"
XIV.2. Graph of the macro "dataserverLoadASCIIFile.C"
XIV.3. Graph of the macro "dataserverLoadASCIIFileYoungsModulus.C"
XIV.4. Graph of the macro "dataserverLoadASCIIFileIonosphere.C"
XIV.5. Graph of the macro "dataserverComputeQuantile.C"
XIV.6. Graph of the macro "dataserverDrawQQPlot.C"
XIV.7. Graph of the macro "dataserverDrawPPPlot.C"
XIV.8. Graph of the macro "samplingFlowrate.C"
XIV.9. Graph of the macro "samplingLHS.C"
XIV.10. Graph de la macro "samplingLHSCorrelation.C"
XIV.11. Graph of the macro "samplingQMC.C"
XIV.12. Graph of the macro "samplingSpaceFilling.C"
XIV.13. Graph of the macro "samplingMaxiMinLHSFromLHSGrid.C"
XIV.14. Graph of the macro "samplingConstrLHSLinear.C"
XIV.15. Graph of the macro "samplingConstrLHSEllipses.C"
XIV.16. Graph of the macro "samplerSingularCorrelationCase.C"
XIV.17. Graph of the macro "launchFunctionDataBase.C"
XIV.18. Graph of the macro "launchFunctionSampling.C"
XIV.19. Graph of the macro "launchFunctionSamplingGraphs.C"
XIV.20. Graph of the macro "launchCodeFlowrateKeyDataBase.C"
XIV.21. Graph of the macro "launchCodeFlowrateKeySampling.C"
XIV.22. Graph of the macro "launchCodeFlowrateXMLSampling.C"
XIV.23. Graph of the macro "launchCodeFlowrateKeySamplingKey.C"
XIV.24. Graph of the macro "launchCodeFlowrateKeyRecreateSampling.C"
XIV.25. Graph of the macro "launchCodeFlowrateKeyRecreateSamplingOutputDataServer.C"
XIV.26. Graph of the macro "launchCodeFlowrateRowRecreateSamplingOutputDataServer.C"
XIV.27. Graph of the macro "launchCodeFlowrateFlagSampling.C"
XIV.28. Graph of the macro "launchCodeFlowrateFlagSamplingKey.C"
XIV.29. Graph of the macro "launchCodeFlowrateKeyFlagSampling.C"
XIV.30. Graph of the macro "launchCodeFlowrateKeywithFlagSampling.C"
XIV.31. Graph of the macro "launchCodeFlowrateKeyFailure.C"
XIV.32. Graph of the macro "launchCodeFlowrateFlagFailure.C"
XIV.33. Graph of the macro "launchCodeFlowrateKeyOATMinMax.C"
XIV.34. Graph of the macro "launchCodeFlowrateFlagOATMinMax.C"
XIV.35. Graph of the macro "launchCodeLevelEOutputColumn.C"
XIV.36. Graph of the macro "launchCodeLevelEOutputRow.C"
XIV.37. Graph of the macro "launchCodeLevelEOutputKey.C"
XIV.38. Graph of the macro "launchCodeMultiTypeKey.C"
XIV.39. Graph of the macro "launchCodeMultiTypeKeyCondensate.C"
XIV.40. Graph of the macro "launchCodeMultiTypeDataServer.C"
XIV.41. Graph of the macro "launchCodeMultiTypeColumn.C"
XIV.42. Graph of the macro "launchCodeMultiTypeRow.C"
XIV.43. Graph of the macro "launchCodeMultiTypeXML.C"
XIV.44. Graph of the macro "sensitivityBrutForceMethodFlowrate.C"
XIV.45. Graph of the macro "sensitivityDataBaseFlowrate.C"
XIV.46. Graph of the macro "sensitivityFASTFunctionFlowrate.C"
XIV.47. Graph of the macro "sensitivityRBDFunctionFlowrate.C"
XIV.48. Graph of the macro "sensitivityMorrisFunctionFlowrate.C"
XIV.49. Graph of the macro "sensitivityMorrisFunctionFlowrateRunner.C"
XIV.50. Graph of the macro "sensitivityRegressionFunctionFlowrate.C"
XIV.51. Graph of the macro "sensitivitySobolFunctionFlowrate.C"
XIV.52. Graph of the macro "sensitivitySobolFunctionFlowrateRunner.C"
XIV.53. Graph of the macro "sensitivityRegressionLeveLE.C"
XIV.54. Graph of the macro "sensitivitySobolLeveLE.C"
XIV.55. Graph of the macro "sensitivitySobolRe-estimation.C"
XIV.56. Graph of the macro "sensitivitySobolWithData.C"
XIV.57. Graph of the macro "sensitivitySobolLoadFile.C"
XIV.58. Graph of the macro "sensitivityJohnsonRWFunctionFlowrate.C"
XIV.59. Graph of the macro "sensitivityJohnsonRWCorrelatedFunctionFlowrate.C"
XIV.60. Graph of the macro "sensitivityJohnsonRWJustCorrelationFakeFlowrate.C"
XIV.61. Graph of the macro "sensitivityHSICFunctionFlowrate.C"
XIV.62. Graph of the macro "sensitivitySobolRankFunctionFlowrate.C"
XIV.63. Graph of the macro "modelerCornellLinearRegression.C"
XIV.64. Graph of the macro "modelerFlowrateLinearRegression.C"
XIV.65. Graph of the macro "modelerFlowrateMultiLinearRegression.C"
XIV.66. Graph of the macro "modelerFlowrateNeuralNetworks.C"
XIV.67. Graph of the macro "modelerFlowrateNeuralNetworksLoadingPMML.C"
XIV.68. Graph of the macro "modelerClassificationNeuralNetworks.C"
XIV.69. Graph of the macro "modelerbuildSimpleGPEstim.C"
XIV.70. Graph of the macro "modelerbuildSimpleGPEstimWithCov.C"
XIV.71. Graph of the macro "modelerTestKriging.C"
XIV.72. Graph of the macro "optimizeFunctionRosenbrock.C"
XIV.73. Graph of the macro "optimizeFunctionRosenbrockNewInputOutput.C"
XIV.74. Graph of the macro "optimizeCodeRosenbrockKey.C"
XIV.75. Graph of the macro "optimizeCodeRosenbrockKeyNewInputOutput.C"
XIV.76. Graph of the macro "optimizeCodeRosenbrockRow.C"
XIV.77. Graph of the macro "optimizeCodeRosenbrockKeyRowRecreate.C"
XIV.78. Graph of the macro "optimizeCodeRosenbrockRowRecreate.C"
XIV.79. Graph of the macro "optimizeCodeRosenbrockRowRecreateOutputDataServer.C"
XIV.80. Evolution of searched parameters a and b throw iterations
XIV.81. Evolution of searched parameters a and b throw iterations
XIV.82. Representation of the output as a function of the first input with a colZ option
XIV.83. Representation of the output as a function of the first input with a colZ option
XIV.84. Representation of the output as a function of the first input with a colZ option
XIV.85. Representation of the output as a function of the first input with a colZ option
XIV.86. Representation of the output as a function of the first input with a colZ option
XIV.87. Representation of the output as a function of the first input with a colZ option when using either the classical or dedicated constructor
XIV.88. Representation of the output data point when the code is asked to fail on purpose.
XIV.89. Graph of the macro "relauncherCodeMultiTypeKey.C"
XIV.90. Graph of the macro "relauncherCodeMultiTypeKeyEmptyVectors.C"
XIV.91. Graph of the macro "relauncherCodeMultiTypeKeyEmptyVectorsAsFailure.C"
XIV.92. Graph of the macro "reoptimizeHollowBarCodeVizir.C"
XIV.93. Graph of the macro "reoptimizeHollowBarVizirMoead.C"
XIV.94. Graph of the macro "reoptimizeHollowBarVizirSplitRuns.C"
XIV.95. The core and its assemblies
XIV.96. Graph of the macro "calibrationMinimisationFlowrate1D.C"
XIV.97. Residual graph of the macro "calibrationLinBayesFlowrate1D.C"
XIV.98. Parameter graph of the macro "calibrationLinBayesFlowrate1D.C"
XIV.99. Residual graph of the macro "calibrationRejectionABCFlowrate1D.C"
XIV.100. Parameter graph of the macro "calibrationRejectionABCFlowrate1D.C"
XIV.101. Trace graph of the macro "calibrationMetropHastingFlowrate1D.C"
XIV.102. Residual graph of the macro "calibrationMetropHastingFlowrate1D.C"
XIV.103. Parameter graph of the macro "calibrationMetropHastingFlowrate1D.C"
XIV.104. Trace graph of the macro "calibrationMetropHastingLinReg.C"
XIV.105. Acceptation rate graph of the macro "calibrationMetropHastingLinReg.C"
XIV.106. Residual graph of the macro "calibrationMetropHastingLinReg.C"
XIV.107. Parameter graph of the macro "calibrationMetropHastingLinReg.C"
XIV.108. Residual graph of the macro "calibrationMinimisationFlowrate2DVizir.C"
XIV.109. Parameter graph of the macro "calibrationMinimisationFlowrate2DVizir.C"
XIV.110. Graph of the macro macro "uncertModelerTestsYoungsModulus.C"
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