13.6.9. Macro “sensitivitySobolFunctionFlowrate.py”

13.6.9.1. Objective

The objective of this macro is to perform Sobol sensitivity analysis on a set of eight parameters used in the flowrateModel model described in Presentation of the problem.

13.6.9.2. Macro Uranie

"""
Example of Sobol estimation for the flowrate function
"""
from URANIE import DataServer, Sensitivity
import ROOT

ROOT.gROOT.LoadMacro("UserFunctions.C")

# Define the DataServer
tds = DataServer.TDataServer("tdsflowreate", "DataBase flowreate")
tds.addAttribute(DataServer.TUniformDistribution("rw", 0.05, 0.15))
tds.addAttribute(DataServer.TUniformDistribution("r", 100.0, 50000.0))
tds.addAttribute(DataServer.TUniformDistribution("tu", 63070.0, 115600.0))
tds.addAttribute(DataServer.TUniformDistribution("tl", 63.1, 116.0))
tds.addAttribute(DataServer.TUniformDistribution("hu", 990.0, 1110.0))
tds.addAttribute(DataServer.TUniformDistribution("hl", 700.0, 820.0))
tds.addAttribute(DataServer.TUniformDistribution("l", 1120.0, 1680.0))
tds.addAttribute(DataServer.TUniformDistribution("kw", 9855.0, 12045.0))

ns = 100000
tsobol = Sensitivity.TSobol(tds, "flowrateModel", ns, "rw:r:tu:tl:hu:hl:l:kw",
                            "flowrateModel", "DummyPython")
tsobol.setDrawProgressBar(False)
tsobol.computeIndexes()

tsobol.getResultTuple().Scan("*", "Algo==\"--first--\" || Algo==\"--total--\"")

cc = ROOT.TCanvas("c1", "histgramme", 5, 64, 1270, 667)
pad = ROOT.TPad("pad", "pad", 0, 0.03, 1, 1)
pad.Draw()
pad.Divide(2, 1)
pad.cd(1)
tsobol.drawIndexes("Flowrate", "", "nonewcanv, hist, all")

pad.cd(2)
tsobol.drawIndexes("Flowrate", "", "nonewcanv, pie, first")

ROOT.gSystem.Rename("_sobol_launching_.dat", "ref_sobol_launching_.dat")
tds.exportData("_onlyMandN_sobol_launching_.dat",
               "rw:r:tu:tl:hu:hl:l:kw:flowrateModel",
               "sobol__n__iter__tdsflowreate < 100")

The function flowrateModel is loaded from the macro UserFunctions.C (the file can be found in ${URANIESYS}/share/uranie/macros)

ROOT.gROOT.LoadMacro("UserFunctions.C")

Each parameter is related to the TDataServer as a TAttribute and obeys an uniform law on specific interval:

tds = DataServer.TDataServer("tdsflowreate", "DataBase flowreate")
tds.addAttribute(DataServer.TUniformDistribution("rw", 0.05, 0.15))
tds.addAttribute(DataServer.TUniformDistribution("r", 100.0, 50000.0))
tds.addAttribute(DataServer.TUniformDistribution("tu", 63070.0, 115600.0))
tds.addAttribute(DataServer.TUniformDistribution("tl", 63.1, 116.0))
tds.addAttribute(DataServer.TUniformDistribution("hu", 990.0, 1110.0))
tds.addAttribute(DataServer.TUniformDistribution("hl", 700.0, 820.0))
tds.addAttribute(DataServer.TUniformDistribution("l", 1120.0, 1680.0))
tds.addAttribute(DataServer.TUniformDistribution("kw", 9855.0, 12045.0))

To instantiate the TSobol, one uses the TDataServer, the name of the function and the number of samplings needed to perform sensitivity analysis (here ns=600):

tsobol = Sensitivity.TSobol(tds, "flowrateModel", ns, "rw:r:tu:tl:hu:hl:l:kw",
                            "flowrateModel", "DummyPython")

The last argument is the option field, which in most cases is empty. Here it is filled with “DummyPython” which helps specify to python which constructor to choose. There are indeed several possible constructors these 5 five first arguments, but C++ can make the difference between them as the literal members are either std::string, ROOT::TString, Char_t* or even Option_t*. For python, these format are all PyString, so the sixth argument is compulsory to disentangle the possibilities.

Computation of the sensitivity indexes:

tsobol.computeIndexes()

Data are exported from the TDataServer to an ASCII file:

tds.exportData("_onlyMandN_sobol_launching_.dat",
               "rw:r:tu:tl:hu:hl:l:kw:flowrateModel",
               "sobol__n__iter__tdsflowreate < 100")

13.6.9.3. Graph

../../_images/sensitivitySobolFunctionFlowrate.png — Figure 13.25 Graph of the macro **“sensitivitySobolFunctionFlowrate.py”**

13.6.9.4. Console

--- Uranie v4.11/0 --- Developed with ROOT (6.36.06)
                      Copyright (C) 2013-2026 CEA/DES 
                      Contact: support-uranie@cea.fr 
                      Date: Thu Feb 12, 2026

 <URANIE::WARNING> 
 <URANIE::WARNING> *** URANIE WARNING ***
 <URANIE::WARNING> *** File[${SOURCEDIR}/dataSERVER/souRCE/TDataServer.cxx] Line[8531]
 <URANIE::WARNING> TDataServer::getTuple Error : There is no tree!
 <URANIE::WARNING> *** END of URANIE WARNING ***
 <URANIE::WARNING> 
 <URANIE::INFO> 
 <URANIE::INFO> *** URANIE INFORMATION ***
 <URANIE::INFO> *** File[${SOURCEDIR}/meTIER/sampler/souRCE/TSamplerStochastic.cxx] Line[66]
 <URANIE::INFO> TSamplerStochastic::init: the TDS [tdsflowreate] contains data: we need to empty it ! 
 <URANIE::INFO> *** END of URANIE INFORMATION ***
 <URANIE::INFO> 
 ** Case of Output atty [flowrateModel]  nSimPerIndex 10000
 ** Input att [rw] First [0.830033] Total Order[0.865762]
 ** Input att [r] First [0] Total Order[0.000102212]
 ** Input att [tu] First [0] Total Order[0.0001]
 ** Input att [tl] First [0] Total Order[0.000110756]
 ** Input att [hu] First [0.0417298] Total Order[0.0554922]
 ** Input att [hl] First [0.0367345] Total Order[0.0526188]
 ** Input att [l] First [0.0384214] Total Order[0.0535728]
 ** Input att [kw] First [0.00669831] Total Order[0.0132316]
************************************************************************************************************
*    Row   *   Out.Out *   Inp.Inp * Order.Ord * Method.Me * Algo.Algo * Value.Val * CILower.C * CIUpper.C *
************************************************************************************************************
*        0 * flowrateM *        rw *     First *     Sobol * --first-- * 0.8300331 * 0.8238356 * 0.8360321 *
*        4 * flowrateM *        rw *     Total *     Sobol * --total-- * 0.8657619 * 0.8465652 * 0.8850599 *
*        8 * flowrateM *         r *     First *     Sobol * --first-- *         0 *         0 * 0.0196004 *
*       12 * flowrateM *         r *     Total *     Sobol * --total-- * 0.0001022 * 9.828e-05 * 0.0001062 *
*       16 * flowrateM *        tu *     First *     Sobol * --first-- *         0 *         0 * 0.0196004 *
*       20 * flowrateM *        tu *     Total *     Sobol * --total-- * 0.0001000 * 9.615e-05 * 0.0001039 *
*       24 * flowrateM *        tl *     First *     Sobol * --first-- *         0 *         0 * 0.0196004 *
*       28 * flowrateM *        tl *     Total *     Sobol * --total-- * 0.0001107 * 0.0001064 * 0.0001151 *
*       32 * flowrateM *        hu *     First *     Sobol * --first-- * 0.0417297 * 0.0221474 * 0.0612800 *
*       36 * flowrateM *        hu *     Total *     Sobol * --total-- * 0.0554921 * 0.0534156 * 0.0576470 *
*       40 * flowrateM *        hl *     First *     Sobol * --first-- * 0.0367345 * 0.0171464 * 0.0562944 *
*       44 * flowrateM *        hl *     Total *     Sobol * --total-- * 0.0526187 * 0.0506469 * 0.0546652 *
*       48 * flowrateM *         l *     First *     Sobol * --first-- * 0.0384214 * 0.0188352 * 0.0579782 *
*       52 * flowrateM *         l *     Total *     Sobol * --total-- * 0.0535727 * 0.0515661 * 0.0556552 *
*       56 * flowrateM *        kw *     First *     Sobol * --first-- * 0.0066983 *         0 * 0.0262952 *
*       60 * flowrateM *        kw *     Total *     Sobol * --total-- * 0.0132315 * 0.0127261 * 0.0137570 *
*       64 * flowrateM *   __sum__ *     First *     Sobol * --first-- * 0.9536171 *        -1 *        -1 *
*       65 * flowrateM *   __sum__ *     Total *     Sobol * --total-- * 1.0409902 *        -1 *        -1 *
************************************************************************************************************
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