13.6.16. Macro “sensitivityJohnsonRWFunctionFlowrate.py”

13.6.16.1. Objective

The objective of this macro is to perform a sensitivity analysis using the Johnson’s relative weight method on a set of eight parameters used in the flowrateModel model described in Presentation of the problem.

13.6.16.2. Macro Uranie

"""
Example of Johnson relative weight method applied to flowrate
"""
from URANIE import DataServer, Sensitivity
import ROOT

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

# Define the DataServer
tds = DataServer.TDataServer("tdsflowrate", "DataBase flowrate")
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))

# param Size of a sampling.
nS = 1000
FuncName = "flowrateModel"

tjrw = Sensitivity.TJohnsonRW(tds, FuncName, nS,
                              "rw:r:tu:tl:hu:hl:l:kw", FuncName)
tjrw.computeIndexes()

# Get the results on screen
tjrw.getResultTuple().Scan("Out:Inp:Method:Value", "Order==\"First\"")

# Get the results as plots
cc = ROOT.TCanvas("canhist", "histgramme")
tjrw.drawIndexes("Flowrate", "", "nonewcanv,hist,first")
cc.Print("appliUranieFlowrateJohnsonRW1000Histogram_py.png")

ccc = ROOT.TCanvas("canpie", "TPie")
tjrw.drawIndexes("Flowrate", "", "nonewcanv,pie")
ccc.Print("appliUranieFlowrateJohnsonRW1000Pie_py.png")

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

# Define the DataServer
tds = DataServer.TDataServer("tdsflowrate", "DataBase flowrate")
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 TJohnsonRW object, one uses the TDataServer, the name of the function, the number of samplings needed to perform sensitivity analysis (here $n_S$ =4000) and the input and output variables:

tjrw = Sensitivity.TJohnsonRW(tds, FuncName, nS,
                              "rw:r:tu:tl:hu:hl:l:kw", FuncName)

Computation of sensitivity indexes:

tjrw.computeIndexes()

The rest is very common to all sensitivity macros discussed here: it will produce two plots (the first one being a histogram show below) and the console is also shown below for completness.

13.6.16.3. Graph

../../_images/appliUranieFlowrateJohnsonRW1000Histogram_py.png — Figure 13.32 Graph of the macro **“sensitivityJohnsonRWFunctionFlowrate.py”**

13.6.16.4. 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 [tdsflowrate] contains data: we need to empty it ! 
 <URANIE::INFO> *** END of URANIE INFORMATION ***
 <URANIE::INFO> 
************************************************************
*    Row   *       Out *       Inp *    Method *     Value *
************************************************************
*        0 * flowrateM *        rw * JohnsonRW * 0.8636266 *
*        2 * flowrateM *         r * JohnsonRW * 4.598e-05 *
*        4 * flowrateM *        tu * JohnsonRW * 8.775e-06 *
*        6 * flowrateM *        tl * JohnsonRW * 9.689e-05 *
*        8 * flowrateM *        hu * JohnsonRW * 0.0439173 *
*       10 * flowrateM *        hl * JohnsonRW * 0.0435594 *
*       12 * flowrateM *         l * JohnsonRW * 0.0378304 *
*       14 * flowrateM *        kw * JohnsonRW * 0.0109144 *
*       16 * flowrateM *    __R2__ * JohnsonRW * 0.9447092 *
*       18 * flowrateM *   __R2A__ * JohnsonRW * 0.9442633 *
************************************************************
==> 10 selected entries