---
myst:
    substitutions:
        macro:
            python: 1-5,19-38,42-49,52-55,58
            cpp: 4-6,13-28,32-39,42-45,48
        bloc1:
            python: "20"
            cpp: "13"
        bloc2:
            python: 22-31
            cpp: 5,15-22
        bloc3:
            python: 37-38
            cpp: "28"
        bloc4:
            python: "42"
            cpp: "32"
        console:
            python: 2-33
            cpp: 6-37
        suffix:
            python: "_py"
            cpp: ""
---
(use_cases_macro_sensitivity_johnson_rw)=
# Macro "**sensitivityJohnsonRWFunctionFlowrate.{{extension}}**"

## 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 
[](#launcher_introduction_simple_case_problem).

(use_cases_macro_sensitivity_johnson_rw_macro)=
## Macro {{uranie}}

{{
    "```{" "literalinclude" "} " + parent_dir +
        "/roottest/uranie/doc/sensitivity/use_cases/" + language + "/sensitivityJohnsonRWFunctionFlowrate." 
        + extension
    + "\n"
    + ":language: " + language + "\n"
    + ":lines: " + macro[language] + "\n"
    + "```"
}}
            
The function `flowrateModel` is loaded from the macro `UserFunctions.C` (the file can be found in 
`${URANIESYS}/share/uranie/macros`)

{{
    "```{" "literalinclude" "} " + parent_dir +
        "/roottest/uranie/doc/sensitivity/use_cases/" + language + "/sensitivityJohnsonRWFunctionFlowrate." 
        + extension
    + "\n"
    + ":language: " + language + "\n"
    + ":lines: " + bloc1[language] + "\n"
    + "```"
}}
            
Each parameter is related to the {{tds}} as a `TAttribute` and obeys an uniform law on specific interval

{{
    "```{" "literalinclude" "} " + parent_dir +
        "/roottest/uranie/doc/sensitivity/use_cases/" + language + "/sensitivityJohnsonRWFunctionFlowrate." 
        + extension
    + "\n"
    + ":language: " + language + "\n"
    + ":lines: " + bloc2[language] + "\n"
    + "```"
}}
            
To instantiate the `TJohnsonRW` object, one uses the {{tds}}, the name of the function, the number of 
samplings needed to perform sensitivity analysis (here $n_S$ =4000) and the input and output variables:

{{
    "```{" "literalinclude" "} " + parent_dir +
        "/roottest/uranie/doc/sensitivity/use_cases/" + language + "/sensitivityJohnsonRWFunctionFlowrate." 
        + extension
    + "\n"
    + ":language: " + language + "\n"
    + ":lines: " + bloc3[language] + "\n"
    + "```"
}}
            
Computation of sensitivity indexes:

{{
    "```{" "literalinclude" "} " + parent_dir +
        "/roottest/uranie/doc/sensitivity/use_cases/" + language + "/sensitivityJohnsonRWFunctionFlowrate." 
        + extension
    + "\n"
    + ":language: " + language + "\n"
    + ":lines: " + bloc4[language] + "\n"
    + "```"
}}
            
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.

## Graph

{{
    "```{" "figure" "} " + parent_dir +
        "/roottest/build/uranie/doc/sensitivity/use_cases/" + language 
        + "/johnson_rw/appliUranieFlowrateJohnsonRW1000Histogram" + suffix[language] + ".png\n"
    + ":align: center\n"
    + ":name: use_cases_sensitivityJohnsonRWFunctionFlowrate\n"
    + figure_scale + "\n"
    + "\n"
    + "Graph of the macro **\"sensitivityJohnsonRWFunctionFlowrate." + extension + "\"**" + "\n"
    + "```"
}}
            
## Console

{{
    "```{" "literalinclude" "} " + parent_dir +
        "/roottest/build/uranie/doc/sensitivity/use_cases/" + language 
        + "/sensitivityJohnsonRWFunctionFlowrate_clean.log"
    + "\n"
    + ":language: none\n"
    + ":lines: " + console[language] + "\n"
    + "```"
}}