---
myst:
    substitutions:
        macro:
            python: 1-5,18-45,48-54,56-68
            cpp: 6-10,17-38,41-47,49-61
        bloc1:
            python: 19-20
            cpp: 6,17
        bloc2:
            python: 24-26
            cpp: 21-22
        bloc3:
            python: "28"
            cpp: "24"
        bloc4:
            python: 34-41
            cpp: 27-34
        bloc5:
            python: 45,48
            cpp: 38,41
        bloc6:
            python: 50,54,57
            cpp: 43,47,50
---
# Macro "**modelerFlowrateMultiLinearRegression.{{extension}}**"

## Objective

The objective of the macro is to build a multilinear regression between the predictors {{floinputs}} 
and a target variable **yhat** from the database contained in the ASCII file 
`flowrate_sampler_launcher_500.dat` defining values for these eight variables described in 
[](#launcher_introduction_simple_case_problem) on 500 patterns. Parameters of the regression are then 
exported in a .{{extension}} file `_FileContainingFunction_.C`:

{{
    "```{literalinclude} " + parent_dir +
        "/usermanual/use_cases/files/_FileContainingFunction_.C"
    + "\n"
    + ":language: cpp\n"
    + "```"
}}
            
This file contains a `MultiLinearFunction` function. Comparison is made with a database generated 
from random variables obeying uniform laws and output variable calculated with this database and the 
`MultiLinearFunction` function.

## Macro {{uranie}}

{{
    "```{literalinclude} " + parent_dir +
        "/roottest/uranie/doc/modeler/use_cases/" + language + "/modelerFlowrateMultiLinearRegression." 
        + extension
    + "\n"
    + ":language: " + language + "\n"
    + ":lines: " + macro[language] + "\n"
    + "```"
}}
            
The {{tds}} is loaded with the database contained in the file `flowrate_sampler_launcher_500.dat` 
with the `fileDataRead` method:

{{
    "```{literalinclude} " + parent_dir +
        "/roottest/uranie/doc/modeler/use_cases/" + language + "/modelerFlowrateMultiLinearRegression." 
        + extension 
    + "\n"
    + ":language: " + language + "\n"
    + ":lines: " + bloc1[language] + "\n"
    + "```"
}}
            
The linear regression is initialised and characteristic values are computed for each variable with 
the `estimate` method:

{{
    "```{literalinclude} " + parent_dir +
        "/roottest/uranie/doc/modeler/use_cases/" + language + "/modelerFlowrateMultiLinearRegression." 
        + extension 
    + "\n"
    + ":language: " + language + "\n"
    + ":lines: " + bloc2[language] + "\n"
    + "```"
}}

```{only} py
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.
```

The model is exported in an external file in C++ language `_FileContainingFunction_.C` where the 
function name is `MultiLinearFunction`:

{{
    "```{literalinclude} " + parent_dir +
        "/roottest/uranie/doc/modeler/use_cases/" + language + "/modelerFlowrateMultiLinearRegression." 
        + extension 
    + "\n"
    + ":language: " + language + "\n"
    + ":lines: " + bloc3[language] + "\n"
    + "```"
}}
            
A second {{tds}} is created. The previous variables then obey uniform laws and are linked as 
`TAttribute` in this new {{tds}}:

{{
    "```{literalinclude} " + parent_dir +
        "/roottest/uranie/doc/modeler/use_cases/" + language + "/modelerFlowrateMultiLinearRegression." 
        + extension 
    + "\n"
    + ":language: " + language + "\n"
    + ":lines: " + bloc4[language] + "\n"
    + "```"
}}
            
A sampling is realised with a LHS method on 1000 patterns:

{{
    "```{literalinclude} " + parent_dir +
        "/roottest/uranie/doc/modeler/use_cases/" + language + "/modelerFlowrateMultiLinearRegression." 
        + extension 
    + "\n"
    + ":language: " + language + "\n"
    + ":lines: " + bloc5[language] + "\n"
    + "```"
}}
            
The previously exported macro `_FileContainingFunction_.C` is loaded so as to perform calculation 
over the database in the second {{tds}} with the function `MultiLinearFunction`. Results are stored 
in the **ymod** variable:

{{
    "```{literalinclude} " + parent_dir +
        "/roottest/uranie/doc/modeler/use_cases/" + language + "/modelerFlowrateMultiLinearRegression." 
        + extension 
    + "\n"
    + ":language: " + language + "\n"
    + ":lines: " + bloc6[language] + "\n"
    + "```"
}}
            
## Graph

{{
    "```{figure} " + parent_dir +
        "/roottest/build/uranie/doc/modeler/use_cases/" + language 
        + "/multi_linear_regression/modelerFlowrateMultiLinearRegression.png\n"
    + ":align: center\n"
    + ":name: use_cases_modelerFlowrateMultiLinearRegression\n"
    + figure_scale + "\n"
    + "\n"
    + "Graph of the macro **\"modelerFlowrateMultiLinearRegression." + extension + "\"**" + "\n"
    + "```"
}}