---
myst:
    substitutions:
        macro:
            python: 1-5,11-24,29-77
            cpp: 6-8,11-22,30-78
        bloc1:
            python: 30-31
            cpp: 30-32
        bloc2:
            python: 34,36
            cpp: 35,37
        bloc3:
            python: 39-44
            cpp: 39-40,42-45
        console:
            python: 2-6,34-54
            cpp: 5-9,22-42
---
# Macro "**modelerFlowratePolynChaosIntegration.{{extension}}**"

## Objective

The objective of this macro is to build a polynomial chaos expansion in order to get a surrogate model 
along with a global sensitivity interpretation for the `flowrate` function, whose purpose and 
behaviour have been already introduced in [](#launcher_introduction_simple_case_problem). The method 
used here is the regression one, as discussed below.

## Macro {{uranie}}

{{
    "```{literalinclude} " + parent_dir +
        "/roottest/uranie/doc/modeler/use_cases/" + language + "/modelerFlowratePolynChaosIntegration." 
        + extension
    + "\n"
    + ":language: " + language + "\n"
    + ":lines: " + macro[language] + "\n"
    + "```"
}}
            
The first part is just creating a {{tds}} and providing the attributes needed to define the problem. 
From there, a `TNisp` object is created, providing the dataserver that specifies the inputs. This 
class is used to generate the sample (Petras being a {{doe}} dedicated to integration problem).

{{
    "```{literalinclude} " + parent_dir +
        "/roottest/uranie/doc/modeler/use_cases/" + language + "/modelerFlowratePolynChaosIntegration." 
        + extension 
    + "\n"
    + ":language: " + language + "\n"
    + ":lines: " + bloc1[language] + "\n"
    + "```"
}}
            
The function is launched through a `TLauncherFunction` instance in order to get the output values 
that will be needed to train the surrogate model.

{{
    "```{literalinclude} " + parent_dir +
        "/roottest/uranie/doc/modeler/use_cases/" + language + "/modelerFlowratePolynChaosIntegration." 
        + extension 
    + "\n"
    + ":language: " + language + "\n"
    + ":lines: " + bloc2[language] + "\n"
    + "```"
}}
            
Finally, a `TPolynomialChaos` instance is created and the computation of the coefficients is 
performed by requesting a truncature on the resulting degree of the polynomial expansion (set to 4) 
and the use of a regression method.

{{
    "```{literalinclude} " + parent_dir +
        "/roottest/uranie/doc/modeler/use_cases/" + language + "/modelerFlowratePolynChaosIntegration." 
        + extension 
    + "\n"
    + ":language: " + language + "\n"
    + ":lines: " + bloc3[language] + "\n"
    + "```"
}}
            
The rest of the code is showing how to access the resulting sensitivity indices either one-by-one, 
or ordered up to a chosen threshold of the output variance.

## Console

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