Note

Click here to download the full example code

# Correlations¶

In this example, we illustrate the use of the `Correlations`

plot
on the Sobieski’s SSBJ problem.

```
from __future__ import absolute_import, division, print_function, unicode_literals
from future import standard_library
```

## Import¶

The first step is to import some functions from the API and a method to get the design space.

```
from gemseo.api import configure_logger, create_discipline, create_scenario
from gemseo.problems.sobieski.core import SobieskiProblem
configure_logger()
standard_library.install_aliases()
```

## Create disciplines¶

Then, we instantiate the disciplines of the Sobieski’s SSBJ problem: Propulsion, Aerodynamics, Structure and Mission

```
disciplines = create_discipline(
[
"SobieskiPropulsion",
"SobieskiAerodynamics",
"SobieskiStructure",
"SobieskiMission",
]
)
```

## Create design space¶

We also read the design space from the `SobieskiProblem`

.

```
design_space = SobieskiProblem().read_design_space()
```

## Create and execute scenario¶

The next step is to build a MDO scenario in order to maximize the range, encoded ‘y_4’, with respect to the design parameters, while satisfying the inequality constraints ‘g_1’, ‘g_2’ and ‘g_3’. We can use the MDF formulation, the SLSQP optimization algorithm and a maximum number of iterations equal to 100.

```
scenario = create_scenario(
disciplines,
formulation="MDF",
objective_name="y_4",
maximize_objective=True,
design_space=design_space,
)
scenario.set_differentiation_method("user")
for constraint in ["g_1", "g_2", "g_3"]:
scenario.add_constraint(constraint, "ineq")
scenario.execute({"algo": "SLSQP", "max_iter": 10})
```

Out:

```
{'algo': 'SLSQP', 'max_iter': 10}
```

## Post-process scenario¶

Lastly, we post-process the scenario by means of the `Correlations`

plot which provides scatter plots of correlated variables among design
variables, outputs functions and constraints any of the constraint or
objective functions w.r.t. optimization iterations or sampling snapshots.
This method requires the list of functions names to plot.

```
scenario.post_process("Correlations", save=False, show=True)
```

Out:

```
<gemseo.post.correlations.Correlations object at 0x7fc298a53dc0>
```

**Total running time of the script:** ( 0 minutes 2.063 seconds)