.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/scalable/plot_diagonal.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_examples_scalable_plot_diagonal.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_scalable_plot_diagonal.py:


Scalable diagonal discipline
============================

Let us consider the
:class:`~gemseo.problems.sobieski.wrappers.SobieskiAerodynamics` discipline.
We want to build its :class:`.ScalableDiscipline` counterpart,
using a :class:`.ScalableDiagonalModel`

For that, we can use a 20-length :class:`.DiagonalDOE`
and test different sizes of variables or different settings
for the scalable diagonal discipline.

.. GENERATED FROM PYTHON SOURCE LINES 36-40

.. code-block:: default

    from __future__ import division, unicode_literals

    from matplotlib import pyplot as plt








.. GENERATED FROM PYTHON SOURCE LINES 41-43

Import
------

.. GENERATED FROM PYTHON SOURCE LINES 43-54

.. code-block:: default

    from gemseo.api import (
        configure_logger,
        create_discipline,
        create_scalable,
        create_scenario,
    )
    from gemseo.problems.sobieski.core import SobieskiProblem

    configure_logger()






.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 55-59

Learning dataset
----------------
The first step is to build an :class:`.AbstractFullCache` dataset
from a :class:`.DiagonalDOE`.

.. GENERATED FROM PYTHON SOURCE LINES 61-66

Instantiate the discipline
~~~~~~~~~~~~~~~~~~~~~~~~~~
For that, we instantiate the
:class:`~gemseo.problems.sobieski.wrappers.SobieskiAerodynamics` discipline
and set it up to cache all evaluations.

.. GENERATED FROM PYTHON SOURCE LINES 66-69

.. code-block:: default

    discipline = create_discipline("SobieskiAerodynamics")
    discipline.set_cache_policy(discipline.MEMORY_FULL_CACHE)








.. GENERATED FROM PYTHON SOURCE LINES 70-73

Get the input space
~~~~~~~~~~~~~~~~~~~
We also define the input space on which to sample the discipline.

.. GENERATED FROM PYTHON SOURCE LINES 73-76

.. code-block:: default

    input_space = SobieskiProblem().read_design_space()
    input_space.filter(discipline.get_input_data_names())





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none


    <gemseo.algos.design_space.DesignSpace object at 0x7fb745f00490>



.. GENERATED FROM PYTHON SOURCE LINES 77-83

Build the DOE scenario
~~~~~~~~~~~~~~~~~~~~~~
Lastly, we sample the discipline by means of a :class:`.DOEScenario`
relying on both discipline and input space.
In order to build a diagonal scalable discipline,
a :class:`.DiagonalDOE` must be used.

.. GENERATED FROM PYTHON SOURCE LINES 83-88

.. code-block:: default

    scenario = create_scenario(
        [discipline], "DisciplinaryOpt", "y_2", input_space, scenario_type="DOE"
    )
    scenario.execute({"algo": "DiagonalDOE", "n_samples": 20})





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

        INFO - 12:58:29:  
        INFO - 12:58:29: *** Start DOE Scenario execution ***
        INFO - 12:58:29: DOEScenario
        INFO - 12:58:29:    Disciplines: SobieskiAerodynamics
        INFO - 12:58:29:    MDOFormulation: DisciplinaryOpt
        INFO - 12:58:29:    Algorithm: DiagonalDOE
        INFO - 12:58:29: Optimization problem:
        INFO - 12:58:29:    Minimize: y_2(x_shared, x_2, y_32, y_12)
        INFO - 12:58:29:    With respect to: x_shared, x_2, y_32, y_12
        INFO - 12:58:29: DOE sampling:   0%|          | 0/20 [00:00<?, ?it]
        INFO - 12:58:29: DOE sampling: 100%|██████████| 20/20 [00:00<00:00, 435.93 it/sec, obj=[7.72500000e+04 1.27392070e+04 6.06395673e+00]]
        INFO - 12:58:29: Optimization result:
        INFO - 12:58:29: Objective value = 25508.372961119574
        INFO - 12:58:29: The result is feasible.
        INFO - 12:58:29: Status: None
        INFO - 12:58:29: Optimizer message: None
        INFO - 12:58:29: Number of calls to the objective function by the optimizer: 20
        INFO - 12:58:29: Design space:
        INFO - 12:58:29: +----------+-------------+-------+-------------+-------+
        INFO - 12:58:29: | name     | lower_bound | value | upper_bound | type  |
        INFO - 12:58:29: +----------+-------------+-------+-------------+-------+
        INFO - 12:58:29: | x_shared |     0.01    |  0.01 |     0.09    | float |
        INFO - 12:58:29: | x_shared |    30000    | 30000 |    60000    | float |
        INFO - 12:58:29: | x_shared |     1.4     |  1.4  |     1.8     | float |
        INFO - 12:58:29: | x_shared |     2.5     |  2.5  |     8.5     | float |
        INFO - 12:58:29: | x_shared |      40     |   40  |      70     | float |
        INFO - 12:58:29: | x_shared |     500     |  500  |     1500    | float |
        INFO - 12:58:29: | x_2      |     0.75    |  0.75 |     1.25    | float |
        INFO - 12:58:29: | y_32     |    0.235    | 0.235 |    0.795    | float |
        INFO - 12:58:29: | y_12     |    24850    | 24850 |    77250    | float |
        INFO - 12:58:29: | y_12     |     0.45    |  0.45 |     1.5     | float |
        INFO - 12:58:29: +----------+-------------+-------+-------------+-------+
        INFO - 12:58:29: *** DOE Scenario run terminated ***

    {'eval_jac': False, 'algo': 'DiagonalDOE', 'n_samples': 20}



.. GENERATED FROM PYTHON SOURCE LINES 89-91

Scalable diagonal discipline
----------------------------

.. GENERATED FROM PYTHON SOURCE LINES 93-98

Build the scalable discipline
-----------------------------
The second step is to build a :class:`.ScalableDiscipline`,
using a :class:`.ScalableDiagonalModel` and the cache of the discipline,
converted to a :class:`.Dataset`.

.. GENERATED FROM PYTHON SOURCE LINES 98-101

.. code-block:: default

    dataset = discipline.cache.export_to_dataset()
    scalable = create_scalable("ScalableDiagonalModel", dataset)








.. GENERATED FROM PYTHON SOURCE LINES 102-113

Visualize the input-output dependencies
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
We can easily access the underlying :class:`.ScalableDiagonalModel`
and plot the corresponding input-output dependency matrix
where the level of gray and the number (in [0,100]) represent
the degree of dependency between inputs and outputs.
Input are on the left while outputs are at the top.
More precisely, for a given output component located at the top of the graph,
these degrees are contributions to the output component and they add up to 1.
In other words, a degree expresses this contribution in percentage
and for a given column, the elements add up to 100.

.. GENERATED FROM PYTHON SOURCE LINES 113-115

.. code-block:: default

    scalable.scalable_model.plot_dependency(save=False, show=False)




.. image:: /examples/scalable/images/sphx_glr_plot_diagonal_001.png
    :alt: plot diagonal
    :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none


    'None'



.. GENERATED FROM PYTHON SOURCE LINES 116-120

Visualize the 1D interpolations
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
For every output, we can also visualize a spline interpolation of the output
samples over the diagonal of the input space.

.. GENERATED FROM PYTHON SOURCE LINES 120-122

.. code-block:: default

    scalable.scalable_model.plot_1d_interpolations(save=False, show=False)




.. rst-class:: sphx-glr-horizontal


    *

      .. image:: /examples/scalable/images/sphx_glr_plot_diagonal_002.png
          :alt: 1D interpolation of sdm_SobieskiAerodynamics.g_2
          :class: sphx-glr-multi-img

    *

      .. image:: /examples/scalable/images/sphx_glr_plot_diagonal_003.png
          :alt: 1D interpolation of sdm_SobieskiAerodynamics.y_2
          :class: sphx-glr-multi-img

    *

      .. image:: /examples/scalable/images/sphx_glr_plot_diagonal_004.png
          :alt: 1D interpolation of sdm_SobieskiAerodynamics.y_2
          :class: sphx-glr-multi-img

    *

      .. image:: /examples/scalable/images/sphx_glr_plot_diagonal_005.png
          :alt: 1D interpolation of sdm_SobieskiAerodynamics.y_2
          :class: sphx-glr-multi-img

    *

      .. image:: /examples/scalable/images/sphx_glr_plot_diagonal_006.png
          :alt: 1D interpolation of sdm_SobieskiAerodynamics.y_21
          :class: sphx-glr-multi-img

    *

      .. image:: /examples/scalable/images/sphx_glr_plot_diagonal_007.png
          :alt: 1D interpolation of sdm_SobieskiAerodynamics.y_23
          :class: sphx-glr-multi-img

    *

      .. image:: /examples/scalable/images/sphx_glr_plot_diagonal_008.png
          :alt: 1D interpolation of sdm_SobieskiAerodynamics.y_24
          :class: sphx-glr-multi-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none


    []



.. GENERATED FROM PYTHON SOURCE LINES 123-127

Increased problem dimension
---------------------------
We can repeat the construction of the scalable discipline for different sizes
of variables and visualize the input-output dependency matrices.

.. GENERATED FROM PYTHON SOURCE LINES 129-132

Twice as many inputs
~~~~~~~~~~~~~~~~~~~~
For example, we can increase the size of each input by a factor of 2.

.. GENERATED FROM PYTHON SOURCE LINES 132-139

.. code-block:: default

    sizes = {
        name: discipline.cache.varsizes[name] * 2
        for name in discipline.get_input_data_names()
    }
    scalable = create_scalable("ScalableDiagonalModel", dataset, sizes)
    scalable.scalable_model.plot_dependency(save=False, show=False)




.. image:: /examples/scalable/images/sphx_glr_plot_diagonal_009.png
    :alt: plot diagonal
    :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none


    'None'



.. GENERATED FROM PYTHON SOURCE LINES 140-143

Twice as many outputs
~~~~~~~~~~~~~~~~~~~~~
Or we can increase the size of each output by a factor of 2.

.. GENERATED FROM PYTHON SOURCE LINES 143-150

.. code-block:: default

    sizes = {
        name: discipline.cache.varsizes[name] * 2
        for name in discipline.get_output_data_names()
    }
    scalable = create_scalable("ScalableDiagonalModel", dataset, sizes)
    scalable.scalable_model.plot_dependency(save=False, show=False)




.. image:: /examples/scalable/images/sphx_glr_plot_diagonal_010.png
    :alt: plot diagonal
    :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none


    'None'



.. GENERATED FROM PYTHON SOURCE LINES 151-154

Twice as many variables
~~~~~~~~~~~~~~~~~~~~~~~
Or we can increase the size of each input and each output by a factor of 2.

.. GENERATED FROM PYTHON SOURCE LINES 154-160

.. code-block:: default

    names = list(discipline.get_input_data_names())
    names += list(discipline.get_output_data_names())
    sizes = {name: discipline.cache.varsizes[name] * 2 for name in names}
    scalable = create_scalable("ScalableDiagonalModel", dataset, sizes)
    scalable.scalable_model.plot_dependency(save=False, show=False)




.. image:: /examples/scalable/images/sphx_glr_plot_diagonal_011.png
    :alt: plot diagonal
    :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none


    'None'



.. GENERATED FROM PYTHON SOURCE LINES 161-174

Binary IO dependencies
----------------------
By default, any output component depends on any input component
with a random level.
We can also consider sparser input-output dependency
by means of binary input-output dependency matrices.
For that, we have to set the value of the fill factor
which represents the part of connection between inputs and outputs.
Then, a connection is represented by a black square
while an absence of connection is presented by a white one.
When the fill factor is equal to 1, any input is connected to any output.
Conversely, when the fill factor is equal to 0,
there is not a single connection between inputs and outputs.

.. GENERATED FROM PYTHON SOURCE LINES 176-178

Fill factor = 0.2
~~~~~~~~~~~~~~~~~

.. GENERATED FROM PYTHON SOURCE LINES 178-181

.. code-block:: default

    scalable = create_scalable("ScalableDiagonalModel", dataset, sizes, fill_factor=0.2)
    scalable.scalable_model.plot_dependency(save=False, show=False)




.. image:: /examples/scalable/images/sphx_glr_plot_diagonal_012.png
    :alt: plot diagonal
    :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none


    'None'



.. GENERATED FROM PYTHON SOURCE LINES 182-184

Fill factor = 0.5
~~~~~~~~~~~~~~~~~

.. GENERATED FROM PYTHON SOURCE LINES 184-187

.. code-block:: default

    scalable = create_scalable("ScalableDiagonalModel", dataset, sizes, fill_factor=0.5)
    scalable.scalable_model.plot_dependency(save=False, show=False)




.. image:: /examples/scalable/images/sphx_glr_plot_diagonal_013.png
    :alt: plot diagonal
    :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none


    'None'



.. GENERATED FROM PYTHON SOURCE LINES 188-190

Fill factor = 0.8
~~~~~~~~~~~~~~~~~

.. GENERATED FROM PYTHON SOURCE LINES 190-193

.. code-block:: default

    scalable = create_scalable("ScalableDiagonalModel", dataset, sizes, fill_factor=0.8)
    scalable.scalable_model.plot_dependency(save=False, show=False)




.. image:: /examples/scalable/images/sphx_glr_plot_diagonal_014.png
    :alt: plot diagonal
    :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none


    'None'



.. GENERATED FROM PYTHON SOURCE LINES 194-196

Heterogeneous dependencies
--------------------------

.. GENERATED FROM PYTHON SOURCE LINES 196-201

.. code-block:: default

    scalable = create_scalable(
        "ScalableDiagonalModel", dataset, sizes, fill_factor={"y_2": 0.2}
    )
    scalable.scalable_model.plot_dependency(save=False, show=False)




.. image:: /examples/scalable/images/sphx_glr_plot_diagonal_015.png
    :alt: plot diagonal
    :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none


    'None'



.. GENERATED FROM PYTHON SOURCE LINES 202-204

Group dependencies
------------------

.. GENERATED FROM PYTHON SOURCE LINES 204-210

.. code-block:: default

    scalable = create_scalable(
        "ScalableDiagonalModel", dataset, sizes, group_dep={"y_2": ["x_shared"]}
    )
    scalable.scalable_model.plot_dependency(save=False, show=False)
    # Workaround for HTML rendering, instead of ``show=True``
    plt.show()



.. image:: /examples/scalable/images/sphx_glr_plot_diagonal_016.png
    :alt: plot diagonal
    :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  3.535 seconds)


.. _sphx_glr_download_examples_scalable_plot_diagonal.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download sphx-glr-download-python

     :download:`Download Python source code: plot_diagonal.py <plot_diagonal.py>`



  .. container:: sphx-glr-download sphx-glr-download-jupyter

     :download:`Download Jupyter notebook: plot_diagonal.ipynb <plot_diagonal.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_