:orphan:

.. _Functional modeling:

Functional modeling
===================



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Univariate functions
--------------------



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    <div class="sphx-glr-thumbcontainer" tooltip="The univariate functions considered in this example can be, in some cases, orthogonal to a distribution, but this is not a necessary condition to create univariate functions. For example, Legendre polynomials are orthogonal with respect to the uniform distribution, but the monomials of the canonical polynomial basis are not necessarily orthogonal.">

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  .. image:: /auto_functional_modeling/univariate_functions/images/thumb/sphx_glr_plot_create_univariate_function_thumb.svg
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  :doc:`/auto_functional_modeling/univariate_functions/plot_create_univariate_function`

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      <div class="sphx-glr-thumbnail-title">Create univariate functions</div>
    </div>


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    </div>


Vectorial functions
-------------------



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    <div class="sphx-glr-thumbcontainer" tooltip="Create a composed function">

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  .. image:: /auto_functional_modeling/vectorial_functions/images/thumb/sphx_glr_plot_composed_function_thumb.png
    :alt:

  :doc:`/auto_functional_modeling/vectorial_functions/plot_composed_function`

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      <div class="sphx-glr-thumbnail-title">Create a composed function</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Create an aggregated function">

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  .. image:: /auto_functional_modeling/vectorial_functions/images/thumb/sphx_glr_plot_aggregated_function_thumb.png
    :alt:

  :doc:`/auto_functional_modeling/vectorial_functions/plot_aggregated_function`

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      <div class="sphx-glr-thumbnail-title">Create an aggregated function</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Create a symbolic function">

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  .. image:: /auto_functional_modeling/vectorial_functions/images/thumb/sphx_glr_plot_symbolic_function_thumb.svg
    :alt:

  :doc:`/auto_functional_modeling/vectorial_functions/plot_symbolic_function`

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      <div class="sphx-glr-thumbnail-title">Create a symbolic function</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Create a linear combination of functions">

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  .. image:: /auto_functional_modeling/vectorial_functions/images/thumb/sphx_glr_plot_linear_combination_function_thumb.png
    :alt:

  :doc:`/auto_functional_modeling/vectorial_functions/plot_linear_combination_function`

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      <div class="sphx-glr-thumbnail-title">Create a linear combination of functions</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Create a quadratic function">

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  .. image:: /auto_functional_modeling/vectorial_functions/images/thumb/sphx_glr_plot_quadratic_function_thumb.svg
    :alt:

  :doc:`/auto_functional_modeling/vectorial_functions/plot_quadratic_function`

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      <div class="sphx-glr-thumbnail-title">Create a quadratic function</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Increase the output dimension of a function">

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  .. image:: /auto_functional_modeling/vectorial_functions/images/thumb/sphx_glr_plot_functions_outputDim_thumb.png
    :alt:

  :doc:`/auto_functional_modeling/vectorial_functions/plot_functions_outputDim`

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      <div class="sphx-glr-thumbnail-title">Increase the output dimension of a function</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Create a parametric function">

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  .. image:: /auto_functional_modeling/vectorial_functions/images/thumb/sphx_glr_plot_parametric_function_thumb.png
    :alt:

  :doc:`/auto_functional_modeling/vectorial_functions/plot_parametric_function`

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      <div class="sphx-glr-thumbnail-title">Create a parametric function</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Create a Python function">

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  .. image:: /auto_functional_modeling/vectorial_functions/images/thumb/sphx_glr_plot_python_function_thumb.png
    :alt:

  :doc:`/auto_functional_modeling/vectorial_functions/plot_python_function`

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      <div class="sphx-glr-thumbnail-title">Create a Python function</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Increase the input dimension of a function">

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  .. image:: /auto_functional_modeling/vectorial_functions/images/thumb/sphx_glr_plot_functions_inputDim_thumb.png
    :alt:

  :doc:`/auto_functional_modeling/vectorial_functions/plot_functions_inputDim`

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      <div class="sphx-glr-thumbnail-title">Increase the input dimension of a function</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Defining Python and symbolic functions: a quick start introduction to functions">

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  .. image:: /auto_functional_modeling/vectorial_functions/images/thumb/sphx_glr_plot_quick_start_functions_thumb.png
    :alt:

  :doc:`/auto_functional_modeling/vectorial_functions/plot_quick_start_functions`

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      <div class="sphx-glr-thumbnail-title">Defining Python and symbolic functions: a quick start introduction to functions</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Create multivariate functions">

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  .. image:: /auto_functional_modeling/vectorial_functions/images/thumb/sphx_glr_plot_create_multivariate_function_thumb.png
    :alt:

  :doc:`/auto_functional_modeling/vectorial_functions/plot_create_multivariate_function`

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      <div class="sphx-glr-thumbnail-title">Create multivariate functions</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Get the gradient and Hessian as functions">

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  .. image:: /auto_functional_modeling/vectorial_functions/images/thumb/sphx_glr_plot_functions_grad_hess_thumb.png
    :alt:

  :doc:`/auto_functional_modeling/vectorial_functions/plot_functions_grad_hess`

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      <div class="sphx-glr-thumbnail-title">Get the gradient and Hessian as functions</div>
    </div>


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    </div>


Functional basis
----------------



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    <div class="sphx-glr-thumbcontainer" tooltip="Create a multivariate basis of functions from scalar multivariable functions">

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  .. image:: /auto_functional_modeling/functional_basis/images/thumb/sphx_glr_plot_multidimensional_basis_thumb.png
    :alt:

  :doc:`/auto_functional_modeling/functional_basis/plot_multidimensional_basis`

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      <div class="sphx-glr-thumbnail-title">Create a multivariate basis of functions from scalar multivariable functions</div>
    </div>


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    </div>


Field functions
---------------



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    <div class="sphx-glr-thumbcontainer" tooltip="Value function">

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  .. image:: /auto_functional_modeling/field_functions/images/thumb/sphx_glr_plot_value_function_thumb.png
    :alt:

  :doc:`/auto_functional_modeling/field_functions/plot_value_function`

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      <div class="sphx-glr-thumbnail-title">Value function</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Vertex value function">

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  .. image:: /auto_functional_modeling/field_functions/images/thumb/sphx_glr_plot_vertexvalue_function_thumb.png
    :alt:

  :doc:`/auto_functional_modeling/field_functions/plot_vertexvalue_function`

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      <div class="sphx-glr-thumbnail-title">Vertex value function</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Define a function with a field output: the viscous free fall example">

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  .. image:: /auto_functional_modeling/field_functions/images/thumb/sphx_glr_plot_viscous_fall_field_function_thumb.svg
    :alt:

  :doc:`/auto_functional_modeling/field_functions/plot_viscous_fall_field_function`

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      <div class="sphx-glr-thumbnail-title">Define a function with a field output: the viscous free fall example</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Define a connection function with a field output">

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  .. image:: /auto_functional_modeling/field_functions/images/thumb/sphx_glr_plot_viscous_fall_field_function_connection_thumb.svg
    :alt:

  :doc:`/auto_functional_modeling/field_functions/plot_viscous_fall_field_function_connection`

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      <div class="sphx-glr-thumbnail-title">Define a connection function with a field output</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Logistic growth model">

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  .. image:: /auto_functional_modeling/field_functions/images/thumb/sphx_glr_plot_logistic_growth_model_thumb.svg
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  :doc:`/auto_functional_modeling/field_functions/plot_logistic_growth_model`

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      <div class="sphx-glr-thumbnail-title">Logistic growth model</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Create a process sample from a sample">

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  .. image:: /auto_functional_modeling/field_functions/images/thumb/sphx_glr_plot_process_sample_thumb.svg
    :alt:

  :doc:`/auto_functional_modeling/field_functions/plot_process_sample`

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      <div class="sphx-glr-thumbnail-title">Create a process sample from a sample</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Function manipulation">

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  .. image:: /auto_functional_modeling/field_functions/images/thumb/sphx_glr_plot_function_manipulation_thumb.svg
    :alt:

  :doc:`/auto_functional_modeling/field_functions/plot_function_manipulation`

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      <div class="sphx-glr-thumbnail-title">Function manipulation</div>
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Link to an external code
------------------------



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    <div class="sphx-glr-thumbcontainer" tooltip="Link to a computer code with coupling tools">

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  .. image:: /auto_functional_modeling/link_to_an_external_code/images/thumb/sphx_glr_plot_link_computer_code_coupling_tools_thumb.png
    :alt:

  :doc:`/auto_functional_modeling/link_to_an_external_code/plot_link_computer_code_coupling_tools`

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      <div class="sphx-glr-thumbnail-title">Link to a computer code with coupling tools</div>
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    </div>


.. toctree::
   :hidden:
   :includehidden:


   /auto_functional_modeling/univariate_functions/index.rst
   /auto_functional_modeling/vectorial_functions/index.rst
   /auto_functional_modeling/functional_basis/index.rst
   /auto_functional_modeling/field_functions/index.rst
   /auto_functional_modeling/link_to_an_external_code/index.rst