Skip to content

Commit

Permalink
Doc: Fix reference
Browse files Browse the repository at this point in the history
  • Loading branch information
jschueller committed Oct 28, 2024
1 parent a12fddd commit 40db6b3
Showing 1 changed file with 18 additions and 13 deletions.
31 changes: 18 additions & 13 deletions python/doc/user_manual/user_manual.rst
Original file line number Diff line number Diff line change
Expand Up @@ -11,24 +11,29 @@ The method focuses on the notion of elementary effects and is known to require v
of the influent factors.

Roughly speeking, the method relies on One At Time designs (OAT) and acts as follows:
- The input design space is discretized (in a p-levels grid), of step :math:`\Delta`;
- We randomly choose a starting `point` in this grid;
- We randomly select a direction and thus we get the new point,
- We iterate the previous process on the :math:`p-1` remaining directions to get a full `path`, where :math:`p` is the input dimension.
Note that :math:`p+1` experiments are needed to define this `path`. (See hereafter an example in case :math:`p=2`)

.. image:: scheme-path-morris.png
- The input design space is discretized (in a p-levels grid), of step :math:`\Delta`;
- We randomly choose a starting `point` in this grid;
- We randomly select a direction and thus we get the new point,
- We iterate the previous process on the :math:`p-1` remaining directions to get a full `path`, where :math:`p` is the input dimension.
Note that :math:`p+1` experiments are needed to define this `path`. (See hereafter an example in case :math:`p=2`)

.. image:: scheme-path-morris.png
:height: 350 px
:width: 600 px
:align: center

- From this path (:math:`X_p`), we compute the response answer :math:`Y_p=f(X_p)`;
- It is easy to see that the difference between two consecutive points of this `path` represents the elementary effect relative to the choosen direction. Indeed
we compute both :math:`dX_p` and :math:`dY_p` where :math:`dX_p` represents the difference between two consecutive elements of :math:`X_p`. We deduce elementary
effects from these vectors of size :math:`p` by solving the linear system :math:`X_p\ ee = Y_p` (:math:`ee` are the elementary effects)
- We iterate the steps 2-5 :math:`r` times in order to get `r` replicates of the elementary effects. Here after an illustration in case :math:`p=2, r=5`.

.. image:: scheme-path-examples.png
- From this path (:math:`X_p`), we compute the response answer :math:`Y_p=f(X_p)`;
- It is easy to see that the difference between two consecutive points of this `path` represents the elementary effect
relative to the choosen direction.
Indeed we compute both :math:`dX_p` and :math:`dY_p` where :math:`dX_p` represents the difference between
two consecutive elements of :math:`X_p`.
We deduce elementary effects from these vectors of size :math:`p` by solving the linear system
:math:`X_p\ ee = Y_p` (:math:`ee` are the elementary effects)
- We iterate the steps 2-5 :math:`r` times in order to get `r` replicates of the elementary effects.
Here after an illustration in case :math:`p=2, r=5`.

.. image:: scheme-path-examples.png
:height: 350 px
:width: 400 px
:align: center
Expand Down

0 comments on commit 40db6b3

Please sign in to comment.