.. Copyright 2021 IRT Saint ExupĂ©ry, https://www.irt-saintexupery.com This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA. .. Contributors: :author: Matthias De Lozzo .. _analyticdiscipline: How to build an analytic discipline? ==================================== A simple :class:`.MDODiscipline` can be created using analytic formulas, e.g. :math:`y_1=2x^2` and :math:`y_2=5+3x^2z^3`, thanks to the class :class:`.AnalyticDiscipline` which is a quick alternative to model a simple analytic MDO problem! Create the dictionary of analytic outputs ***************************************** First of all, we have to define the output expressions in a dictionary where keys are output names and values are formula with :code:`string` format: .. code:: expressions = {'y_1': '2*x**2', 'y_2': '5+3*x**2+z**3'} Create and instantiate the discipline ************************************* Then, we create and instantiate the corresponding :class:`.AnalyticDiscipline` inheriting from :class:`.MDODiscipline` by means of the API function :meth:`~gemseo.api.create_discipline` with: - :code:`discipline_name="AnalyticDiscipline"`, - :code:`name="analytic"`, - :code:`expressions=expr_dict`. In practice, we write: .. code:: from gemseo.api import create_discipline disc = create_discipline("AnalyticDiscipline", name="analytic", expressions=expressions) .. note:: |g| takes care of the grammars and :meth:`!MDODiscipline._run` method generation from the :code:`expressions` argument. In the background, |g| considers that :code:`x` is a monodimensional float input parameter and :code:`y_1` and :code:`y_2` are monodimensional float output parameters. Execute the discipline ********************** Lastly, this discipline can be executed as any other: .. code:: from numpy import array input_data = {"x": array([2.0]), "z": array([3.0])} out = disc.execute(input_data) print("y_1 =", out["y_1"]) print("y_2 =", out["y_2"]) which results in: .. code:: y_1 = [ 8.] y_2 = [ 44.] About the analytic jacobian *************************** The discipline will provide analytic derivatives (Jacobian) automatically using the `sympy library `_, by means of the :meth:`!AnalyticDiscipline._compute_jacobian` method. This can be checked easily using :meth:`.MDODiscipline.check_jacobian`: .. code:: disc.check_jacobian(input_data, derr_approx=disc.FINITE_DIFFERENCES, step=1e-5, threshold=1e-3) which results in: .. code:: INFO - 10:34:33 : Jacobian: dp y_2/dp x succeeded! INFO - 10:34:33 : Jacobian: dp y_2/dp z succeeded! INFO - 10:34:33 : Jacobian: dp y_1/dp x succeeded! INFO - 10:34:33 : Jacobian: dp y_1/dp z succeeded! INFO - 10:34:33 : Linearization of MDODiscipline: AnalyticDiscipline is correct ! True