Create a discipline from a Python function

There is a simplified and straightforward way of integrating a discipline from a Python function that:

• returns variables, e.g. return x or return x, y, but no expression like return a+b or return a+b, y,

• must have a default value per argument if the AutoPyDiscipline is used by an MDA (deriving from BaseMDA), as in the case of MDF and BiLevel formulations.

from __future__ import annotations

from numpy import array

from gemseo import create_discipline

In this example, we will illustrate this feature using the Python function:

def f(x, y=0.0):
    """A simple Python function taking float numbers and returning a float number."""
    z = x + 2 * y
    return z

Warning

Note that the Python function must return one or more variables. The following Python function would not be suitable as it returns an expression instead of a variable:

def g(x, y=0.):
    """A simple Python function returning an expression."""
    return x + 2*y

Note

Note also that by default, the arguments and the returned variables of the Python function are supposed to be either float numbers or NumPy arrays with dimensions greater than 1. At the end of the example, we will see how to use other types.

Then, we can consider the AutoPyDiscipline class to wrap this Python function into a Discipline. For that, we can use the create_discipline() high-level function with the string "AutoPyDiscipline" as first argument:

discipline = create_discipline("AutoPyDiscipline", py_func=f)

WARNING - 16:15:06: The Args section is missing.

The input variables of the discipline are the arguments of the Python function f:

discipline.io.input_grammar.names

KeysView(Grammar name: f_discipline_input
   Required elements:
      x:
         Type: array
         Items:
            Type: number
      y:
         Type: array
         Items:
            Type: number
   Optional elements:)

the output variables of the discipline are the variables returned by f:

discipline.io.output_grammar.names

KeysView(Grammar name: f_discipline_output
   Required elements:
      z:
         Type: array
         Items:
            Type: number
   Optional elements:)

and the default input values of the discipline are the default values of the arguments of f:

discipline.io.input_grammar.defaults

{'y': array([0.])}

Note

The argument x of the Python function f shall have a default value when the discipline is used by an MDA (deriving from BaseMDA), as in the case of MDF and BiLevel formulations, in presence of strong couplings. This is not the case in this example.

Execute the discipline

Then, we can execute this discipline easily, either considering default input values:

discipline.execute({"x": array([1.0])})

{'x': array([1.]), 'y': array([0.]), 'z': array([1.])}

or custom ones:

discipline.execute({"x": array([1.0]), "y": array([-3.2])})

{'x': array([1.]), 'y': array([-3.2]), 'z': array([-5.4])}

Warning

You may have noticed that the input data are passed to the AutoPyDiscipline as NumPy arrays even if the Python function f is expecting float numbers.

Define the Jacobian function

Here is an example of a Python function returning the Jacobian matrix as a 2D NumPy array:

def df(x, y):
    """Function returning the Jacobian of z=f(x,y)"""
    return array([[1.0, 2.0]])

We can create a new AutoPyDiscipline from f and df:

discipline = create_discipline("AutoPyDiscipline", py_func=f, py_jac=df)

WARNING - 16:15:06: The Args section is missing.

and compute its Jacobian at {"x": array([1.0]), "y": array([0.0])}:

discipline.linearize(input_data={"x": array([1.0])}, compute_all_jacobians=True)
discipline.jac

{'z': {'x': array([[1.]]), 'y': array([[2.]])}}

Use custom types

By default, the AutoPyDiscipline assumes that the arguments and the returned variables of the Python function are either float numbers or NumPy arrays with dimensions greater than 1. This behaviour can be changed in two different ways.

NumPy arrays

We can force AutoPyDiscipline to consider all arguments and variables as NumPy arrays by setting the option use_arrays to True, as illustrated here:

def copy_array(a):
    a_copy = a.copy()
    return a_copy


discipline = create_discipline("AutoPyDiscipline", py_func=copy_array, use_arrays=True)
discipline.execute({"a": array([1.0])})

{'a': array([1.]), 'a_copy': array([1.])}

User types

We can also define specific types for each argument and return variable.

Warning

If you forget to annotate an argument or a return variable, all the types you have specified will be ignored.

As a very simple example, we can consider a Python function which replicates a string n times:

def replicate_string(string: str = "a", n: int = 3) -> str:
    final_string = string * n
    return final_string

Then, we create the discipline:

discipline = create_discipline("AutoPyDiscipline", py_func=replicate_string)

execute it with its default input values:

discipline.execute()

{'string': 'a', 'n': 3, 'final_string': 'aaa'}

and with custom ones:

discipline.execute({"string": "ab", "n": 5})

{'string': 'ab', 'n': 5, 'final_string': 'ababababab'}