partially fix documentation (#80)

pina/problem/parametric_problem.py

@@ -1,9 +1,45 @@
+"""Module for the ParametricProblem class"""
 from abc import abstractmethod
 
 from .abstract_problem import AbstractProblem
 
 
 class ParametricProblem(AbstractProblem):
+    """
+    The class for the definition of parametric problems, i.e., problems
+    with parameters among the input variables.
+
+    Here's an example of a spatial parametric ODE problem, i.e., a spatial
+    ODE problem with an additional parameter `alpha` as coefficient of the
+    derivative term.
+
+    :Example:
+        >>> from pina.problem import SpatialProblem, ParametricProblem
+        >>> from pina.operators import grad
+        >>> from pina import Condition, Span
+        >>> import torch
+
+        >>> class ParametricODE(SpatialProblem, ParametricProblem):
+
+        >>>     output_variables = ['u']
+        >>>     spatial_domain = Span({'x': [0, 1]})
+        >>>     parameter_domain = Span({'alpha': {1, 10}})
+
+        >>>     def ode_equation(input_, output_):
+        >>>         u_x = grad(output_, input_, components=['u'], d=['x'])
+        >>>         u = output_.extract(['u'])
+        >>>         alpha = input_.extract(['alpha'])
+        >>>         return alpha * u_x - u
+
+        >>>     def initial_condition(input_, output_):
+        >>>         value = 1.0
+        >>>         u = output_.extract(['u'])
+        >>>         return u - value
+
+        >>>     conditions = {
+        >>>         'x0': Condition(Span({'x': 0, 'alpha':[1, 10]}), initial_condition),
+        >>>         'D': Condition(Span({'x': [0, 1], 'alpha':[1, 10]}), ode_equation)}
+    """
 
     @abstractmethod
     def parameter_domain(self):