partially fix documentation (#80)

pina/problem/timedep_problem.py

@@ -1,14 +1,62 @@
+"""Module for the TimeDependentProblem class"""
 from abc import abstractmethod
 
 from .abstract_problem import AbstractProblem
 
 
 class TimeDependentProblem(AbstractProblem):
+    """
+    The class for the definition of time-dependent problems, i.e., for problems
+    depending on time.
+
+    Here's an example of a 1D wave problem.
+
+    :Example:
+        >>> from pina.problem import SpatialProblem, TimeDependentProblem
+        >>> from pina.operators import grad, nabla
+        >>> from pina import Condition, Span
+        >>> import torch
+
+        >>> class Wave(TimeDependentSpatialProblem):
+
+        >>>     output_variables = ['u']
+        >>>     spatial_domain = Span({'x': [0, 3]})
+        >>>     temporal_domain = Span({'t': [0, 1]})
+
+        >>>     def wave_equation(input_, output_):
+        >>>         u_t = grad(output_, input_, components=['u'], d=['t'])
+        >>>         u_tt = grad(u_t, input_, components=['dudt'], d=['t'])
+        >>>         nabla_u = nabla(output_, input_, components=['u'], d=['x'])
+        >>>         return nabla_u - u_tt
+
+        >>>     def nil_dirichlet(input_, output_):
+        >>>         value = 0.0
+        >>>         return output_.extract(['u']) - value
+
+        >>>     def initial_condition(input_, output_):
+        >>>         u_expected = (-3*torch.sin(2*torch.pi*input_.extract(['x']))
+        >>>             + 5*torch.sin(8/3*torch.pi*input_.extract(['x'])))
+        >>>         u = output_.extract(['u'])
+        >>>         return u - u_expected
+
+        >>>     conditions = {
+        >>>         't0': Condition(Span({'x': [0, 3], 't':0}), initial_condition),
+        >>>         'gamma1': Condition(Span({'x':0, 't':[0, 1]}), nil_dirichlet),
+        >>>         'gamma2': Condition(Span({'x':3, 't':[0, 1]}), nil_dirichlet),
+        >>>         'D': Condition(Span({'x': [0, 3], 't':[0, 1]}), wave_equation)}
+
+    """
 
     @abstractmethod
     def temporal_domain(self):
+        """
+        The temporal domain of the problem.
+        """
         pass
 
     @property
     def temporal_variable(self):
+        """
+        The time variable of the problem.
+        """
         return self.temporal_domain.variables