equation class, fix minor bugs, diff domain (#89)

* equation class
* difference domain
* dummy dataloader
* writer class
* refactoring and minor fix

pina/equation/equation.py

@@ -0,0 +1,10 @@
+""" Module """
+from .equation_interface import EquationInterface
+
+class Equation(EquationInterface):
+
+    def __init__(self, equation):
+        self.__equation = equation
+
+    def residual(self, input_, output_):
+        return self.__equation(input_, output_)

pina/equation/equation_factory.py

@@ -0,0 +1,37 @@
+""" Module """
+from .equation import Equation
+from ..operators import grad, div, nabla
+
+
+class FixedValue(Equation):
+    
+    def __init__(self, value, components=None):
+        def equation(input_, output_):
+            if components is None:
+                return output_ - value
+            return output_.extract(components) - value 
+        super().__init__(equation)
+
+
+class FixedGradient(Equation):
+
+    def __init__(self, value, components=None, d=None):
+        def equation(input_, output_):
+            return grad(output_, input_, components=components, d=d) - value
+        super().__init__(equation)
+
+
+class FixedFlux(Equation):
+
+    def __init__(self, value, components=None, d=None):
+        def equation(input_, output_):
+            return div(output_, input_, components=components, d=d) - value
+        super().__init__(equation)
+
+
+class Laplace(Equation):
+
+    def __init__(self, components=None, d=None):
+        def equation(input_, output_):
+            return nabla(output_, input_, components=components, d=d)
+        super().__init__(equation)

pina/equation/equation_interface.py

@@ -0,0 +1,13 @@
+""" Module for EquationInterface class """
+from abc import ABCMeta, abstractmethod
+
+
+class EquationInterface(metaclass=ABCMeta):
+    """
+    The abstract `AbstractProblem` class. All the class defining a PINA Problem
+    should be inheritied from this class.
+
+    In the definition of a PINA problem, the fundamental elements are:
+    the output variables, the condition(s), and the domain(s) where the
+    conditions are applied.
+    """

pina/equation/system_equation.py

@@ -0,0 +1,24 @@
+""" Module """
+import torch
+from .equation import Equation
+
+class SystemEquation(Equation):
+
+    def __init__(self, list_equation):
+        if not isinstance(list_equation, list):
+            raise TypeError('list_equation must be a list of functions')
+
+        self.equations = []
+        for i, equation in enumerate(list_equation):
+            if not callable(equation):
+                raise TypeError('list_equation must be a list of functions')
+            
+            self.equations.append(Equation(equation))
+
+    def residual(self, input_, output_):
+        return torch.mean(
+            torch.stack([
+                equation.residual(input_, output_)
+                for equation in self.equations
+            ]),
+            dim=0)