SumFunction, SubsetSumFunction, BlockFunction

[epapoutsellis]

In the cil directory there is an implementation of the SubsetSumFunction which behave similar to the BlockFunction but they are not the same.

The SubsetSumFunction is

$$f(x) = \sum_{i=1}^{n}f_{i}(x)$$ where $f_{i}$ are Functions and n is the number of subsets

The BlockFunction is

$$f(x) = f(x_{1}, x_{2}, x_{3}, \cdots, x_{n} ) = \sum_{i=1}^{n}f_{i}(x_{i})$$

1. The __call__ method is similar to both Functions. However, in the BlockFunction a BlockDataContainer is expected. In cases where the BlockFunction is used we have different domain in $f_{1}$ and a different domain in $f_{2}$.
2. There are no proximal or proximal_conjugate methods in SubsetSumFunction. SubsetSumFunction which inherits from SumFunction has no analytical formulas to compute the proximal.
3. The gradient method is similar to the __call__ method. However, we have again the difference between a DataContainer for the first class and a BlockDataContainer for the second class.