User-extendable Abstract RealMatrix implementation
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                 Key: MATH-231
                 URL: https://issues.apache.org/jira/browse/MATH-231
             Project: Commons Math
          Issue Type: New Feature
    Affects Versions: 2.1
         Environment: Any
            Reporter: Sujit Pal
            Priority: Minor


Many algorithms are described using Matrices. In some situations, the Matrices 
for applications are too large to fit into memory, so it makes sense to use 
custom implementations that are backed by a sparse map or list, or backed by 
Lucene indexes or database tables, etc. This allows the algorithm 
implementations (in the application) to be clean and mimic the algorithm 
itself, making it easy to understand and debug. 

However, the only way to make a custom implementation currently is to implement 
RealMatrix, and to implement all its methods, or to extend and override methods 
in RealMatrixImpl. The former involves a knowledge of matrix operations, which 
is not guaranteed for people who are business programmers (which may be the 
reason they are using commons-math in the first place). The latter involves 
looking at the existing code and making the overrides where needed, again 
something that is not expected from a commons-math user. A simpler way would be 
to have something generic mostly built, except the getEntry() and setEntry() 
methods which would be declared abstract and hence meant to be overriden, and 
all the other methods to be pre-built based on getEntry() and setEntry().

This would make the creation of custom matrices very flexible, and would also 
remove the burden of providing "common matrix impls" from the commons-math 
project, since clients can very simply create custom versions of their own.

I suggest the following:

<<RealMatrix.java>> <-- RealMatrixImpl
                                        <-- (AbstractRealMatrixImpl)

The SparseRealMatrixImpl I contributed in MATH-230 could be a user-defined 
custom subclass of AbstractRealMatrixImpl and not have to belong to the 
commons-math project at all. Or it could be included as an example if there is 
enough need.


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