Remove methods from RealMatrix Interface
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Key: MATH-608
URL: https://issues.apache.org/jira/browse/MATH-608
Project: Commons Math
Issue Type: Improvement
Affects Versions: 3.0
Environment: Java
Reporter: greg sterijevski
Priority: Minor
The RealMatrix interface describes several methods which take a RealMatrix and
yield a RealMatrix return. They are:
RealMatrix multiply(RealMatrix m);
RealMatrix preMultiply(RealMatrix m);
RealMatrix power(final int p);
RealMatrix add(RealMatrix m)
RealMatrix subtract(RealMatrix m)
There is nothing inherently wrong in making all subclasses of RealMatrix
implement these methods. However, as the number of subclasses of RealMatrix
increases, the complexity of these methods will also increase. I think these
methods should be part of a separate class of 'operators' which handle matrix
multiplication, addition, subtraction and exponentiation.
Say for example, I implement SymmetricRealMatrix. I would like to store the
data of a real symmetric in compressed form, so that I only consume (nrow +
1)*nrow /2 space in memory. When it comes time to implement multiply (for
example), I must test to see if the RealMatrix given in the argument is also of
Type SymmetricRealMatrix, since that will affect the algorithm I use to do the
multiplication. I could access each element of the argument matrix via its
getter, but efficiency will suffer. One can think of cases where we might have
a DiagonalRealMatrix times a DiagonRealMatrix. One would not want to store the
resultant diagonal in a general matrix storage. Keeping track of all of the
permutations of Symmetrics, Diagonals,..., and their resultants inside of the
body of a function makes for very brittle code. Furthermore, anytime a new type
of matrix is defined all matrix multiplication routines would have to be
updated.
There are special types of operations which result in particular matrix
patterns. A matrix times its transpose is itself a symmetric. A general matrix
sandwiched between another general matrix and its transpose is a symmetric.
Cholesky decompositions form upper and lower triangular matrices. These are
common enough occurrences in statistical techniques that it makes sense to put
them in their own class (perhaps as static methods). It would keep the contract
of the RealMatrix classes very simple. The ReaMatrix would be nothing more than:
1. Marker (is the matrix General, Symmetric, Banded, Diagonal,
UpperTriangular..)
2. Opaque data store (except for the operator classes, no one would need to
know how the data is actually stored).
3. Indexing scheme.
The reason I bring this up, is that I am attempting to write a
SymmetricRealMatrix class to support variance-covariance matrices. I noticed
that there are relatively few subclasses of RealMatrix. While it would be easy
to hack it up for the handful of implementations that exist, that would
probably create more problems as the number of types of matrices increases.
Thank you,
-Greg
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