I could think of the following extension to RealVector:
boolean isSparse();
void setSparse(boolean sparse);
double calcSparse(double sparseThresholdInPercent);
Explanation:
Default value from isSparse on ArrayRealvector is false and on
OpenMapRealvector is true (set in constructor).
setSparse allows the developer to set a vector/matrix in a known state
(densesparse).
calcSparse iterates internally over all entries(ArrayRealVector) or just
reads the value (OpenMapRealVector). If the fillstate is bigger than
sparseThresholdInPercent the field sparse will be set to false otherwise
to true. The actual fillstate will be returned.
SparseIterator of ArrayRealvector returns only entries != 0.
If anyone is interested in a draft implementation I can do the work and
add a patch the JIRA MATH628 (next week).
Am Mittwoch, den 17.08.2011, 16:39 0700 schrieb Ted Dunning:
> On Wed, Aug 17, 2011 at 4:24 PM, Greg Sterijevski <gsterijevski@gmail.com>wrote:
>
> > On symmetrics, diagonal, banded and so on, I disagreeas I have made clear
> > in the past. In the case of White standard errors or panel regressions, you
> > typically have long strings of multiplication by diagonals and symmetrics,
> > sandwich products and so forth. There are enough of these types of
> > operations that a math/stat library should support these forms of matrices.
> > isSparse() will not cut it. A symmetric matrix is typically NOT sparse, it
> > is typically dense in these cases. More importantly, the number of
> > operations you save by explicitly recognizing the special structure is not
> > insignificant.
> >
>
> I agree pretty much for the symmetric case. The savings for banded matrices
> is surprisingly small and you can have all of those savings as a left
> operand. It is the right operand where simple sparsity accounts for almost
> everything.
>
> >
> > > For banded arrays, the economies available beyond simple sparse
> > algorithms
> > > are even more limited.
> > >
> > >
> > I am confused, Ted, since when I suggested that some of the multiplication
> > issues could solved by method overloading, you thought it would not work.
> > Probably a miscommunication on my part.
> >
>
> No. What I mean is that when a sparse matrix is the right operand and not
> subject overloading due to dynamic typing, you get most of the advantages of
> the fancy optimizations without any need for anything more than isSparse and
> a sparse iterator. You don't get all of the benefit, but you do get most of
> it and you get it for a wide variety of left operands.
>
>
> > > Symmetric and triangular matrices also have special properties but it is
> > > hard to decide what is really important there. Many of the special
> > > operations for these kinds of matrix are subject to solving by overloads
> > > instead of indicators since we aren't dealing with binary operations.
> > For
> > > example, left and right inverse multiplication with triangular matrices
> > is
> > > handled by normal single dispatch and qualifying an argument for real
> > > Cholesky decomposition is specific to the Cholesky decomposition itself.
> > >
> > >
> > While on the discussion of extending RealMatrix in any direction, I would
> > humbly offer that the objects are too complex. Pardon this foolish
> > question,
> > but what are the uses for the methods " double
> > walkInRowOrder(RealMatrixChangingVisitor visitor)" When I think of having
> > to
> > fill in all those methods for any extension, my head spins.
> >
>
> Exactly. I think that you shouldn't need that. The abstract super class
> should have a moderately fancy operation that is limited to handling
> generically sparse and dense matrices reasonably well and dense x dense
> cases really well. The writer of a new matrix type should not need to know
> about that at all.
>
> What I was suggesting is that if you have a leftInverseMultiply method that
> solves for x in the system Ax = b, then that method knows the type of A
> because the natural method call is A.leftInverseMultiply(b). Thus, if A has
> special structure, you get what you need from normal method dispatch.
>
> It is the cases like A.times(b) or A.plus(b) that will be best supported by
> generic sparsity support in the abstract class.

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