Re: [ublas] permutation matrix type

From: Dan Elliott (c_reply_to_at_[hidden])
Date: 2006-06-30 18:46:08

Thanks for the reply Gunter.  Let's start simply with the three questions listed at the bottom of this message...
>>>>> "Gunter" == Gunter Winkler <guwi17_at_[hidden]> writes:

    Gunter> On Wednesday 17 May 2006 05:26, Dan Elliott wrote:

    >> I see that the lu.hpp file has a data type permutation_matrix
    >> which inherits from the vector type.  However, I would like to
    >> discuss the merits of creating a matrix permutation matrix type
    >> that would behave more like a matrix (e.g. matrix operators for
    >> right and left had operations).  Permutation matrices could
    >> even fall under a larger family of transformation matrices!

    Gunter> It would be very convenient to have a transformation
    Gunter> matrix that behaves like a matrix. But for the simple task
    Gunter> of solving linear equations the current permutation_matrix
    Gunter> is sufficient. The permutation_matrix class does not store
    Gunter> the mapping (old index) -> (new index) but a list of swap
    Gunter> operations needed for inplace reordering of vectors (or
    Gunter> matrices). Therefore we should keep this class - maybe
    Gunter> with a better name.

I am interested in a permutation matrix class that could be a specific version of a larger class of transformation matrices.  For now, I am mostly concerned with permutation matrices.

In code that uses the class already contained within the lu.hpp file, I have been able to, at times, take advantage of the data representation you describe above.  Other times, I use a more traditional representation of permutation matrices.  So with respect to permutation matrices, and other highly-specialized types of transformation matrices, I believe that the underlying representation should be highly flexible to suit the particular needs of the user.

    >> Operations of other types against this type could have
    >> specialized algorithms which take advantage of their particular
    >> structure.  For example, if T were a permutation matrix, and S
    >> were diagonal, the operation transpose(T) * S * T has a
    >> predictable structure as it goes from left to right.

    Gunter> This would be a very interesting extension because
    Gunter> symmetric products are repeatedly requested on this
    Gunter> list. I think a new matrix_ternary_expression class can
    Gunter> cover all products of this type and can be dispatched to
    Gunter> specialized algorithms. 

I suppose the discussion of the implementation of such an expression class is contingent upon the answer to the question below.

    Gunter> However, I am not sure if this
    Gunter> should be part of ublas or at a higher level of
    Gunter> abstraction (e.g. some glas frontend).

OK, do matrix_ternary_expressions belong in uBLAS?  
What does your question imply about algorithms like LU and some of the other higher-level methods within uBLAS like prod, etc?  
Where do you all plan on drawing the line on the functionality of the uBLAS library?

Thanks.

-- 
Dan