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Ublas : |
Subject: Re: [ublas] Extended/overloading ublas
From: kayhman (kayhman_at_[hidden])
Date: 2009-06-08 04:15:24
2009/6/8 saupin guillaume <guillaume.saupin_at_[hidden]>
>
>
> 2009/6/5 Paul C. Leopardi <paul.leopardi_at_[hidden]>
>
>> On Thu, 4 Jun 2009, kayhman wrote:
>> > Concerning what I'm doing, I'd like to extend uBLAS with :
>> > - an object representing an element of the Lie group SE(3), using a
>> vector
>> > of 7 doubles,
>> > - and another object representing an element of the Lie algebra
>> associated
>> > se(3) using a vector of 6 doubles.
>> >
>> > For these objects, I need to redefine the inner and outer product as
>> well
>> > as adding mapping operations log and exponential.
>> >
>> > Besides, I want to be able to use proxies for these two objects, as
>> > eventually I will maniupalte a cartesian product of Lie goup elements
>> which
>> > will be stored in a global vector. Using proxies, I'd like to map each
>> lie
>> > group element to the corresponding double sub array in the global
>> vector.
>> >
>> > And finally, for performances, I want to benefit from the template
>> > expression mecanism to eliminates temporaries.
>>
>> Hi kayhman,
>> I'm not sure if you really need inheritance here. Maybe you need to model
>> "has
>> a" rather than "is a".
>
> This may be the way to do it, but I think I'll lose the template expression
mecanism if I do that, no ?
>>
>
>>
>>
>> Besides vector addition and scalar multiplication, I'm not sure that your
>> objects share much in common with uBLAS vectors. For example, does it make
>> sense to multiply an element of SE(3) by a 7x7 matrix? Or multiply an
>> element
>> of se(3) by a 6x6 matrix?
>>
>> In GluCat ( http://glucat.sf.net ) for the matrix representation of
>> Clifford
>> algebras, I used a multivector class containing a uBLAS matrix, rather
>> than
>> inheritance, even though the Clifford operations of addition and
>> multiplication are essentially the same (actually there are algebra
>> injections involved: see "A generalized FFT for Clifford algebras",
>> Bulletin
>> of the Belgian Mathematical Society - Simon Stevin, Volume 11, Number 5,
>> 2005, pp. 663-688. MR 2130632.
>> http://www.maths.unsw.edu.au/applied/files/2004/amr04_17.pdf ). I did
>> this
>> because the matrix representation is with respect to an algebra, which in
>> Glucat is decribed by using an index set, so I needed the multivector
>> class
>> to contain an index set as well as a matrix.
>>
>> See also
>> http://www.objectmentor.com/resources/articles/lsp.pdf
>> http://www.berniecode.com/writing/inheritance/
>> Best, Paul
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>
>