Re: [boost] different matrix library?

Subject: Re: [boost] different matrix library?
From: Edward Grace (ej.grace_at_[hidden])
Date: 2009-08-15 05:40:23

On 15 Aug 2009, at 07:28, joel wrote:

> Edward Grace wrote:
>> Err - surely the point of overloading is to assign meaningful context
>> specific behaviour to the same operator, so.
>>
>>  unsigned a,b,c; c = a ^ b; // ^ => XOR makes sense.
>>
>>  pseudovector<3> c;
>>  vector<3> a,b;  c = a ^ b;     // ^ => Wedge product makes sense XOR
>> does not.
>>
> Well, except there is use case in computer vision or machien  
> learning in
> which you have large matrix of integer on which you apply bitwise
> operation before feeding to some solver. ^ is clearly 'elementwise  
> xor'
> in this context.

Hmm, is the 'vector' and 'matrix' paradime you have in mind in the  
same manner as MATLAB?  There they seem to be two-faced, they are  
mathematical vectors and matricies but also just collections of values.

Perhaps there needs to be a reasonable distinction between element  
wise operations and global operations on the object, for instance all  
the different types of product

  - Matrix product    (* in MATLAB)
  - Hadamard product  (.* in MATLAB)
  - Kronecker product (kron(A,B) in MATLAB)

  - Tensor product    (tprod MATLAB Mex http://www.mathworks.com/ 
matlabcentral/fileexchange/16275)

> so wedge_product is a better alternative.

Fair enough...

>> If, for example, b and c were pseudovectors then s would be a (true)
>> scalar and could be assigned to the concrete type double.  This is
>> where carrying along some (meta) information concerning the
>> transformation rules of these different entities would be both tricky
>> and crucial.
> In NT2 matrix of size(1,1) are castable to scalar and such operations
> works flawlessly.

Hmm, on second thoughts distinguishing between a pseudo<vector/ 
scalar> and vector/scalar probably doesn't matter for any practical  
purposes.

-ed