Re: [boost] Re: matrix library ?

From: Dave Steffen (steffend_at_[hidden])
Date: 2001-03-12 20:32:56

Howard Hinnant writes:
 > >It's not crazy to imagine *inner* and *outer*. Of course we might
 > >need to use 2 separate namespaces for the different defaults of
 > >plain operator* ;-(.
 > 
 > This is coming completely out of the blue, and I don't yet know how
 > to implement it.  But terms like *inner* and *outer* can be
 > limiting.  Tensor notation can be very liberating.  It would be
 > cool if we could do something like:
 > 
 > TensorIndex i, j, k, l;
 > 
 > A[i][j][l] = B[i][k] * C[k][j] * D[k][l] * E[k];
 > 
 > Probably just a pipe dream...

 Not at all - this is more or less how Blitz++ does it, although the
 syntax isn't quite as clean. It looks something like 

 A = sum(B(i,k) * C(k,j), k); // A_ij = B_ik * C_jk 

 Yes, it would be nice if your example generated code that only had
 one loop (summing on k) instead of 4; but this is exactly the kind of
 problem that (AFAIK) Blitz++ is trying to solve. 

 While it'd be really nice to implement full-blown tensor notation, I
 suspect that 

         A) most people really only use vectors and matrices, so we
            don't really need higher-rank tensors right away;

         B) most people really just need inner and outer products, so
            if we can get those right, we're in reasonably good shape;

         C) most people need _either_ inner _or_ outer products in
            a given project; that is, the number of programming tasks
            requiring _both_ inner _and_ outer products is fairly
            small.

 I also suspect that deciding whether operator*() implements an inner
 or outer product will generate a lot of heat, and either way people
 won't be happy.  It would be nice to allow both; there are several
 mechanisms that might do the trick.

 So: I'd restrict our efforts to first and second order tensors
 (i.e. vectors and matrices), and settle for writing 

 A = B * C * D;

 for the product of three matrices.

--------------------------------------------------------------------------
Dave Steffen                      Wave after wave will flow with the tide
Dept. of Physics                    And bury the world as it does
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