One option is to define a 'minilanguage' for matrix manipulations, and
implement it as a new bit of syntax that you can implement with
"syntax-rules" or "syntax-case":
(matrixy (multiply (transpose A) B))
If you want something that doesn't require operations to be structured
like this syntactically to optimize them, then two more options:
* Make your matrix objects be 'lazy' about the operations. So, for
example, instead of actually performing the transpose, you represent the
input to the transpose and the fact that a transpose operation should be
applied. Then you represent that a multiply should be applied. Then,
when you finally want access actual numbers within a matrix object, you
see the sequence of transformations at once and can choose an efficient
algorithm. The user of the matrix object does not need to know that
this is happening.
* Implement a language that translates to Scheme after reasoning about
data flow.
These are off-the-cuff. I'm sure there are more ideas out there.
--
http://www.neilvandyke.org/
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