Glas List: Re: [glas] arithmetic operations

From: Karl Meerbergen (Karl.Meerbergen_at_[hidden])
Date: 2005-10-28 02:23:52

Andrew Lumsdaine wrote:

>I think this would be a very dangerous path to go down.
>
>One important reason for introducing operator notation for linear  
>algebra operations is so that the program notation can match the  
>corresponding mathematics.  This is a very powerful correspondence.   
>It makes code more straightforward to write, but just as importantly  
>(or perhaps even more importantly) it makes the code more  
>straightforward to read.  By corresponding to an established language  
>of mathematics, the code itself communicates significant mathematical  
>meanings.
>
>If we start introducing non-mathematical meanings to operators, that  
>subverts in a very significant way the expressiveness of the  
>mathematical operator notation.  There may be a few more things that  
>can be expressed with operators in this case, but the clarity of  
>expression is ruined -- the reader (and writer) of the code can no  
>longer have confidence in the "language" being used -- it is no  
>longer the well established language of mathematics.
>

A computer language cannot reflect the richness of mats notation, 
otherwise we would not have this discussion.

It makes sense to use * for a product. But what does it mean for a 
vector? inner product, outer product, element wise product? And why 
prefer one to another?

To make the choice easier, we could assume that a vector is a column (as 
is always the case in linear algebra). In this case
trans(x)*y = dot product
x*trans(y) = outer product
herm(x)*y = hermitian inner product

This is probably the closest we can get to linear algebra notation.

Karl

>
>Even worse is the case where the meaning of the operators might not  
>have any fixed meaning at all.  In that case, the expression of  
>statements with operators has no fixed meaning and doesn't  
>communicate anything.
>
>I really think that for mathematical libraries, the use of  
>mathematical notation absolutely must conform to their mathematical  
>meanings.
>
>  
>