Vectors and matrices

[Andrei Alexandrescu]

Lars Kyllingstad wrote:
> I am writing a D library based some of the stuff in SLATEC, and I've 
> come to a point where I need to decide on a way to manipulate vectors 
> and matrices. To that end, I have some ideas and questions I would like 
> comments on from the community.
> 
> Ideally, I want to restrict the user as little as possible, so I'm 
> writing heavily templated code in which one can use both library-defined 
> vector/matrix types and built-in arrays (both static and dynamic). My 
> reasons for this are:
> 
>    a) Different problems may benefit from different types. Sparse 
> matrices, dense matrices, triangular matrices, etc. can all be 
> represented differently based on efficiency and/or memory requirements.

I use all of the above. It would be great to have them all within an 
integrated framework.

>    b) I hope that, at some point, my library will be of such a quality 
> that it may be useful to others, and in that event I will release it. 
> Interoperability with other libraries is therefore a goal for me, and a 
> part of this is to let the user choose other vector/matrix types than 
> the ones provided by me.

Yes please. It would be great if you considered submitting it to Phobos.

>    c) Often, for reasons of both efficiency and simplicity, it is 
> desirable to use arrays directly.

Yah.

> My first question goes to those among you who do a lot of linear algebra 
> in D: Do you think supporting both library  types and arrays is worth 
> the trouble? Or should I just go with one and be done with it?

If you go templated you don't need to explicitly support built-in arrays 
- they'll just work.

> A user-defined matrix type would have opIndex(i,j) defined, and to 
> retrieve elements one would write m[i,j].

Yah.

> However, the syntax for 
> two-dimensional arrays is m[i][j], and this means I have to put a lot of 
> static ifs around my code, in order to check the type every time I 
> access a matrix.

No, that's not a two-dimensional array; it's an array of arrays. If you 
want to make your lib work with arrays of arrays, you could easily build 
a little wrapper arround it (e.g. JaggedMatrix).

> This leads me to my second question, which is a 
> suggestion for a language change, so I expect a lot of resistance. :)
> 
> Would it be problematic to define m[i,j,...] to be equivalent to 
> m[i][j][...] for built-in arrays, so that arrays and user-defined types 
> could be used interchangeably?
> 
> (And, importantly, are there anyone but me who think they would benefit 
> from this?)

This wouldn't harm, but it would be a special case.


Andrei