Vectors and matrices

[Lars Kyllingstad]

Bill Baxter wrote:
> On Wed, Apr 15, 2009 at 7:07 AM, Lars Kyllingstad
> <public at kyllingen.nospamnet> 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.
>>
>>   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.
>>
>>   c) Often, for reasons of both efficiency and simplicity, it is desirable
>> to use arrays directly.
>>
>> 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?
>>
>>
>> A user-defined matrix type would have opIndex(i,j) defined, and to retrieve
>> elements one would write m[i,j]. 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. 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?)
> 
> How about just making a lightweight array-view class that provides
> your interface, but manipulates an underlying m[] passed to the
> constructor by the user?
> 
> Another point is that if you are willing to write code like
> index(m,i,j) inside your lib instead of m[i,j], then you only need the
> static conditional inside the index() function.
> 
> --bb

Those are good points. In both cases I guess the function call can be 
inlined, so there is little or no performance hit.

-Lars