Re: [Boost-users] proto for array expressions

Subject: Re: [Boost-users] proto for array expressions
From: Daniel Oberhoff (daniel.oberhoff_at_[hidden])
Date: 2009-01-03 18:21:15

>> Sorry for the delay, the holidays, you know ...
>>
>> Daniel Oberhoff wrote:
>> > On 2008-12-18 23:46:40 +0100, Eric Niebler <eric <at> boost- 
>> consulting.com>
>> > said:
>> >
>> >> Daniel Oberhoff wrote:
>> >>>
>> >>> Now with proto I was wondering how hard it would be to build an  
>> et
>> >>> engine for array math. Basically I am interested in general  
>> tensor
>> >>> notation, and the resulting expressions should be iteratable
>> >>> efficiently. think (advanced example):
>> >>>
>> >>> a_ij = b_i * (c_j - sum(d_ijk, k = [i-1,1])
>> >>
>> >> I don't understand your notation. What are a_ij et. al.?
>> >
>> > Sorry, the underscripts where meant to be indices. So a is a 2d  
>> array, b
>> > and c are 1d arrays, and d is a 3d array. The statement says: to
>> > calculate a at a given index pair i,j (say 0,0) you substitute  
>> for i,j
>> > on the right. And the sum sums over the third index of the 3d  
>> array d.
>> > The notation further says that the bounds for the summation  
>> depend on
>> > what you substitute for i. So to fill the array a like that you  
>> need to
>> > substitute all values in the domian (say both indices run from 0  
>> to 99
>> > for a 100x100 array), and for efficiency it would be best if the  
>> right
>> > hand side would result in an iterator that substitutes subsequent  
>> all
>> > values in series.
>>
>> OK, the syntax for your tensor expressions needs work, but I think  
>> what
>> you're shooting for is certainly doable. How about a syntax like  
>> this:
>>
>>      a[i][j] = b[i] * ( c[j] - sum( (d[i][j][k], k = (i-1,1)) ) )
>>
>> This is a valid C++ expression, and I think there could be enough  
>> type
>> information in it to make it do something useful. Here is a simple
>> program that makes the above well-formed, and also defines a very
>> rudimentary the grammar for tensor expressions, with transforms that
>> calculate the expression's dimensionality. That's important because  
>> you
>> don't want to assign a 2-D array to a 1-D array, for instance.
>>
>> [...]
>
> Hey, wow, a full implementation as a response :). Seems very lean  
> and mean, and I will have to look at it further. What I just tried  
> was defining two domains very similar to the calculator example, and  
> then I was going to have syntax with round brackets like this:
>
> a(i, j) = b(i) * ( c(j) - sum( d(i,j,k), k, i-1, 1) ) )
> so one domain was to be for arrays (a,b,c,d) and one for the indices  
> (i,j,k). But I could not get the grammar to check for the function  
> syntax. somehow the proto extends mechanism just passed through all  
> kinds of function call expressions, even though I explicitly  
> specified only things like:
>
> boost::proto::function< array_grammar, index_grammar >
>
> and still things like a(a) compile. any ideas where I am going wrong?
>

ok, answering my own question. Turns out the calculator example used a  
grammar with a match-all-terminals to specify terminals, so it could  
not distinguish between index placeholders and arrays. got that now  
and got my first fully grammar checked expression tree printed. now  
moving towards contractions, dimension checks, and actually getting my  
array implementation in there and generating iterators to evaluate the  
expressions.

stay tuned for more problems (and again much thanks to eric niebler  
for the prompt and insightful response!).

Daniel