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Sorry for the delay, the holidays, you know ...

Daniel Oberhoff wrote:

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On 2008-12-18 23:46:40 +0100, Eric Niebler said:

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Daniel Oberhoff wrote:

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Now with proto I was wondering how hard it would be to build an

et

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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.

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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