Does anyone know if triangular arrays have been implemented in julia or in a package yet? Triangular array In mathematics and computing, a triangular array of numbers, polynomials, or the like, is a doubly indexed sequence in which each row is only as long as the row's own index. That is…

The wiki article is quite brief. Could you explain a little more about what kind of operations you’d like a triangular array to support. In particular, what is “the indexing behavior” and “element-wise” operations in the context of triangular arrays?

So if you’re familiar with the dist class from R, it is very similar. It represents a matrix, or rather the lower half of a matrix underneath the diagonal (as the matrix is assumed to be symmetrical with 0 values as the diagonal, there is no point in storing both halfs), and so each row has a diffe…

Question: is it possible to store upper/lower triangular matrices in compact form and still pass that representation efficiently to BLAS operations? I.e. can that storage format be represented with the kinds of strides that BLAS understands?

Sounds like Symmetric, except that it saves some space by not storing upper entries (as our implementation currently does) nor diagonal entries (which are assumed to be zero). I’d start by making Symmetric more efficient as regards memory layout in Julia Base. Not storing diagonal elements sounds li…

[image] StefanKarpinski: Question: is it possible to store upper/lower triangular matrices in compact form and still pass that representation efficiently to BLAS operations? I.e. can that storage format be represented with the kinds of strides that BLAS understands? Is it still going to be mu…

I did not know about Symmetric, I can live with storing the 0 values in the diagonal! I’ve no idea when it comes to BLAS I’m afraid.

[image] ChrisRackauckas: Is it still going to be much better to use BLAS? For square lower triangular matrices you have less than half of the operations to do, and with @polly being added, could the difference between BLAS and not-BLAS be around 2x? Even if there are only about half operation…

You could just wrap a float in a new type and define the needed operations. This should dispatch to the generic versions of the linear algebra library.

For linear algebra, there is a significant overhead when using the packed format. This is partly because the indexing operations are slightly more complicated but more importantly, it is because the compact storage doesn’t allow blocked (BLAS-3) linear algebra operations. This was the main reason I …

Thanks for the example. Is the linear index similar to the indexing into the underlying vector or is it similar to a full matrix representation, i.e. can you m[n^2] or is the last index m[div(n*(n-1),2)]? Can you tell a little more about what kind of operations you’d like to perform on the triangul…

Triangular Arrays in julia?

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dlfivefifty December 20, 2016, 8:39am 28

I think it’d make more sense in a TriangularMatrices.jl package

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Triangular Arrays in julia?

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