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Subject: Re: [boost] Preliminary submission: generic linear algebra algorithms library Boost LA
From: Jeffrey Hellrung (jhellrung_at_[hidden])
Date: 2009-10-23 02:13:53

Emil Dotchevski wrote:
> For determinants, I wanted to have at least the 2x2 3x3 and 4x4
> versions done efficiently because those are used in 2D and 3D
> graphics. The formula is certainly not efficient, but (perhaps a bit
> naively?) I relied on compiler optimizations: the generated functions
> pull all scalars in local variables, which should untie the optimizer
> to figure out which series of multiplication/addition operations are
> identical and can be computed only once.

FWIW, I read somewhere (can try to dig up reference if desired) that 4x4
(and 5x5) determinants are most efficiently calculated via dynamic
programming, so you might consider explicitly implementing that rather
than relying on the compiler.

Also, signed volumes of small matrices might be useful, and I believe
they can be implemented more efficiently than simply taking the
determinant of a matrix adjoined with 1's.

> I'm not sure why we're talking about 3D arrays, those can't possibly
> represent vectors or matrices.

I just have to take issue with the strong "can't" here ;) It is
certainly imaginable that a 3D array could represent a linear operator
from 2D arrays to 1D arrays, or from 1D arrays to 2D arrays. Using
multidimensional arrays as your vectors might be more convenient than
flattening them for a given application.

- Jeff

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