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A formulation of the Hexad algorithm using the geometry of the Fano projective plane
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    We have described a new formulation of the ‘Hexad Algorithm’ for decomposing a given 3D symmetric positive-definite aspect tensor on a lattice into its six unique local line generators and corresponding projected rank-one aspect tensor contributions. The new formulation adheres strictly to the symmetries possessed by the associated Fano projective plane and Galois field, GF(8). A bonus of adopting these constraints is that the computer code in the new algorithm is relatively succinct. The motivation for this work has been to provide a supporting algorithmic framework for the production of a computationally efficient way to generate anisotropic and spatially inho-mogeneous covariances, initially for NOAAs new 3D RTMA, but also for more general data assimilation applications later.
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