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object --+ | Function --+ | TestFunc --+ | BorderMethod
Border method: [A B][V] = [0] [C^T D][G] [1] where r = corank and: A = (n,m) s = max(n,m) p = s-m+r, q = s-n+r B = (n,p) C = (m,q) D = 0_(q,p) V = (m,q) G = (p,q) 0 = (n,q) 1 = (q,q) F:R^nm --> R^pq, F(A) = G It can also be written as: [W^T G][A B] = [0 1] [C^T D] where now: W = (n,p) 0 = (p,m) 1 = (p,p) This is important for calculating derivatives: S_{z} = -W^T x A_{z} x V This is implemented in the diff method. In order to use the Function class, the matrices are put into vector form.
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F: R^a --> R^b Note: I did not assign b automatically (although I could - it would just be b = p*q) since you may not want to use all of the entries of S. Some bordering methods are not minimally augmented systems and thus only require certain entries of S.
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