Class BorderMethod

source code

object --+        
         |        
  Function --+    
             |    
      TestFunc --+
                 |
                BorderMethod

Known Subclasses:

• Branch_Bor
• , Fold_Bor
• , Hopf_Bor
• , Hopf_Double_Bor_One
• , Hopf_Double_Bor_Two

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.