Multiscale flat norm (MSFN)

medianshape.core.msfn.msfn(points, simplices, subsimplices, input_current, lambda_, w=[], v=[], cons=[])[source]

MSFN - Multiscale flat norm

Accepts simplicial settings, an input current, multiscale factor(\(\lambda\)). Returns flat norm decomposition of the input current and the flat norm. Let K be an underlying simplicial complex of dimension q.

Parameters:
  • points (float) – points in K.
  • simplices (int) – (p+1)-simplices in K, an array of dimension (nx(p+1)) where \(p+1 \leq q\) and n is the number of p+1-simplices in K.
  • subsimplices (int) – p-simplices in K, an array of dimension (mxp) where \(p \leq q\) and m is the number of p-simplice in K.
  • input_current (int) – a vector for an input current.
  • lambda (float) – multiscale factor.
  • w (float) – a vector of subsimplices volumes.
  • v (float) – a vector of simplices volumes.
  • cons (int) – a constraint matrix A.
Returns:

x, s, norm– p-chain, (p+1)-chain of flat norm decompostion, flat norm.
Return type:

int, int, float.