Discrete Pasch-Hausdorff envelope
ph = pl_ph_direct(X, Y, S, lambda)
column vector of size m.
column vector of size m.
column vector of size n.
constant. Scaling parameter for the norm function.
The Pasch-Hausdorff envelope evaluated at S.
Computes the Pasch-Hausdorff envelope of a function described by the vectors X and Y, where y(i)=f(x(i)). Returns the envelope evaluated at the points in the vector S. The Pasch-Hausdorff envelope is the inf-convolution of the function with a scaled norm term,
The discrete Pasch-Hausdorff envelope is computed using the formulaS = min [y_i + lambda |x_i - s_i|]. i | ![]() | ![]() |
This function runs in O(mn) time.
Bryan Gardiner
, University of British Columbia, BC, Canada