<< pl_me_plt pl plq >>

CCA (Computational Convex Analysis) >> pl > pl_ph_direct

pl_ph_direct

Discrete Pasch-Hausdorff envelope

Calling Sequence

ph = pl_ph_direct(X, Y, S, lambda)

Parameters

X

column vector of size m.

Y

column vector of size m.

S

column vector of size n.

lambda

constant. Scaling parameter for the norm function.

ph

The Pasch-Hausdorff envelope evaluated at S.

Description

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 formula

This function runs in O(mn) time.

Examples

lambda = 0.5;
X = [-2;-1;0;1;2];
Y = abs(abs(X)-1);
S = X;
ph = pl_ph_direct(X,Y,S,lambda),

Authors

Bryan Gardiner, University of British Columbia, BC, Canada


Report an issue
<< pl_me_plt pl plq >>