Scilab Function
Last update : 3/11/2006

me_direct - [For comparison only] Moreau envelope, direct computation

Calling Sequence

[M,p,P] = me_direct(X,f,S)

Parameters

Description

Compute numerically the discrete Moreau envelope of a set of planar points (X(i),f(i)) at slopes S(j), i.e.

	   				      2
	   M(j) = min f(i) + || s(j) - x(i) ||.
		   i
					          2
	   p(j) in Argmin f(i) + || s(j) - x(i) ||.
		      i
						 2
	   P(j) = Argmin f(i) + || s(j) - x(i) ||.
		      i
It uses straight computation for a quadratic-time algorithm theta(n*m) with n=length(X)=length(f) and m=length(S).

Examples

	X=[-5:0.5:5]';
	Y=X.^2;
	S=(Y(2:size(Y,1))-Y(1:size(Y,1)-1))./(X(2:size(X,1))-X(1:size(X,1)-1));
	[M,p,P]=me_direct(X,Y,S)

See Also

me_direct2d ,   me_llt ,   me_nep ,   me_pe ,   me_brute2d ,  

Author

Yves Lucet, University of British Columbia, BC, Canada

Bibliography

Y. Lucet, 2006, Fast Moreau Envelope Computation I: Numerical Algorithms, Numerical Algorithms, 43 (2006), 235-249