fusionsci - [Internal function] Merge 2 increasing sequences using scilab syntax; used to compute the Legendre-Fenchel conjugate.

Calling Sequence

fH = fusionsci(C,S)

Parameters

• C : Column vector. C(i) = (f(X(i+1) - f(X(i)) / (X(i+1) - X(i)) for some function f on a grid X.
• S : Column vector. The grid on which we want to compute the conjugate: f* is evaluated on S.
• fH : Column vector. Index at which the slope S(i) support the epigraph.

Description

Calling fusionsci(C,S) is equivalent to calling fusion(C,S). While the former uses scilab built-in functions to speed-up computation, contrary to the later it does not guarantee a linear worst-case running time. See fusion for more information.

This function is not intended to be used directly but to be called during the computation of the conjugate using the LLT algorithm by the function lft_llt.

Examples

    X=[-5:0.5:5]';
    Y=X.^2;
    C=(Y(2:size(Y,1))-Y(1:size(Y,1)-1))./(X(2:size(X,1))-X(1:size(X,1)-1));
    S=C-0.25*ones(size(C, 1));
    [fH]=fusionsci(C,S)
  

See Also

fusion,  lft_llt,  

Author

Yves Lucet, University of British Columbia, BC, Canada