## Name

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 pl_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 , pl_lft_llt

## Authors

`Yves Lucet`, University of British Columbia, BC, Canada