lft_plt - Parametric Legendre Transform, PLT algorithm

Calling Sequence

[Conj, S] = lft_plt(X, f, df)

Parameters

• X : column vector. A grid of points on which the function is sampled.
• f : column vector. The value of the function on the grid X: usually Y(i)=f(X(i)) for some function f.
• df : column vector. The value of the derivative of the function f evaluated on X, which is also the slope.

Description

Compute numerically the Legendre Fenchel transform by generating a uniform grid between an interval a,b and computing s[i] = f'(x), and f*(s[i]) = x[i]s[i] - f(x[i]). Which returns a set S of slopes in the dom of f* and the values of f* on S.

Examples

    function y = f(x), y=0.5 * x.^2, endfunction;
    function s = df(x), s= x, endfunction;
    b=%T;n=8;
    X=(-n/2:1:n/2)';S=df(X);Y=f(X);
    [Conj, S] = lft_plt(X, f, df);
  

See Also

lft_llt,  lft_direct,  

Author

Yves Lucet, University of British Columbia, BC, Canada