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CCA (Computational Convex Analysis) >> pl > pl_lft_plt

pl_lft_plt

Parametric Legendre Transform, PLT algorithm

Calling Sequence

[Conj, S] = pl_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] = pl_lft_plt(X, f, df);

See Also

Authors

Yves Lucet, University of British Columbia, BC, Canada

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