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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

- pl_lft_llt
- pl_lft_direct

### Authors

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

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