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CCA (Computational Convex Analysis) >> op > op_fitz_brute

op_fitz_brute

[For comparison only] Evaluate the Fitzpatrick function of a given operator on a grid.

Calling Sequence

F = op_fitz_brute(A, n, x, xstar)

Parameters

A

matrix. An operator [a;a*] where a and a* are row vectors.

n

integer. The order of the Fitzpatrick function to compute.

x

column vector. The x values of the grid on which the Fitzpatrick function is evaluated.

xstar

column vector. The x* values of the grid on which the Fitzpatrick function is evaluated.

Description

Warning: This function is provided only for comparison and unit testing. Faster results are achieved by using op_fitz.

Evaluates the Fitzpatrick function with order n of an operator A on a grid (x,x*).

This function uses the brute-force approach given by following formula. For each (x,x*) combination, it computes the maximum of the sums from all permutations of n-1 (a,a*) pairs. The algorithm runs in exponential O(n*m^(n-1)*N) time, and if m==Nx==Nxstar, then it runs O(n*m^(n+1)).

Examples

a = 1:4;
astar = 2*a^2 - 9;
x = 0:5;
xstar = -1:5;
F = op_fitz_brute([a; astar], 2, x, xstar),

clf(); alpha=51; theta=162;
plot3d(x, xstar, F, alpha=alpha, theta=theta);

See Also

Authors

Bryan Gardiner, University of British Columbia, BC, Canada


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