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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

- op_fitz_direct
- op_fitz
- op_fitzinf
- plq_fitzinf0
- plq_fitzinf0_direct
- plq_rock

### Authors

`Bryan Gardiner`, University of British Columbia, BC, Canada

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