[For comparison only] Evaluate the Fitzpatrick function of a given operator on a grid.
F = op_fitz_brute(A, n, x, xstar)
matrix. An operator [a;a*] where a and a* are row vectors.
integer. The order of the Fitzpatrick function to compute.
column vector. The x values of the grid on which the Fitzpatrick function is evaluated.
column vector. The x* values of the grid on which the Fitzpatrick function is evaluated.
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)).
Bryan Gardiner
, University of British Columbia, BC, Canada