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CCA (Computational Convex Analysis) >> op > op_fitz

op_fitz

Evaluate the Fitzpatrick function of a given operator on a grid using the LLT2d algorithm.

Calling Sequence

F = op_fitz(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

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

This function uses a recursive algorithm that employs LLT2d to achieve a running time of O(n*m^2 + m*Nxstar + N). When m==Nx==Nxstar, the running time is O(m^3).

Examples

a = -2:2;
astar = 3*a - a + 3;
x = -3:3;
xstar = -3:3;
F1 = op_fitz([a; astar], 1, x, xstar);
F2 = op_fitz([a; astar], 2, x, xstar);
F3 = op_fitz([a; astar], 3, x, xstar);

clf(); alpha=60; theta=-60;
subplot(131); plot3d(x, xstar, F1, alpha=alpha, theta=theta);
subplot(132); plot3d(x, xstar, F2, alpha=alpha, theta=theta);
subplot(133); plot3d(x, xstar, F3, alpha=alpha, theta=theta);

See Also

Authors

Bryan Gardiner, University of British Columbia, BC, Canada


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