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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

- op_fitz_brute
- op_fitz_direct
- op_fitzinf
- plq_fitzinf0
- plq_fitzinf0_direct
- plq_rock

### Authors

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

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