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CCA (Computational Convex Analysis) >> op > op_fitzinf

# op_fitzinf

Evaluate the Fitzpatrick function of infinite order of an operator on a grid using Rockafellar functions.

### Calling Sequence

    F = op_fitzinf(B, x, xstar)

### Parameters

B

  matrix. An matrix [a;bm;bp] where a, bm (b-), and bp (b+) are row vectors as defined below.

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 of infinite order of an operator A on a grid (x,x*) using Rockafellar functions, where B is defined as:

This function computes the Rockafellar functions R(A,a(k)) for all k=1..m, evaluates the functions at (x,x*), then uses LLT1d algorithm to find the maximum result. It runs in O(m^2 + m*Nx + N) time, or O(m^2) when m==Nx==Nxstar. See also plq_rock, which returns PLQ Rockafellar functions, and plq_fitzinf0, which returns PLQ Fitzpatrick functions.

### Examples

    a = -4:4;
    bm = [-15,-13,-10,-7,-6,-4,0.5,1,1];
    bp = [-13,-11,- 8,-6,-5, 0,  1,1,2];
    B = [a;bm;bp];
    x = -10:10;
    xstar = -10:10;
    F = op_fitzinf(B, x, xstar),

    clf(); alpha=30; theta=60;
    plot3d(x, xstar, F, alpha=alpha, theta=theta);

### See Also

- op_fitz_brute
- op_fitz_direct
- op_fitz
- plq_fitzinf0
- plq_fitzinf0_direct
- plq_rock

### Authors

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

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