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CCA (Computational Convex Analysis) >> plq > plq_fitzinf0_direct

# plq_fitzinf0_direct

[For comparison only] Compute the PLQ Fitzpatrick function of infinite order of an operator on an (x,0) grid using Rockafellar functions.

### Calling Sequence

    F = plq_fitzinf0_direct(B)

### Parameters

B

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

F

  The infinite-order, PLQ Fitzpatrick function of the operator A.

### Description

Warning: This function is provided only for comparison and unit testing. Faster results are achieved by using plq_fitzinf0.

Compute the PLQ Fitzpatrick function of infinite order of an operator A on a grid (x,0) as a maximum over Rockafellar functions, where B is defined as:

This function computes the PLQ Fitzpatrick function in quadratic time by calculating R(A,a(k)) for each k=1:m and taking the PLQ maximum. See also plq_rock, which plq_fitzinf0_direct uses to generate Rockafellar 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 = -6:6;
    F = plq_fitzinf0_direct(B),
    plq_eval(F, x),

### See Also

- op_fitz_brute
- op_fitz_direct
- op_fitz
- op_fitzinf
- plq_fitzinf0
- plq_rock

### Authors

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

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