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CCA (Computational Convex Analysis) >> plq > plq_deconv_lft

# plq_deconv_lft

Piecewise linear quadratic (plq), deconvolution (via LFT)

### Calling Sequence

    plqic = plq_deconv_lft(plqf, plqg)

### Parameters

plqf

  matrix. A PLQ function.

plqg

  matrix. A PLQ function.

plqic

  matrix. The PLQ function that is the deconvolution of plqf and plqg.

### Description

Computes the deconvolution of two convex PLQ functions. The deconvolution is defined by the formula

Under certain conditions, deconvolution can be rewritten to use the Legendre-Fenchel conjugate (denoted *),

This deconvolution is also a PLQ function. This algorithm runs in O(n + m) time, where n and m are the size of f and g, respectively.

### Examples

    plqf = [-2.5,0,-1,-1.25; -2,1,4,5; 0,0,0,1; 0.5,1,0,1; %inf,0,1,0.75];
    plqg = [%inf,1,2,1];
    plqdc = plq_deconv_lft(plqf, plqg),
    plq_plotMultiple(-4, 3, plqf, plqg, plqdc);
    xtitle("PLQ Convex Deconvolution");
    legend(["f", "g", "f dc g"]);

### See Also

- plq_infconv_lft
- plq_function

### Authors

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

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