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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

Authors

Bryan Gardiner, University of British Columbia, BC, Canada


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