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CCA (Computational Convex Analysis) >> plq > plq_gph

plq_gph

Convert a PLQ subdifferential model to a standard PLQ model.

Calling Sequence

plq = plq_gph(gph)

Parameters

gph

matrix. The subdifferential of a PLQ function.

Description

Converts the graph of the subdifferential of a PLQ function into the corresponding PLQ data structure. Uses the value of the function stored at each x value in gph and integrates across each segment.

This function runs in linear time with respect to the number of points in the input graph.

Examples

// The indicator function I_[-1,1].
// Defined to be 0 inside [-1,1] and %inf outside.
gph = [-1, -1, 1, 1; ..
       -1, 0, 0, 1; ..
       %inf, 0, 0, %inf];
plq = plq_gph(gph),
// plq  =
// 
//  - 1.    0.    0.   Inf  
//    1.    0.    0.    0.  
//   Inf    0.    0.   Inf  

// A PLQ function:
//   x in [-1,1]: 0
//     otherwise: x^2 - 1
gph = [-2, -1, -1, 1, 1, 2; ..
       -4, -2, 0, 0, 2, 4; ..
       3, 0, 0, 0, 0, 3];
plq = plq_gph(gph),
// plq  =
// 
//  - 1.    1.    0.  - 1.  
//    1.    0.    0.    0.  
//   Inf    1.    0.  - 1.

See Also

Authors

Bryan Gardiner, University of British Columbia, BC, Canada


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