cplfunction {ConConPiWiFun} R Documentation

## This class implements continuous convex piecewise linear functions

### Description

This includes functions that are ccpl (resp. ccpq) on a convex set (i.e. an interval or a point) and infinite out of the domain. These functions can be very usefull for a large class of optimisation problems. Efficient manipulation (such as log(N) insertion) of such data structure is obtained with map standard template library of C++ (that hides balanced trees). This package is a wrapper on such a class based on Rcpp modules.

### Author(s)

Robin Girard

to See Also as cplfunction,

### Examples

##
#Construction of a piecewise linear function
##

Slopes=c(-1,2,Inf) # increasing ! convexity is required
Breakpoints=c(-Inf,2,4) # increasing. length is number of slopes +1
FirstNonInfBreakpointVal=3
CCPWLfunc1=new(cplfunction,Slopes,Breakpoints,FirstNonInfBreakpointVal)
plot(CCPWLfunc1) #visualisation method

###Etoile transformation (legendre transform of f)
# Changes f no return value
CCPWLfunc1$Etoile() plot(CCPWLfunc1) #if f = CCPWLfunc1 CCPWLfunc1 becomes is f^*(y) =inf_x {xy-f(x)} CCPWLfunc1$Etoile()
plot(CCPWLfunc1)   ## (f^*)^* is f !

###Squeeze function
# Changes f, no return value
left=-Inf; right=3
CCPWLfunc1$Squeeze(left,right) # CCPWLfunc1 is now infinite (or not definite) out of [left,right] # i.e. all breakpoints out of [left,right] removed ###Swap function # Changes f no return value ! y=2; CCPWLfunc1$Swap(y)
plot(CCPWLfunc1); #now f = CCPWLfunc1 is replaced by x -> f(y-x)

### Sum function (uses fast insertion) do not affect operands
CCPWLfunc1=new(cplfunction,c(-1,2,Inf) ,c(-Inf,2,4),0)
CCPWLfunc2=new(cplfunction,c(-1,2,Inf),c(-Inf,1,3),0)
CCPWLfunc1plus2=Suml(CCPWLfunc1,CCPWLfunc2)
CCPWLfunc1plus2

par(mfrow=c(1,3))
plot(CCPWLfunc2,col='red');
plot(CCPWLfunc1,col='blue');
plot(CCPWLfunc1plus2);

rm(list=ls())
gc()



[Package ConConPiWiFun version 0.4.6.1 Index]