cpqfunction {ConConPiWiFun}

This class implements continuous convex piecewise quadratic functions

Description

This includes functions that are 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

See Also

to See Also as cplfunction,

Examples

##
#Construction of a piecewise quadratic function
##
Slopes1=c(-1,2) 
Slopes0=c(-2,0)# increasing ! convexity is required
Breakpoints=c(-Inf,2,4) # increasing. length is number of slopes +1
FirstNonInfBreakpointVal=3
CCPWLfunc1=new(cpqfunction,Slopes0,Slopes1,Breakpoints,FirstNonInfBreakpointVal)
CCPWLfunc1$get_BreakPoints_() ## return Breaks AND Slopes
plot(CCPWLfunc1)

###Etoile transformation (legendre transform of f)
# Changes f no return value
CCPWLfunc1$Etoile()
CCPWLfunc1$get_BreakPoints_()
CCPWLfunc1$Etoile()
CCPWLfunc1$get_BreakPoints_()  ## (f^*)^* is f !


###Squeeze function 
# Changes f, no return value
left=-1; right=4
CCPWLfunc1$Squeeze(left,right) # CCPWLfunc1 is now infinite (or not definite) out of [left,right]
# i.e. all breakpoints out of [left,right] removed
CCPWLfunc1$get_BreakPoints_() 

###Swap function 
# Changes f  no return value !
y=2;
CCPWLfunc1$Swap(y)
CCPWLfunc1$get_BreakPoints_() #now f = CCPWLfunc1 is replaced by x -> f(y-x) 


### Sum function (uses fast insertion) do not affect operands 
CCPWLfunc1=new(cpqfunction,Slopes0,Slopes1,Breakpoints,FirstNonInfBreakpointVal)
CCPWLfunc2=new(cpqfunction,Slopes0,Slopes1+1,Breakpoints,FirstNonInfBreakpointVal)
CCPWLfunc1plus2=Sumq(CCPWLfunc1,CCPWLfunc2)
CCPWLfunc1plus2$get_BreakPoints_()


rm(list=ls())
gc()