|
#############################################################################
##
#W threl_def.gi Victor Bovdi <vbovdi@gmail.com>
#W Vasyl Laver <vasyllaver@uzhnu.edu.ua>
##
##
#Y Copyright (C) 2018, UAE University, UAE
##
#############################################################################
##
## This file contains some generic methods for threshold elements.
##
#############################################################################
##
##
## Example
## gap> t:=ThresholdElement([1,2],3);
## < threshold element with weight vector [ 1, 2 ] and threshold 3 >
## gap> Display(t);
## Weight vector = [ 1, 2 ], Threshold = 3.
## Threshold Element realizes the function f =
## [ 0, 0 ] || 0
## [ 0, 1 ] || 0
## [ 1, 0 ] || 0
## [ 1, 1 ] || 1
##
#############################################################################
##
#R
###########################################################################
DeclareRepresentation("IsThresholdElementRep", IsComponentObjectRep, ["weights","threshold"]);
######################################################################
##
#F ThresholdElement(Weights, Threshold)
##
## Produces a threshold element
## Weights are given as a list, the threshold is represented
## by a single number.
##
InstallGlobalFunction( ThresholdElement, function(Weights, Threshold)
local t,Func,A, alph, tel, F, i, j, x, y, TE, l;
if not IsVector(Weights) then
Error("Weights have to be presented as a vector");
fi;
if not IsRat(Threshold) then
Error("Please present Threshold as a rational number");
fi;
# Construct the family of all threshold elements.
F:= NewFamily( "Threshold Elements" , IsThresholdElementObj );
tel := rec(weights := Weights,
threshold := Threshold,
);
TE := Objectify( NewType( F, IsThresholdElementObj and IsThresholdElementRep and IsAttributeStoringRep ),
tel );
# Return the threshold element.
return TE;
end);
######################################################################
##
#F OutputOfThresholdElement(TE)
##
InstallGlobalFunction( OutputOfThresholdElement, function(TE)
local Func,t,i;
if not IsThresholdElementObj(TE) then
Error("The argument to OutputOfThresholdElement must be a threshold element");
fi;
if TE!.weights = [] then
Error("There must be an assigned weights vector to a threshold element");
fi;
Func:=[];
t:=IteratorOfTuples([0,1], Size(TE!.weights));
for i in t do
if i*TE!.weights<TE!.threshold then Add(Func,0);
else
Add(Func,1);
fi;
od;
return(LogicFunction(Size(TE!.weights),2,Func));
end);
######################################################################
##
#F StructureOfThresholdElement(TE)
##
InstallGlobalFunction( StructureOfThresholdElement, function(TE)
if not IsThresholdElementObj(TE) then
Error("The argument of StructureOfThresholdElement must be a threshold element");
fi;
if TE!.weights = [] then
Error("There must be an assigned weights vector to a threshold element");
fi;
return([TE!.weights,TE!.threshold]);
end);
#############################################################################
##
#M ViewObj( <A> ) . . . . . . . . . . . print threshold element
##
InstallMethod( ViewObj,
"displays a threshold element",
true,
[IsThresholdElementObj and IsThresholdElementRep], 0,
function( A )
Print("< threshold element with weight vector ", A!.weights, " and threshold ", A!.threshold, " >");
end);
#############################################################################
##
#M PrintObj( <A> ) . . . . . . . . . . . print threshold element
##
InstallMethod( PrintObj,
"displays a threshold element",
true,
[IsThresholdElementObj and IsThresholdElementRep], 0,
function( A )
Print("[",A!.weights,", ",A!.threshold,"]");
end);
#############################################################################
##
#M Display( <A> ) . . . . . . . . . . . print threshold element
##
InstallMethod( Display,
"displays a threshold element",
true,
[IsThresholdElementObj and IsThresholdElementRep], 0,
function( A )
local i,t,ff,k;
if A!.weights<>[] then
Print("Weight vector = ",A!.weights,", Threshold = ",A!.threshold,".\n");
Print("Threshold Element realizes the function f : \n");
ff:=OutputOfThresholdElement(A);
k:=1;
if Size(A!.weights)<=4 then
Display(ff);
fi;
Print(THELMA_INTERNAL_VectorToFormula(THELMA_INTERNAL_BFtoGF(ff)),"\n");
fi;
end);
#############################################################################
##
#F IsThresholdElement(A)
##
## Tests if A is a threshold element
##
InstallGlobalFunction( IsThresholdElement, function(A)
return(IsThresholdElementObj(A));
end);
#############################################################################
##
#F RandomThresholdELement(N)
##
## Given the number of the input variables, this function returns a pseudo
## random threshold element.
##
##
InstallGlobalFunction(RandomThresholdElement, function(N, lo, hi)
local i,w,t;
if not IsPosInt(N) then
Error("The number of variables must be a positive integer");
fi;
if lo>hi then
Error("The lower bound has to be less or equal than the upper bound!");
fi;
w:=List([1..N],i->Random([lo..hi]));
t:=Random([lo..hi]);
return ThresholdElement(w,t);
end);
############################################################################
##
#M Methods for the comparison operations for threshold elements.
##
InstallMethod( \=,
"for two threshold elements",
[ IsThresholdElementObj and IsThresholdElementRep,
IsThresholdElementObj and IsThresholdElementRep, ],
0,
function( x, y )
return(OutputOfThresholdElement(x) = OutputOfThresholdElement(y));
end );
InstallMethod( \<,
"for two threshold elements",
[ IsThresholdElementObj and IsThresholdElementRep,
IsThresholdElementObj and IsThresholdElementRep, ],
0,
function( x, y )
return(OutputOfThresholdElement(x) < OutputOfThresholdElement(y));
end );
[ Dauer der Verarbeitung: 0.34 Sekunden
(vorverarbeitet)
]
|
