#C9.txt Feb. 21, 2019

Help:=proc() print(`PA1(L) , ArData(L1,H1,N,c), TestP(L,c) , NoisyData(L1,H1,N,c,p) `): end:



#L:=[[TadeusBalaban, #Publ , #Citations,  #h-index   ,1],

#   [RobertBeals,                            2],

#....

#   [DoronZeilberger,  210,2404,    , 2],

 #  [WujunZhang,              ]]



#1D perceptron algorithm,

#PA1(L): inputs a list of pairs [heightIncm,{0,1}] where 0 if she or he did not make it 1 if he or she did

#outputs a numnber c a "predictor" that if x>c then they get to be admitted

PA1:=proc(L)  local i,c,n:

c:=0:

n:=nops(L):

for i from 1 to  n do

   if L[i][2]=1 and L[i][1]<c  then

 #False positive then

   c:=c-L[i][1]:

 elif L[i][2]=0 and L[i][1]>c  then

 #False  negative then

   c:=c+L[i][1]:

fi:

od:



c:



end:



#inputs L1 and H1 (low and high heights in basketball players and the number N of applicants

#and a cut-off c that >=c gets 1 (admitted) and 0 (rejected) 

ArData:=proc(L1,H1,N,c) local  L,ra,i,t:

ra:=rand(L1..H1):



L:=[]:



for i from 1 to N do

 t:=ra():

 if t>=c then

   L:=[op(L),[t,1]]:

 else

  L:=[op(L),[t,0]]:

 fi:

od:

L:

end:



#Inputs a data set of pairs [height,1 or 0] and a cut-off c, outputs the

#triple # of false negatives and # of false positive, total number of data entries

TestP:=proc(L,c) local fn,fp,i:

fn:=0:

 fp:=0:



  for i from 1 to nops(L) do

    if L[i][1]>=c and L[i][2]=0 then

       fp:=fp+1:

    elif L[i][1]<c and L[i][2]=1 then

       fn:=fn+1:

    fi:

 od:



[fn,fp,nops(L)]:



end:





 

#inputs L1 and H1 (low and high heights in basketball players and the number N of applicants

#and a cut-off c that >=c gets 1 (admitted) and 0 (rejected) and a prob. p of mis-classifying

#outputs the noisy data set

NoisyData:=proc(L1,H1,N,c,p) local  L,ra,i,t,ra1:

ra:=rand(L1..H1):

ra1:=rand(0.0..1.0):





L:=[]:



for i from 1 to N do

 t:=ra():

  

 if t>=c then

    if ra1()<=p then

    L:=[op(L),[t,0]]:

     else

   L:=[op(L),[t,1]]:

    fi:

 else

   if ra1()<=p then

    L:=[op(L),[t,1]]:

   else

  L:=[op(L),[t,0]]:

   fi:

 fi:

od:

L:

end:





ArDataMV:=proc(A::posint,v::list,N::posint) local i, n, retL, x, c2, rd:

	with(ListTools):



	n:=nops(v):

	rd:=rand(-A+10^(-12)..A-10^(-12)):



	retL:=[]:

	for i from 1 to N do

		x:=[seq(rd(), i=1..n)]:

		if DotProduct(v, x)<0 then 

			c2:=0:

		else

			c2:=1:

		fi:

		retL:=[op(retL),[x,c2]]:

	od:

	retL;

end:



 

PAmv:=proc(L::list,n::posint)  local i,c,cc,j:

with(ListTools):

	c:=[seq(0, i=1..n)]:	



	for i from 1 to n do

		cc:=DotProduct(L[i][1],c):

	if (cc < 0) and (L[i][2] = 1) then

		for j from 1 to n do

			c[j]:=c[j]+L[i][1][j]:

		od:

	elif (cc >= 0) and (L[i][2] = 0) then

		for j from 1 to n do

			c[j]:=c[j]-L[i][1][j]:

		od:

	fi:

	od:

	c:

end:





TestPMV:=proc(L::list,v::list) local i,j,n,nL,fp,fn:

	with(ListTools):

	

	n:=nops(v):

	nL:=nops(L):

	fp:=0:

	fn:=0:

	for i from 1 to nL do:

		if (DotProduct(L[i][1],v)<0) and (L[i][2]=1) then

			fn:=fn+1:		

		elif (DotProduct(L[i][1],v)>=0) and (L[i][2]=0) then

			fp:=fp+1:

		fi:

	od:

	[fp,fn,nops(L)]:

end:





PA1Corrected:=proc(L::list) local i, retL, n:

	n:=nops(L):

	retL:=[]:



	for i from 1 to n do

		retL:=[op(retL),[[L[i][1],1],L[i][2]]]:	

	od:

	PAmv(retL,2):

end:



MethodCompare:=proc(L::list):

	printf("PA1 time: %f\n", time(PA1(L))):

	printf("PA1correctedtime: %f\n", time(PA1Corrected(L))):

end: