#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: