#Terence Coelho Hw 9 2-24-2019
#importing
#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:
#problems start here

#dot product
dot:=proc(L1,L2) local ret,i:
ret:=0:
for i from 1 to nops(L1) do
ret:=ret+L1[i]*L2[i]
od:
ret:
end:

#2.
#ArDataMV(A,v,n): given a list v, and an integer A, generates nops(v) random numbers from [-A,A] x, 
# then adds pair [x,1]/[x,0] if v.x>0, v.x<=0 respectively. Does this n times.
ArDataMV:=proc(A,v,n) local s,i,ret,x,j,ra:
ret:=[]:
s:=nops(v):
ra:=rand(-A*1.0...A*1.0):
for j from 1 to n do
x:=[]:
for i from 1 to s do
x:=[op(x),ra()]:
od:
if dot(x,v)<=0 then 
ret:=[op(ret),[x,0]]:
fi:
if dot(x,v)>0 then 
ret:=[op(ret),[x,1]]:
fi:
od:
ret:
end:

#3
#PAmv(L,n): given list of data of form [x,{0,1}] where x has length n, find x that splits data as above.
PAmv:=proc(L,n) local w,b,i,flag,L2,j:
w:=[0$n]:
b:=0:
flag:=-1:
L2:=L:
#Going to use -1 instead of 0 to use sign function for shorter code.
for i from 1 to nops(L2) do 
if L2[i][2]=0 then 
L2[i][2]:=-1:
fi:
od:
for j from 1 to 1000*n while flag=-1 do 
flag:=1:
for i from 1 to nops(L2) do
if not sign(dot(L2[i][1],w)+b)=L2[i][2] then 
w:= w+L2[i][2]*L2[i][1]:
b:=b+L2[i][2]:
flag:=-1:
fi:
od:
od:
[w,b]:
end:

#4:
#Inputs a data set of pairs [x,1 or 0] and a "cut-off" v and n outputs the
#triple of false negatives and # of false positive, total number of data entries
TestP:=proc(L,v) local fn,fp,i:
fn:=0:
 fp:=0:

  for i from 1 to nops(L) do
    if dot(v,L[i][1])<0 and L[i][2]=1 then
       fp:=fp+1:
    elif dot(v,L[i][1])>0 and L[i][2]=0 then
       fn:=fn+1:
    fi:
 od:

[fn,fp,nops(L)]:

end:

#5:
#Given list of [height,{0,1}], map to list of [[height,1],{0,1}], then use procedure PAmv(L,n) to get 
#a,b such that L[i][2]=1 in case ax+b>=0
#Since the perceptron algorithm used above accidentally already outputs of form mx+b, assuming an implicit
#1 in the entries, this will be just:
PA1corrected:=proc(L):
PAmv(L,1):
end:
#The original PA1 could potentially loop forever if one were to make it loop until it didn't misclassify
#any data. I got such a list experimentally when testing the method in class but can't seem to get lucky now.