#OK to post
#Yonah Biers-Ariel
#Homework 9

ArDataMV:=proc(A,v,N) local ra,x,i,produ,L,j:
	ra:=rand(-A*1.0..A*1.0):
	L:=[]:
	for j from 1 to N do
		x := [seq(ra(),i=1..nops(v))]:
		produ := add(x[i]*v[i],i=1..nops(v)):
		if produ < 0 then
			L:=[op(L),[x,0]]:
		else
			L:=[op(L),[x,1]]:
		fi:
	od:
	L:
end:

PAmv := proc(L,n,lambda:=1) local v, produ,i,j:
	v := [0$n]:
	for i from 1 to nops(L) do
		produ := add(L[i][1][j]*v[j],j=1..n):
		if produ < 0 and L[i][2] = 1 then
			v := v + lambda*L[i][1]:
		elif produ >=0 and L[i][2] = 0 then
			v := v - lambda*L[i][1]:
		fi:
	od:
	v:
end:

TestPMV := proc(L,v) local fpos, fneg, n, i, j, guess:
	fpos:=0:
	fneg:=0:
	n:=nops(L):
	for i from 1 to n do
		guess:=add(L[i][1][j]*v[j],j=1..nops(v)):
		if guess < 0 and L[i][2] = 1 then
			fneg := fneg + 1:
		elif guess >=0 and L[i][2] =0 then
			fpos := fpos + 1:
		fi:
	od:
	[fneg, fpos, n]:
end:

PA1corrected := proc(L) local Lnew,i:
	Lnew := [seq([[op(L[i][1]),1],L[i][2]],i=1..nops(L))]:
	PAmv(Lnew,2,.1):
end:

########COPIED FROM C9#########
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:


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:

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: