# Ok to post homework.  
# Name: Tong Cheng    Data: Feb 23th, 2019   Assignment: 9

#------------------------------------------------------------------
# Part 2:
# ArData(A,v,N)
# inputs a pos. number A, and a vector of numbers v (given as a list), (let n:=nops(v))
# outputs a list of length N where each entry is a pair obtained by picking a random # point (a list of length n) in [-A,A]^n and returns the pair [x,0] if v.x (the dot product # of v and x) is negative and [x,1] if it is zero or positive
ArData:=proc(A,v,N)  local L, ra, ra_point, vec_pro, n, i, j:
#A:=abs(A):
ra:=rand(-convert(A,float)..convert(A,float)):
n:=nops(v):
L:=[]:
for j from 1 to N do
	ra_point:=[seq(ra(), i=1..n)]:
	vec_pro:=sum(ra_point[i]*v[i], i=1..n):
	if vec_pro < 0 then
		L:=[op(L), [ra_point,0]]:
	else
		L:=[op(L), [ra_point,1]]:
	fi:
od:
L:
end:

#-----------------------------------------------------------------------
# Part 3:
# PAmv(L,n)
# inputs a list containing data of the form [VectorOfLenghn,ZeroOrOne] where, # VectorOfLengthn is a list of length n, and n is the dimension. 
# To Implement the Perceptron algorithm in n dimensions (n arbitrary)
PAmv:=proc(L,n)  local ra, v, i, Data, Num_Data, j, wrong, ratio, vec_pro:

ra:=rand(0.0..1.0):
v:=[seq(ra(), i=1..n)]:

Num_Data:=nops(L):

for j from 1 to Num_Data do
	vec_pro:=sum(L[j][1][i]*v[i], i=1..n):
	if vec_pro<0 and L[j][2]=1 then
		v:=[seq(v[i]+L[j][1][i], i=1..n)]:
	elif  vec_pro >=0 and L[j][2]=0 then
		v:=[seq(v[i]-L[j][1][i], i=1..n)]:
	fi:	
od: 

v:
end:

#-----------------------------------------------------------------
# Part 4:
# Code from C9.txt
#||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
#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:
#|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

# TestPMV(L,v) 
# inputs v - a vector (list) with n components - and a data set L
# outputs the triple # of false negatives and # of false positive, total number of data # entries
TestPMV:=proc(L,v)  local  fn, fp, j, Num_Data, vec_pro, n:
n:=nops(v):
fn:=0:
fp:=0:
Num_Data:=nops(L):
for j from 1 to Num_Data do
	vec_pro:=sum(L[j][1][i]*v[i], i=1..n):
	if vec_pro<0 and L[j][2]=1 then
		fn:=fn+1:
	elif  vec_pro >=0 and L[j][2]=0 then
		fp:=fp+1:
	fi:	
od: 

[fn, fp, Num_Data]:

end:

#--------------------------------------------------------------------------
# Part 5:
# PA1corrected(L)
# That first transfoms the list L to the format [[data,1],ZeroOrOne], and uses your # procedure PAmv(L,n) with n=2 to outputs two numbers a and b such that L[i][2]=1 # iff ax+b>=0. Compare its performance to PA1(L). 
PA1corrected:=proc(L)  local  Data, i, v:

Data:=[seq([[L[i][1],1],L[i][2]], i=1..nops(L))]:
v:=PAmv(Data, 2):
v:




end:


# Code from C9.txt
#||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
#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_C9:=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:
#|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||s



(* The experimental result is as follows:
Djkk:=ArData_C9(180,220, 1000, 190):
c1:=PA1(Djkk)
                           c1 := 189
TestP(Djkk,c1)
                         [0, 26, 1000]
c2:=PA1corrected(Djkk)
               c2 := [167.1022349, -17.40172346]
Djkkk:=[seq([[Djkk[i][1],1],L[i][2]], i=1..nops(Djkk))]:
TestPMV(Djkkk,c2)
                          [0, 0, 1000]
*)