#open "graphics";;
 
let val x = max x (-x) ;;
 
let identite n = let a = (make_matrix n n) 0 in for i=0 to n-1 do a.(i).(i)<-1 done ; a ;;
 
let sigma a b f = let s=ref 0 in for i=a to b do s:= !s+(f i) done ; !s ;;
 
let nb_li = vect_length ;;
 
let nb_col m = vect_length (m.(0));;

let s_vect a b = let l= vect_length a in if l<>(vect_length b) then failwith "somme vectorielle non définie car longueur différente"
else let p=make_vect l 0 in for i=0 to l-1 do p.(i)<-(a.(i)+b.(i)) mod 2 done ; p ;;

let s_mat a b =
if (nb_col a)<>(nb_col b) then failwith "somme matricielle non définie car nombre de colones différent"
else if (nb_li a)<>(nb_li b) then failwith "somme matricielle non définie car nombre de lignes différent"
else let p=nb_col a in let n=nb_li a in let m=make_matrix n p 0
in for i=0 to n-1 do for j=0 to p-1 do m.(i).(j)<-(a.(i).(j)+b.(i).(j)) mod 2 done done ; m ;;
 
 
let s_mat_li a b i = let m = make_matrix (nb_li a) (nb_col a) 0 in for j=0 to (nb_col a)-1
do m.(i).(j)<-(a.(i).(j)+b.(j)) mod 2 done ; m ;; 

let s_ele_mat m = let c=ref 0 in for i=0 to nb_li m -1 do for j=0 to nb_col m -1 do c:=!c+m.(i).(j) done done ; !c ;;
 
let p_mat a b = if (nb_col a)<>(nb_li b) then failwith "produit matriciel non défini"
else let n=nb_li a in let p=nb_col a in let q=nb_col b in
let M = make_matrix n q 0 in for i=0 to n-1 do for j=0 to q-1 do
M.(i).(j) <- ((sigma 0 (p-1) (fun k -> a.(i).(k)*b.(k).(j))) mod 2 ) done done ; M ;;

let moyenne x y z = if (x+y+z)<2 then 0 else 1 ;;

let val x = max x (-x) ;;

let err m x y (*génère sur un matrice binaire des erreurs à un taux de x/y*) = let a = make_matrix (nb_li m) (nb_col m) 0 
in for i=0 to (nb_li m)-1 do for j=0 to (nb_col m)-1
do let b=random__int y in if b<x then a.(i).(j)<-(m.(i).(j) + 1) mod 2 else a.(i).(j)<-m.(i).(j) done done ; a;;
 
let err_bin m x y (*génère sur un matrice de tableaux à 24 bits des erreurs à un taux de x/y*) = 
let a = make_matrix (nb_li m) (nb_col m) [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|]
in for i=0 to (nb_li m)-1 do for j=0 to (nb_col m)-1 do a.(i).(j)<-[|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|] done done ;
for i=0 to (nb_li m)-1 do for j=0 to (nb_col m)-1 do for k=0 to 23 do
let b=random__int y in if b<x then a.(i).(j).(k)<-(m.(i).(j).(k) + 1) mod 2 else a.(i).(j).(k)<-m.(i).(j).(k) done done done ; a;;
 
let rec puiss2 k = if k=0 then 1 else
if k mod 2=0 then let y = puiss2 (k/2) in y*y
else 2*puiss2 (k-1) ;;
 
let int_to_bin n k (*convertit un integer en binaire dans un tableau de k bits*)= let res=make_vect k 0 and m= ref n and i=ref 0 in
while !m>0 do res.(!i)<-(!m mod 2) ; m:=!m/2 ; incr i done ; res ;;

 
let bin_to_int m k = let a=ref 0 in for i=0 to k-1 do a:=!a+m.(i)*(puiss2 i) done ; !a ;;

let n_lignes m = let n=nb_li m and p=nb_col m in match n*p mod 4 with
|0-> n*p/4
|_-> n*p/4 + 1 ;;
 
let transfo_quelc_mat4 m (*transforme une matrice quelconque en une matrice à 4 colones*) = 
let p=nb_col m and n=nb_li m and k=ref 0 and l=ref 0 in 
let r = make_matrix (n_lignes m) 4 0 in
for i=0 to (n-1) do 
for j=0 to (p-1) do 
r.(!k).(!l) <- m.(i).(j) ; if !l=3 then (l:=0 ; incr k) else incr l done done; r ;;

let transfo_mat4_quelc matrice n p = let i = ref 0 in let m = (nb_li matrice-1) and a = ref 0 and b = ref 0 and
resultat = ref (make_matrix n p 1) and
k=ref 0 and l = ref 0 in while !i < n*p 
 do ((!resultat).(!k).(!l) <- matrice.(!a).(!b); if !l < (p-1) then incr l
  else (incr k ; l:=0);if !b < 3 then incr b else (b:=0 ; incr a);incr i)
 done ; !resultat ;;



(*********************************************************************) ;;



let gen_h = [|[|1;0;0;0;1;1;0|];
              [|0;1;0;0;1;0;1|];
              [|0;0;1;0;0;1;1|];
              [|0;0;0;1;1;1;1|]|] ;;
 
let cod_h m= p_mat m gen_h ;;
 
let mat_ctrl_h = [|[|1;1;0|];
[|1;0;1|];
[|0;1;1|];
[|1;1;1|];
[|1;0;0|];
[|0;1;0|];
[|0;0;1|];|];;
 
let ctrl_h m = p_mat m mat_ctrl_h ;;
 
let decod m (*supprime les bits de parité*) = let p = make_matrix (nb_li m) 4 0 in for i=0 to (nb_li m)-1 do for j=0 to 3 do p.(i).(j) <- m.(i).(j) done done; p;;
 
let correction m  = 
let p=decod m in let c=ctrl_h m in for i=0 to (nb_li m)-1 do if  c.(i)=[|0; 0; 0|] || c.(i) = [|1; 0; 0|]
|| c.(i) = [|0; 1; 0|] || c.(i) = [|0; 0; 1|] then ()
else if c.(i)= [|1; 1; 0|] then p.(i)<- (s_vect (p).(i) [|1; 0; 0; 0|])
else if c.(i)= [|1; 0; 1|] then p.(i)<- (s_vect (p).(i) [|0; 1; 0; 0|])
else if c.(i)= [|0; 1; 1|] then p.(i)<- (s_vect (p).(i) [|0; 0; 1; 0|])
else if c.(i)= [|1; 1; 1|] then p.(i)<- (s_vect (p).(i) [|0; 0; 0; 1|]) done; p ;;



let carré = let c=make_matrix 121 121 0 in
for i=0 to 120 do if i mod 4 = 0 then (
for j=i to 120-i do c.(i).(j)<- 1 ;c.(j).(i)<- 1 done;
for j=120-i to i do c.(i).(j)<- 1 ;c.(j).(i)<- 1 done) done ; c ;;

let convert_one_bit_rbg m  = let p = make_matrix (vect_length m) (nb_col m) white in for i=0 to (nb_li m)-1 do for j=0 to (nb_col m)-1 do 
if m.(i).(j)=1 then p.(i).(j)<-black done done ; p ;;


(*********************************************************************) ;;

let dist_mat a b = s_ele_mat (s_mat a b) ;;
let mat_err m x y = err m x y ;;
let mat_corrige m x y =transfo_mat4_quelc (correction(err (cod_h (transfo_quelc_mat4 m)) x y)) (nb_li m) (nb_col m) ;;
let image m a b = draw_image (make_image(convert_one_bit_rbg m )) a b ;;
let image_err m x y a b = draw_image (make_image(convert_one_bit_rbg (err m x y))) a b ;;
let image_corrige m x y a b =
draw_image (make_image(convert_one_bit_rbg(transfo_mat4_quelc (correction(err (cod_h (transfo_quelc_mat4 m)) x y)) (nb_li m) (nb_col m)))) a b ;;

open_graph "600*4000+10-10";;

image carré 20 20 ;;
image_err carré 1 20 20 160 ;;
image_corrige carré 1 20 20 300 ;;


dist_mat (mat_err carré 1 20) carré ;;
dist_mat (mat_corrige carré 1 20) carré ;;

(*********************************************************************) ;;


let conv_color_bin m (*convertit une matrice couleur en une matrice de tableaux binaires*) = let p = make_matrix (nb_li m) (nb_col m) [||] in
for i=0 to (nb_li m)-1 do for j=0 to (nb_col m)-1 do p.(i).(j)<-[||] done done ;
for i=0 to (nb_li m)-1 do for j=0 to (nb_col m)-1 
do p.(i).(j)<- int_to_bin m.(i).(j) 24 done done ; p ;;
 
let conv_bin_color m = let p = make_matrix (nb_li m) (nb_col m) (white) in
for i=0 to (nb_li m)-1 do for j=0 to (nb_col m)-1 
do p.(i).(j)<- (bin_to_int m.(i).(j) 24) done done ; p ;;
  
 
let compo n (*donne les composantes rgb d'une couleur*) = let res=make_vect 3 0 and m= ref n and i=ref 0 in
while !m>0 do res.(2-(!i))<-(!m mod 256) ; m:=!m/256 ; incr i done ; res ;;

let decompo_16 n (*décompose une composante en un couple (q,r) de 16*)= (n/16 , (n mod 16)) ;;

let decompo_image m
(*décompose les éléments matrice couleur en un tableau de 3 composantes sous la forme [|RRR;GGG;BBB]|*) =
let n=(nb_li m) and p=(nb_col m) in let a= make_matrix n p [|0;0;0|] in
for i=0 to n-1 do for j=0 to p-1 do
a.(i).(j) <- compo m.(i).(j) done done ; a ;;


let decompo_separ c (*décompose une couleur en un tableau de 3 composantes sous la forme (q,r)*)= 
let a=compo c in let m=[|(0,0);(0,0);(0,0)|] in for i=0 to 2 do m.(i)<-decompo_16 a.(i) done ; m ;;

let decompo_image_separ m (*décompose les éléments matrice couleur en un tableau de 3 composantes sous la forme (q,r)*) =
let n=(nb_li m) and p=(nb_col m) in let a= make_matrix n p [|0, 0; 0, 0; 0, 0|] in
for i=0 to n-1 do for j=0 to p-1 do
a.(i).(j) <- decompo_separ m.(i).(j) done done ; a ;;


let image_to_bin_separ m = let a=decompo_image_separ m in let n=(nb_li m) and p=(nb_col m) in 
let b=make_matrix n p  [|[|0;0;0;0|];[|0;0;0;0|];[|0;0;0;0|];[|0;0;0;0|];[|0;0;0;0|];[|0;0;0;0|]|] in 
for i=0 to n-1 do for j=0 to p-1 do b.(i).(j)<- [|[|0;0;0;0|];[|0;0;0;0|];[|0;0;0;0|];[|0;0;0;0|];[|0;0;0;0|];[|0;0;0;0|]|] done done;
	for i=0 to n-1 do
		for j=0 to p-1 do 
			for k=0 to 2 do
				b.(i).(j).(2*k)<-int_to_bin (fst a.(i).(j).(k)) 4 ;
			   b.(i).(j).(2*k+1)<-int_to_bin (snd a.(i).(j).(k)) 4 
			done
		done
	done;
b ;;



let simplifier_matrice m = let n=(nb_li m) and p=(nb_col m) in let a=make_matrix n (144*p) 0 in 
for i=0 to n-1 do
	for j=0 to p-1 do
		for k=0 to 5 do
			for l=0 to 23 do
a.(i).(6*j+24*k+l)<- m.(i).(j).(k).(l)
done done done done ; a ;;

let simplifier_matrice_2 m = let n=(nb_li m) and p=(nb_col m) in let a=make_matrix n (24*p) 0 in 
for i=0 to n-1 do
	for j=0 to p-1 do
		for k=0 to 23 do
a.(i).(24*j+k)<- m.(i).(j).(k)
done done done  ; a ;;

let remplace_matrice m =  let n=(nb_li m) and p=(nb_col m) in
let a=make_matrix n (p/144) 
[|[|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|];
  [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|];
  [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|];
  [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|];
  [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|];
  [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|];
  [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|]|]
in for i=0 to n-1 do for j=0 to p/144-1 do a.(i).(j)<- 
[|[|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|];
  [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|];
  [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|];
  [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|];
  [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|];
  [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|];
  [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|]|] done done ;
for i=0 to n-1 do
	for j=0 to p/144-1 do
		for k=0 to 5 do
			for l=0 to 23 do
a.(i).(j).(k).(l)<- m.(i).(6*j+24*k+l) done done done done ; a ;;

let remplace_matrice_2 m =  let n=(nb_li m) and p=(nb_col m) in
let a=make_matrix n (p/24)  [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|]
in for i=0 to n-1 do for j=0 to (p/24)-1 do a.(i).(j)<-[|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|]done done;
for i=0 to n-1 do
	for j=0 to p/24-1 do
		for k=0 to 23 do
			a.(i).(j).(k)<- m.(i).(24*j+k) done done done ; a ;;




let image_to_bin_redon m = let a=decompo_image_separ m in let n=(nb_li m) and p=(nb_col m) in 
let b=make_matrix n p  [|[||];[||];[||];[||];[||];[||];[||];[||];[||];[||];[||];[||];|] in 
for i=0 to n-1 do for j=0 to p-1 do b.(i).(j)<- [|[||];[||];[||];[||];[||];[||];[||];[||];[||];[||];[||];[||];|] done done;
	for i=0 to n-1 do
		for j=0 to p-1 do 
			for k=0 to 2 do
				b.(i).(j).(4*k)<-int_to_bin (fst a.(i).(j).(k)) 4 ;b.(i).(j).(4*k+1)<-int_to_bin (fst a.(i).(j).(k)) 4;
				b.(i).(j).(4*k+2)<-int_to_bin (fst a.(i).(j).(k)) 4 ; b.(i).(j).(4*k+3)<-int_to_bin (snd a.(i).(j).(k)) 4  
			done
		done
	done;
b ;;


let simplifier_matrice_redon m = let n=(nb_li m) and p=(nb_col m) in let a=make_matrix n (48*p) 0 in 
for i=0 to n-1 do
	for j=0 to p-1 do
		for k=0 to 11 do
			for l=0 to 3 do
a.(i).(48*j+4*k+l)<- m.(i).(j).(k).(l)
done done done done ; a ;;

let corrige m = let n=(nb_li m) and p=(nb_col m) in
let a=make_matrix n p
[|[|0; 0; 0; 0|];
[|0; 0; 0; 0|];
[|0; 0; 0; 0|];
[|0; 0; 0; 0|];
[|0; 0; 0; 0|];
[|0; 0; 0; 0|]|]
in for i=0 to n-1 do for j=0 to p-1 do a.(i).(j)<- 
[|[|0; 0; 0; 0|];
[|0; 0; 0; 0|];
[|0; 0; 0; 0|];
[|0; 0; 0; 0|];
[|0; 0; 0; 0|];
[|0; 0; 0; 0|]|] done done ;
for i=0 to n-1 do
	for j=0 to p-1 do
		for k=0 to 2 do
			for l=0 to 3 do
a.(i).(j).(2*k).(l)  <-moyenne m.(i).(j).(4*k).(l) m.(i).(j).(4*k+1).(l)  m.(i).(j).(4*k+2).(l);
a.(i).(j).(2*k+1).(l)<- m.(i).(j).(4*k+3).(l) done done done done; a ;;

let bin_to_image_2 m = let n=nb_li m and p=nb_col m  in let a=make_matrix n p white in
for i=0 to n-1 do
	for j=0 to p-1 do
a.(i).(j)<-bin_to_int m.(i).(j) 24 done done ; a ;;

let bin_to_image m = let n=nb_li m and p=nb_col m  in let a=make_matrix n p white in
for i=0 to n-1 do
	for j=0 to p-1 do
a.(i).(j)<-rgb 
(16*(bin_to_int m.(i).(j).(0) 4)+bin_to_int m.(i).(j).(1) 4)
(16*(bin_to_int m.(i).(j).(2) 4)+bin_to_int m.(i).(j).(3) 4) 
(16*(bin_to_int m.(i).(j).(4) 4)+bin_to_int m.(i).(j).(5) 4) done done ; a ;;


let remplace_matrice_redon m =  let n=(nb_li m) and p=(nb_col m) in
let a=make_matrix n (p/48) 
[|[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|]|]
in for i=0 to n-1 do for j=0 to (p/48)-1 do a.(i).(j)<- 
[|[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|];
[|0; 0; 0; 0;|]
|] done done ;
for i=0 to n-1 do
	for j=0 to p/48-1 do
		for k=0 to 11 do
			for l=0 to 3 do
a.(i).(j).(k).(l)<- m.(i).(48*j+4*k+l) done done done done ; a ;;

let moyenne_2 a b c= let n=nb_li a and p=nb_col a in let m=make_matrix n p [|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|] in 
for i=0 to n-1 do for j=0 to p-1 do m.(i).(j)<-[|0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0; 0;0|] done done ;
for i=0 to n-1 do for j=0 to p-1 do for k=0 to 23 do m.(i).(j).(k)<-moyenne a.(i).(j).(k) b.(i).(j).(k) c.(i).(j).(k) done done done ; m ;;

(*********************************************************************) ;;

let fr n p =let a=make_matrix n p blue in for i=0 to n-1  do for j=p/3 to 2*(p/3)-1 do a.(i).(j)<-white done ;
for j=2*(p/3) to p-1 do a.(i).(j)<-red done done ; a ;;

let image_color m a b = draw_image (make_image m ) a b ;;

let image_color_err m x y a b = draw_image (make_image (conv_bin_color (err_bin(conv_color_bin m) x y))) a b ;;

let mat_color_err m x y = conv_bin_color (err_bin(conv_color_bin m) x y) ;;

let mat_color_corrige m x y = bin_to_image_2(
remplace_matrice_2(
transfo_mat4_quelc(correction(err(cod_h(transfo_quelc_mat4(simplifier_matrice_2(conv_color_bin m))))x y))  (nb_li m) ((nb_col m)*24))) ;;

let mat_color_corrige_separ m x y =bin_to_image(corrige(remplace_matrice_redon(
transfo_mat4_quelc (correction(err(cod_h(transfo_quelc_mat4(simplifier_matrice_redon(image_to_bin_redon m)))) x y)) 
(nb_li m) ((nb_col m)*48))));;

let image_color_corrige m x y a b = draw_image(
make_image(
bin_to_image_2(
remplace_matrice_2(
transfo_mat4_quelc(correction(err(cod_h(transfo_quelc_mat4(simplifier_matrice_2(conv_color_bin m))))x y))  (nb_li m) ((nb_col m)*24))))) a b ;;

let image_color_corrige_separ m x y a b = 
draw_image (make_image (bin_to_image(corrige(remplace_matrice_redon(
transfo_mat4_quelc (correction(err(cod_h(transfo_quelc_mat4(simplifier_matrice_redon(image_to_bin_redon m)))) x y)) 
(nb_li m) ((nb_col m)*48)))))) a b ;;

let image_color_primitif m x y a b = draw_image (make_image(conv_bin_color (moyenne_2 (err_bin (conv_color_bin m) x y) (err_bin (conv_color_bin m) x y) (err_bin (conv_color_bin m) x y)))) a b ;;

open_graph "";;
image_color (fr 60 100)200 20 ;;
image_color_err (fr 60 100) 1 20 200 120 ;;
image_color_corrige (fr 60 100) 1 20 200 220 ;;
image_color_corrige_separ (fr 60 100) 1 20 200 320 ;;
image_color_primitif (fr 60 100) 1 20 200 420 ;;


image_color_err (fr 60 100) 1 5 400 120 ;;
image_color_corrige (fr 60 100) 1 5 400 220 ;;
image_color_corrige_separ (fr 60 100) 1 5 400 320 ;;
image_color_primitif (fr 60 100) 1 5 400 420 ;;

moyenne_2(err_bin (conv_color_bin (fr 60 100))1 20)(err_bin (conv_color_bin (fr 60 100))1 20)(err_bin (conv_color_bin (fr 60 100))1 20);;

let dist_mat_color m1 m2 = let m3 = decompo_image m1 and m4 = decompo_image m2	 in 
let hauteur = nb_li m1  and longueur = nb_col m1 in let n = ref 0 in 
	for i = 0 to hauteur-1 do 		
		for j = 0 to longueur-1 do 
			for k=0 to 2 do
n:=!n+ val (m3.(i).(j).(k)-m4.(i).(j).(k)) done done done; !n ;;

dist_mat_color (fr 60 100) (mat_color_err (fr 60 100) 1 20) ;;
dist_mat_color (fr 60 100) (mat_color_corrige (fr 60 100) 1 20) ;;
dist_mat_color (fr 60 100) (mat_color_corrige_separ (fr 60 100) 1 20) ;;