1 # Nombre de résultats calculés

     2 # de -N à +N

     3 N = 20;

     4 # Taille du dé

     5 M = 10;

     6 # Nombre de résultats affichés

     7 # de -R à +R

     8 R = 20;

     9 # Nombre de dés

    10 J = 2;

    11 # Nombre de résultats affichés

    12 # de -R à +R

    13 R = 20;

    14 # Prob de 1 à N

    15 P1N = 1:N;

    16 # Prob de -N à N

    17 PDN = 0:2*N;

    18 

    19 NSG = 0:2*N;

    20 

    21 function y = P1_ferme(x,M,J)

    22   if ((x < 1) || (x > M))

    23     y = 0;

    24   else

    25     y = 1/M;

    26   end;

    27 end;

    28 

    29 function y = P1_limite(x,M,J)

    30   if (x < 1)

    31     y = 0;

    32   elseif (x < M)

    33     y = 1/M;

    34   elseif (x < J*M)

    35     y = P1_limite(x-M,M,J)/M;

    36   elseif (x == J*M)

    37     y = (1/M)^J;

    38   else

    39     y = 0;	

    40   end;

    41 end;

    42 

    43 function y = P1_ouvert(x,M,J)

    44   if (x < 1)

    45     y = 0;

    46   elseif (x < M)

    47     y = 1/M;

    48   else

    49     y = P1_ouvert(x-M,M)/M;

    50   end;

    51 end;

    52 

    53 function y = P1(x,M,J)

    54   y = P1_limite(x,M,J);

    55 end;

    56 

    57 function y = diff(x,P1N,N)

    58   if (x < 0)

    59     c = -x;

    60   else

    61     c = x;

    62   end

    63 

    64   if (c >= N)

    65     y = 0;

    66     return;

    67   end

    68 

    69   y = 0;

    70   for i = (c+1):N

    71     y = y + P1N(i) * P1N(i-c);

    72   end;

    73 end;

    74 

    75 function y = prob_real(N, M, J)

    76 # usage: y = prob_real(N, M, J)

    77 # Return a -N:N vector containing

    78 # the compute value of probability

    79 # for J M-side dices.

    80   for i = 1:N

    81     p1(i) = P1(i,M,J);

    82   end;

    83   for i = -N:N

    84     y(i+N+1) = diff(i,p1,N);

    85   end;

    86 end;

    87 

    88 function y = prob_theo(N)

    89 # usage: y = prob_theo(N)

    90 # Return a -N:N vector containing

    91 # the theorical value of probability

    92   for i = -N:N

    93     if (i < 0)

    94       y(i+N+1) = 0.5 * 2^(i/3);

    95     else

    96       y(i+N+1) = 1 - 0.5 * 2^(-i/3);

    97     end;

    98   end;

    99 end;

   100 

   101 PDN = prob_real(N,M,J);

   102 IPDN = cumsum(PDN);

   103 NSG = prob_theo(N);

   104 

   105 RANGE=-R:R;

   106 IRANGE=N-R+1:N+R+1;

   107 

   108 # Affichage des résultats

   109 IPDN(IRANGE)

   110 

   111 title("courbe de probabilité");

   112 plot(RANGE, IPDN(IRANGE), "-.", RANGE, NSG(IRANGE), "-");

   113 r = scanf("%s","C");

   114 title("erreur absolue");

   115 plot(RANGE, abs(IPDN(IRANGE)-NSG(IRANGE))*100);

   116 r = scanf("%s","C");

   117 title("erreur relative");

   118 plot(RANGE, abs(IPDN(IRANGE)-NSG(IRANGE))./NSG(IRANGE)*100);

   119 r = scanf("%s","C");

   120 

   121 function y = diff_sum(P,R)

   122   Psize = size(P,1)

   123   Rsize = size(R,1)

   124   for i = 1:Rsize-1

   125     off = R(i+1)-1

   126     y(i) = sum(P(R(i):off))

   127   end;

   128   y(Rsize) = sum(P(R(Rsize):Psize))

   129 end;

   130 

   131 X = PDN(N:-1:1);

   132 X = X / sum(X);

   133 S = [1;5;10;15]

   134 diff_sum(X,S)

   135