# Nombre de résultats calculés

# de -N à +N

N = 20;

# Taille du dé

M = 10;

# Nombre de résultats affichés

# de -R à +R

R = 20;

# Nombre de dés

J = 2;

# Nombre de résultats affichés

# de -R à +R

R = 20;

# Prob de 1 à N

P1N = 1:N;

# Prob de -N à N

PDN = 0:2*N;

NSG = 0:2*N;

function y = P1_ferme(x,M,J)

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

    y = 0;

  else

    y = 1/M;

  end;

end;

function y = P1_limite(x,M,J)

  if (x < 1)

    y = 0;

  elseif (x < M)

    y = 1/M;

  elseif (x < J*M)

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

  elseif (x == J*M)

    y = (1/M)^J;

  else

    y = 0;	

  end;

end;

function y = P1_ouvert(x,M,J)

  if (x < 1)

    y = 0;

  elseif (x < M)

    y = 1/M;

  else

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

  end;

end;

function y = P1(x,M,J)

  y = P1_limite(x,M,J);

end;

function y = diff(x,P1N,N)

  if (x < 0)

    c = -x;

  else

    c = x;

  end

  if (c >= N)

    y = 0;

    return;

  end

  y = 0;

  for i = (c+1):N

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

  end;

end;

function y = prob_real(N, M, J)

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

# Return a -N:N vector containing

# the compute value of probability

# for J M-side dices.

  for i = 1:N

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

  end;

  for i = -N:N

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

  end;

end;

function y = prob_theo(N)

# usage: y = prob_theo(N)

# Return a -N:N vector containing

# the theorical value of probability

  for i = -N:N

    if (i < 0)

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

    else

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

    end;

  end;

end;

PDN = prob_real(N,M,J);

IPDN = cumsum(PDN);

NSG = prob_theo(N);

RANGE=-R:R;

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

# Affichage des résultats

IPDN(IRANGE)

title("courbe de probabilité");

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

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

title("erreur absolue");

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

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

title("erreur relative");

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

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

function y = diff_sum(P,R)

  Psize = size(P,1)

  Rsize = size(R,1)

  for i = 1:Rsize-1

    off = R(i+1)-1

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

  end;

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

end;

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

X = X / sum(X);

S = [1;5;10;15]

diff_sum(X,S)