assigning a probability to a loop

Hello,

I am making a random walk code, and I want to assign a probability to the direction chosen. I found a way to do this with IF loops, as in the code below, using the variable J:

x=2; %starting poition in X and Y
y=3;
v=50; %number of steps

X=[]; 
Y=[];
X(1)= x;   
Y(1)= y;

for i=1:v       
    J=rand;     % Random value to decide on direction.

      if J<0.3                                 % Go North
          X(i+1)=X(i)+1;
          Y(i+1)=Y(i);

      elseif (J>0.3) && (J<0.45)              % Go NW
          X(i+1)=X(i)+1;
          Y(i+1)=Y(i)-1;

      elseif (J>0.45) && (J<0.6)                %Go NE
          X(i+1)=X(i)+1;
          Y(i+1)=Y(i)+1;

      elseif (J>0.6) && (J<0.7)                 % Go East
          X(i+1)=X(i);
          Y(i+1)=Y(i)+1;

      elseif (J>0.7) && (J<0.8)                 % Go West
          X(i+1)=X(i);
          Y(i+1)=Y(i)-1;

      elseif (J>0.80) && (J<0.875)             % Go SE
          X(i+1)=X(i)-1;
          Y(i+1)=Y(i)+1;

      elseif (J>0.875) && (J<0.95)            % Go SW
          X(i+1)=X(i)-1;
          Y(i+1)=Y(i)-1;

      else                                      %Go south
          X(i+1)=X(i)-1;
          Y(i+1)=Y(i);

      end
      plot (X, Y)

end

I am wondering if there is an easier way to assign a probability of an event happening. Ideally I'm looking for a way to just enter a %. e.g:

for i=1:v       

        In 30% of cases, do this:       %North
            X(i+1)=X(i)+1;
            Y(i+1)=Y(i);

        In 15% of cases, do this:             % Go NW
            X(i+1)=X(i)+1;
            Y(i+1)=Y(i)-1;

and so on.

Thank you.

Answer 1

[Walter Roberson]

Create your probability vector with the per-state probabilities, and then cumsum() the vector to get the boundaries for the range rand() has to fall in.

If you want, you could combine that with a find() to determine the state number, and then switch on the state number rather than on the probabilities.

Answer 2

[Fangjun Jiang]

See this post. random number generation with changing probability