self avoiding random walk
显示 更早的评论
i need help. what i think i have to do is choose a direction at random and then look at a direction i want to go to if it's empty then carry on. if the direction is used then you start another walk. 1000 walks and lenght 1 to 25. how do i calcalute the number of successful walks. the code i have is a random walk
r=[0 0];
X=[0];Y=[0];
for
t= 1:1:100
B=rand(1,1)*4;
if B<1
new_position=r+[1 0];
elseif B<2
new_position=r+[0 1];
elseif B<3
new_position=r+[-1 0];
else
new_position=r+[0 -1];
end
X=[X new_position(1)];
Y=[Y new_position(2)];
r=new_position;
end
plot(X,Y)
2 个评论
Image Analyst
2013-11-18
编辑：Image Analyst
2013-11-18
http://www.mathworks.com/matlabcentral/answers/13205-tutorial-how-to-format-your-question-with-markup How do you define "empty"? Are you trying to avoid having the next step cross any paths on the route so far?
nawal
2013-11-18
采纳的回答
Roger Stafford
2013-11-19
As I see it from all you have stated, Nawal, you wish to "walk" point-to-point starting at (0,0) for a maximum of 25 steps, at each step moving a distance of one unit in one of four possible directions: up, left, down, or right with equal probabilities. However you wish to quit the walk if before 25 successful steps you would occupy a point that has already been traversed. Your aim is to count the number of successful walks, that is, the number in which you successfully reached 25 unoccupied points, out of a total of one thousand attempted walks. Do I state your problem correctly? (Your later remark that "it lands within a certain distance" throws some uncertainty into this interpretation. Are you sure you meant to concede this? You are dealing with exact integral positions here. Based on your earlier remarks, that "certain" distance should be an exact zero!)
In the following code the variable w will count the number of walks, the variable c will count the number of successful walks, the variable s will count the number of successful steps taken in each walk, and the 51 x 51 array Occ will record the positions already occupied during each walk.
c = 0; % This counts the number of "successful" walks
tx = [1,0,-1,0];
ty = [0,1,0,-1];
for w = 1:1000 % w counts the walks attempted
Occ = zeros(51); % Keeps track of occupied points
x = 26; % It is equivalent to start at (26,26) rather than (0,0)
y = 26;
Occ(x,y) = 1; % w counts the walks attempted
s = 0; % Start number of steps at zero for each walk
b = true;
while b & (s<25) % Quit if walk abandoned or succesful
r = randi(4);
x = x + tx(r);
y = y + ty(r);
if Occ(x,y) == 1
b = false;
else
Occ(x,y) = 1;
s = s + 1;
end
end
if s == 25
c = c + 1; % Count the number of successful walks
end
end
6 个评论
nawal
2013-11-19
Roger Stafford
2013-11-20
编辑：Roger Stafford
2013-11-20
Yes, that's easy. Right after each exit from the above while-loop add 1 to an element of a 25-element array indexed by s where the array is initially all zeros. Afterwards the counts in this array when divided by 1000 would be your desired proportions. (The 25th element will actually be the sum of all the cases where the maximum would have been 25 or greater if the steps had been continued beyond 25.)
However, possibly you mean that you wish to repeat the whole thousand-walk experiment for each possible maximum value from 1 to 25. If that is your meaning, you pretty much place the above code within an outer for-loop that varies the limit from 1 to 25. You will have to place the c values in some array indexed by the outer for-loop varying maximum value, which when divided by 1000 would be the desired proportions. Note that these proportions have a different significance than those above. In each case they represent the proportion that would have run this particular maximum value or higher, whereas the earlier proportions were those that stopped exactly at the corresponding maximum value (except of course for the last, 25th value which has the same meaning in both cases.)
Image Analyst
2013-11-20
nawal, you threw us when you used rand() instead of randi(), so your code generated fractional floating point numbers, not integers. But Roger suggested integers and you said that's what you meant (but didn't say). (Saying that in advance would have saved me and you the 5 attempts to get more information and clarification from you.) As he says, it's easy to record and plot the points at each step and I think you can do that yourself so if I were you I'd just mark Roger's answer as "Accepted" to close it out.
Roger Stafford
2013-11-20
Image Analyst, where Nawal wrote
B=rand(1,1)*4;
if B<1
new_position=r+[1 0];
elseif B<2
new_position=r+[0 1];
elseif B<3
new_position=r+[-1 0];
else
new_position=r+[0 -1];
end
in his original problem statement, it was the logical equivalent of using the output of randi as an index, and his code did not produce fractional displacements of x and y but rather changes only by -1, 0, and +1 just as in my code. I only used randi because it produced more compact coding, and not to alter his logic.
Image Analyst
2013-11-20
编辑：Image Analyst
2013-11-20
You're right. I didn't notice that. Comments in the code, and proper indenting, would have been helpful.
nawal
2013-12-8
更多回答（1 个）
Image Analyst
2013-11-19
0 个投票
"By empty I mean the point is occupied/ already visited" - I doubt that will never happen, at least probably not in your lifetime. The chance of a pair of double precision numbers being repeated exactly is vanishingly small.
7 个评论
Walter Roberson
2013-11-19
The direction is random, but it appears the choices of direction are left, right, up, down.
Image Analyst
2013-11-19
Is he then saying that the quadrant has one or more points in it, as opposed to landing exactly on the precise location of a prior point?
nawal
2013-11-19
Image Analyst
2013-11-19
Still unclear. What if I was at (1,0) and I stepped to (2,0). So if I step back in the general direction where I came from (back along the x axis towards the origin) and I would land at exactly (to the maximum precision allowed by the computer) (1,0) I can see that you want to stop. But like I said, you won't ever land there. So what if you'd land at (1.000000001, 0.000009), which is really really close? Do you want to stop in that case too?
nawal
2013-11-19
Image Analyst
2013-11-19
编辑：Image Analyst
2013-11-19
Still unclear. When do you want to stop it?
- If it lands anywhere in the "backwards" half plane?
- Or if it lands within a certain distance from the last point?
- Or if it lands within a certain distance from any prior point?
Which case(s)?
nawal
2013-11-19
类别
在 帮助中心 和 File Exchange 中查找有关 Logical 的更多信息
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
Translated by 
