Sequentially reading down a matrix column in MATLAB - matlab

Question

My original problem was to create a scenario whereby there is a line of a specific length (x=100), and a barrier at specific position (pos=50). Multiple rounds of sampling are carried out, within which a specific amount of random numbers (p) are made. The numbers generated can either fall to left or right of the barrier. The program outputs the difference between the largest number generated to the left of the barrier and the smallest number generated to the right. This is much clearer to see here:
In this example, the system has created 4 numbers (a,b,c,d). It will ignore a and d and output the difference between b and c. Essentially, it will output the smallest possible fragment of the line that still contains the barrier.
The code I have been using to do this is:
x = 100; % length of the grid
pos = 50; % position of the barrier
len1 = 0; % left edge of the grid
len2 = x; % right edge of the grid
sample = 1000; % number of samples to make
nn = 1:12 % number of points to generate (will loop over these)
len = zeros(sample, length(nn)); % array to record the results
for n = 1:length(nn) % For each number of pts to generate
numpts = nn(n);
for i = 1:sample % For each round of sampling,
p = round(rand(numpts,1) * x); % generate 'numpts' random points.
if any(p>pos) % If any are to the right of the barrier,
pright = min(p(p>pos)); % pick the smallest.
else
pright = len2;
end
if any(p<pos) % If any are to the left of the barrier,
pleft = max(p(p<pos)); % pick the largest.
else
pleft = len1;
end
len(i,n) = pright - pleft; % Record the length of the interval.
end
end
My current problem: I'd like to make this more complex. For example, I would like to be able to use more than just one random number count in each round. Specifically I would like to relate this to Poisson distributions with different mean values:
% Create poisson distributions for λ = 1:12
range = 0:20;
for l=1:12;
y = poisspdf(range,l);
dist(:,l) = y;
end
From this, i'd like to take 1000 samples for each λ but within each round of 1000 samples, the random number count is no longer the same for all 1000 samples. Instead it depends on the poisson distribution. For example, within a mean value of 1, the probabilities are:
0 - 0.3678
1 - 0.3678
2 - 0.1839
3 - 0.0613
4 - 0.0153
5 - 0.0030
6 - 0.0005
7 - 0.0001
8 - 0.0000
9 - 0.0000
10 - 0.0000
11 - 0.0000
12 - 0.0000
So for the first round of 1000 samples, 367 of them would be carried out generating just 1 number, 367 carried out generating 2 numbers, 183 carried out generating 3 numbers and so on. The program will then repeat this using new values it gains from a mean value of 2 and so on. I'd then like to simply collect together all the fragment sizes (pright-pleft) into a column of a matrix - a column for each value of λ.
I know I could do something like:
amount = dist*sample
To multiply the poisson distributions by the sample size to gain how many of each number generation it should do - however i'm really stuck on how to incorporate this into the for-loop and alter the code to meet to tackle this new problem. I am also not sure how to read down a column on a matrix to use each probability value to determine how much of each type of RNG it should do.
Any help would be greatly appreciated,
Anna.

Answer 1

You could generate a vector of random variables from a known pdf object using random, if you have the statistics toolbox. Better still, skip the PDF step and generate the random variables using poissrnd. Round off the value to the nearest integer and call rand as you were doing already. In your loop simply iterate over your generated vector of poisson distributed random numbers.
Example:
x = 100; % length of the grid
pos = 50; % position of the barrier
len1 = 0; % left edge of the grid
len2 = x; % right edge of the grid
sample = 1000; % number of samples to make
lambda = 1:12; % lambdas
Rrnd = round(poissrnd(repmat(lambda,sample,1)));
len = zeros(size(Rrnd)); % array to record the results
for n = lambda; % For each number of pts to generate
for i = 1:sample % For each round of sampling,
numpts = Rrnd(i,n);
p = round(rand(numpts,1) * x); % generate 'numpts' random points.
len(i,n) = min([p(p>pos);len2]) - max([p(p<pos);len1]); % Record the length
end
end