Why is the Matches variable too large?

I was playing around with a code that produces a simulator for the birthday paradox. Here's the piece of code:

ready = false;
while ~ ready
    % User inputs and defining variables
    birthday_repeats = input('select the number of birthday repeats from 10-500:');
        if birthday_repeats > 500 || birthday_repeats < 10 || isempty(birthday_repeats) || round(birthday_repeats) ~= birthday_repeats|| isnan(birthday_repeats)
            disp('error')
            continue
        end
    sample_size = input('Select the sample size from 2-365: ');
        if sample_size > 365 || sample_size < 2|| isempty(sample_size) || round(sample_size) ~= sample_size || isnan(sample_size)
            disp('error')
            continue
        end
   matches = zeros(1,sample_size);
   N = 1000;
   days = randi(1,365);
   % simulation run
    for k = 1:birthday_repeats % desired number of trials 
        matches = 0;
        for j = 1:days
            if test(days)
                matches(sample_size) = matches(sample_size) + 1;
            end
        end
        match_tally = matches(sample_size)/N;
    end

I'm not sure why after each iteration of the loop the variable 'matches(sample_size)' is too large and here's the the 'test' function:

function out = test(data)
out = false;
n = length(data);
for k = 1:n
    for i = k+1:n
        if data(k) == data(i)
            out = true;
            break
        end
    end
 end
end

Answer 1

[chicken vector]

Because you initialise the variable matches two times

You first set it as a vector, and then for each loop iteration you set it as a scalar.

matches = zeros(1,sample_size);
N = 1000;
days = randi(1,365);
for k = 1:birthday_repeats
    matches = 0;     %-------------------- DELETE THIS LINE --------------------%
    for j = 1:days
        if test(days)
            matches(sample_size) = matches(sample_size) + 1;
        end
    end
    match_tally = matches(sample_size)/N;
end

[Kiran Sai]

If I just set matches to 0 will the loop work?

[chicken vector]

No, if you set it to zero you can matches as a 1x1 vector.

If sample_size is, for example, 10, by doing:

matches(sample_size)

You are trying to access the 10th element of a 1x1 vector.

I don't how th rest of the code continues so I can't really suggest you the right path to take, but if you need the variable matches to be a number and not a vector, do the following:

matches = 0;
N = 1000;
days = randi(1,365);
for k = 1:birthday_repeats
    for j = 1:days
        if test(days)
            matches = matches + 1;
        end
    end
    match_tally = matches/N;
end

Note that I initialise

matches = 0;

Outside the loop, not inside as you have done before, because otherwise it would reset to zerto at every iteration.

[Kiran Sai]

Here's the actual code:

% User inputs and defining variables
disp('Welcome to the Birtday Paradox')
ready = false;
while ~ ready
    % User inputs and defining variables
    birthday_repeats = input('select the number of birthday repeats from 10-500:');
        if birthday_repeats > 500 || birthday_repeats < 10 || isempty(birthday_repeats) || round(birthday_repeats) ~= birthday_repeats|| isnan(birthday_repeats)
            disp('error')
            continue
        end
    sample_size = input('Select the sample size from 2-365: ');
        if sample_size > 365 || sample_size < 2|| isempty(sample_size) || round(sample_size) ~= sample_size || isnan(sample_size)
            disp('error')
            continue
        end
   days = randi(365,sample_size);
   tally = zeros(1,sample_size);
   match = 0;
   % simulation run
        for k = 2:sample_size
            birthdays = randi(365,1,k);
            for j = 1:birthday_repeats% desired number of trials
                if test(days)
                    match(sample_size) = match(sample_size) + 1;
                end
            end
            match_tally = match/N;
         end
            
         
   
    % plotting graphs
    domain = 2:sample_size;
    figure(1)
    plot(domain,match_tally(2:sample_size))
    xlabel('Number of people Chosen')
    title('Birthday Paradox simulation')
    ylabel('Probability')
    break
end

I tried your change and the match variable is still too large.

[chicken vector]

You are doing a lot of unecessary for loops where each iteration just overwrites the results of the previous.

For this reason, it is not quite clear what you want to plot in th end.

Is this what you are looking for:

%% Input:
% disp('Welcome to the Birtday Paradox')
% birthday_repeats = input('select the number of birthday repeats from 10-500:');
% if birthday_repeats > 500 || birthday_repeats < 10 || isempty(birthday_repeats) || round(birthday_repeats) ~= birthday_repeats|| isnan(birthday_repeats)
%    error('Wrong input');
% end
% sample_size = input('Select the sample size from 2-365: ');
% if sample_size > 365 || sample_size < 2|| isempty(sample_size) || round(sample_size) ~= sample_size || isnan(sample_size)
%     error('Wrong input');
% end

% Uncomment previous and comment this:
birthday_repeats = 500;
sample_size = 23;

%% Process:
domain = 2 : sample_size;
match_tally = zeros(1,sample_size-1);
for j = 2 : sample_size
    matches = zeros(1,j);
    for k = 1 : birthday_repeats
        birthdays = randi(365,1,j);
        matches(k) = any(histcounts(birthdays,1:365) > 1);
    end
    match_tally(j-1) = sum(matches)/birthday_repeats;
end

expected_probability = 1 - prod(((365-sample_size+1):365)./365);

%% Plot:
figure;
hold on;
plot(domain,match_tally)
yline(expected_probability)
text(2,.97*expected_probability,['Expected probability for ' num2str(sample_size) ' people: ' num2str(expected_probability)])
grid on;
xlabel('Number of people chosen')
ylabel('Probability')
title('Birthday Paradox simulation')
subtitle([num2str(birthday_repeats) ' evaluations for each sample'])

[Kiran Sai]

Yeah, I just didn't understand how get my loop working as well as the formula to find the probability of matches. Thank you so much G.

Answer 2

[Walter Roberson]

days = randi(1,365);

That does not request a random number between 1 and 365. That requests 365 x 365 random numbers in the range 1 to 1.

[Kiran Sai]

Will this:

days = randi(365,1,365)

days = 1×365

10 154 189 303 94 360 307 61 191 200 359 232 126 224 303 144 130 192 122 130 171 283 142 151 33 306 9 362 210 111

generate a 1x365 matrix containing random numbers

[Walter Roberson]

Yes, you can see from the summary output

days = 1x365

that it has generated a 1 x 365 array.

Note that many elements in days will be repeated. If you need to have a random permutation of the day numbers, use randperm