How modifying the input of a function : from (unique) vector to matrix ?

Hi,

I have a script that compute an index. The input of the function is:

(i) the vector of weight of each player (l) and;

(ii) the quota (limit).

It works well for a single vector. However, I need help to modify the code in order to compute the index for several cases (several vectors) (the quota "limit" stay always invariable that we specify in the beginning (ex. 50 or 40 or 20...)). In other words, I want that the input will be:

(i) the matrix summarizing several vectors of weight of each player (l) and;

(ii) the quota (limit).

Example:

Instead of doing the computation on l1 = [20 30 15 25 10] then on l2 = [49 2 49 0 0], then l3 ...., I would like that my input in the function will be a matrix with several lines like for example :

(i) L = [20 30 25 25; 49 2 49 0 0; 20 30 15 25 10; 49 2 49 0 0].

(ii) limit = 50

Thank you in advance for your help and for you support.

function [shapley]=shapley(l, limit)
n = length(l);
C = generate_all_coalitions(n);

s = C*l';
shapley = zeros(n,1);
for party = 1:n
    
    sizeT = 0;
    for k = 1:length(s)
        row = C(k,:);
        modrow = row;
        modrow(party) = 0;
        if row(party)
            
            if (row*l' > limit && modrow*l' <= limit)
                sizeT = sum(row);
                shapley(party) = shapley(party) + factorial(sizeT - 1)*factorial(n-sizeT)/factorial(n);
            end
        end
    end
end
end
function [c] = generate_all_coalitions(n)
c = zeros(1,n);

for k = 1:(2^n-1)
    c(k+1,:) = convert_to_binary(k,n);
end
end
function [x] = convert_to_binary(n,max)
x = zeros(1,max);
for k = max-1:-1:0
    if n - 2^k >= 0
        n = n - 2^k;
        x(k+1) = 1;
    else
        x(k+1) = 0;
    end
end
end

Answer 1

[Rik]

You can always add a recursive call in case of a matrix input. Also, to keep your code understandable you should write a short block that describes the goal of the function and it's inputs and outputs. The rest of your function should have explanatory comments, so other people can understand it as well (future you is another person as well). As final remarks: don't ignore m-lint warnings (they are very useful), avoid lower-case L as a variable name (as it is easily confused with numeric 1 when reading), and very importantly: don't use your function name as the name of your output variable.

function shapley_output=shapley(player_weight, limit)
if size(player_weight,1)>1
    shapley_output=shapley(player_weight(1,:), limit);
    for n=2:size(player_weight,1)
        shapley_output(:,n)=shapley(player_weight(n,:), limit);
    end
    return
end

n = numel(player_weight);
C = generate_all_coalitions(n);

s = C*player_weight';
shapley_output = zeros(n,1);
for party = 1:n
    for k = 1:length(s)
        row = C(k,:);
        modrow = row;
        modrow(party) = 0;
        if row(party)
            if (row*player_weight' > limit && modrow*player_weight' <= limit)
                sizeT = sum(row);
                shapley_output(party) = shapley_output(party) + ...
                    factorial(sizeT - 1)*factorial(n-sizeT)/factorial(n);
            end
        end
    end
end
end
function [c] = generate_all_coalitions(n)
c = zeros(1,n);
for k = 1:(2^n-1)
    c(k+1,:) = convert_to_binary(k,n);
end
end
function [x] = convert_to_binary(n,max)
x = zeros(1,max);
for k = max-1:-1:0
    if n - 2^k >= 0
        n = n - 2^k;
        x(k+1) = 1;
    else
        x(k+1) = 0;
    end
end
end

[Guillaume]

With regards to Rik's point about documenting what a function does and what are its inputs and outputs, see this example I posted not too long ago.

edit: I apologise Rik, for mispelling your name.

[Rik]

No problem, if I got a euro for every time my name was spelled with a c I'dd be a rich man ;)

Answer 2

[jaouad daoudi]

Hi Rik,

First, thank you for your implication, your answer and also for your recommandation. I really appreciate.

However, I run your script and it works for a vector and not for a matrix.

For example, when I specify:

limit = 50 and player_weight = [49 2 49 ; 49 2 49], I have the follwing message:

">> shapley_output=shapley(player_weight, limit)

error: shapley: operator *: nonconformant arguments (op1 is 64x6, op2 is 3x2)

error: called from shapley at line 10 column 3"

Please, do you have a solution to fix that?

Thank you again for your support and have a nice day.

[Rik]

It appears I forgot to put in the return after the loop, see my edited code.

Also, you posted this comment in the answer field. Please use the comment field next time, as the order of answers can change, which may cause confusion for future readers.

[jaouad daoudi]

Hi Rik,

THANK YOU VERY MUCH FOR YOUR SUPPORT AND FOR YOUR VERY PRECIOUS HELP. I APPRECIATE IT ENORMOUSLY!

YOUR MODIFICATION WORKS EFFICIENTLY AND SAVE ME LOT OF TIME. THANK YOU!

If it’s not too much to ask, I would like to have your opinion on one point:

In the current matlab file, one of my input (player_weight) is a matrix, but in my reality:

1- I get my data in an Excel file (I send you an example in the attached file), and

2- I must get the results of my Matlab script in Excel readable format so that I can do statistical analysis later.

So, I would like that my Matlab script (i) download the data from the "Input" sheet of my Excel file, (ii) compute the "shapley" function and; (iii) store the result in the "Output" sheet of the same Excel file.

Rik, please, is that feasible with Matlab? if so, can you help me with an adequat script? if no, do you have a proposal to make to me? Your help is more than welcome.

Thank you again Rik and looking forward to hearing from you.

Sincerely...

[Rik]

You can use xlsread and xlswrite to read from and write to excel files. Their documentation pages will list several examples. (note that empty rows and empty columns are generally ignored by xlsread, so you should keep that in mind)

[jaouad daoudi]

Thank you very much Rik. You really helped me!

Your last recommendation works also well. Now, I'm going to move on to serious things and I will start working with real data with thousands of lines. Wish me good luck;) Thanks again.