permutation matrix for process simulation

Hello,

I'd like to test the combined effect of different filtration unit (diafiltration, ultrafiltration,...) and used them in different order. For now I have a manual code that works with a small number of unit filtration, but I would like to find something more generic and that would work with a N filtration units. For that, I need a matrix that contains the different possibilities.

The idea is to test firstly all the filtration units separately and then combine them gradualy while permuting the order.

Separator 1

Separator 2

...

Separator 1 / Separator 2

Separator 2 / Separator 1

Separator 1 / Separator 3

...

Separator 1 / Separator 2 / Separator 3

...

a=1; %Separator1
b=2; %Separator2
c=3; %Separator3
d=4; %Separator4

a1=[perms(a),0,0,0];
a2=[perms(b),0,0,0];
a3=[perms(c),0,0,0];
a4=[perms(d),0,0,0];
a5=[perms([a,b]),zeros(2,2)];
a6=[perms([a,c]),zeros(2,2)];
a7=[perms([a,d]),zeros(2,2)];
a8=[perms([b,c]),zeros(2,2)];
a9=[perms([b,d]),zeros(2,2)];
a10=[perms([c,d]),zeros(2,2)];
a11=[perms([a,b,c]),zeros(6,1)];
a12=[perms([a,b,d]),zeros(6,1)];
a13=[perms([b,c,d]),zeros(6,1)];
a14=perms([a,b,c,d]);
A=[a1;a2;a3;a4;a5;a6;a7;a8;a9;a10;a11;a12;a13;a14];

the results I need is that:

A=
1	0	0	0
2	0	0	0
3	0	0	0
4	0	0	0
2	1	0	0
1	2	0	0
3	1	0	0
1	3	0	0
4	1	0	0
1	4	0	0
3	2	0	0
...

thanks by advance,

bruno

Answer 1

[Jon]

You should be able to loop using perms and nchoosek to do what you need.

Something like this:

% generate filtration test matrix
numFilters = 4

filters = 1:numFilters
A = [];
for i = 1:numFilters
    % generate a matrix with all the ways of choosing the current number of filters
    C = nchoosek(filters,i);
    % loop through each of the possible ways of choosing this many filters
    for j = 1:size(C,1);
        % get all of the permutations of the current selection
        B = perms(C(j,:));
        Z = zeros(size(B,1),numFilters-size(B,2));
        % add the new block of permutations and an appropriately sized block of zeros
        A = [A;[B Z]];
    end
end

By the way, I think in your manual code you forgot the permutations of [1 3 4] ie perms([a,c,d])

The above code grows the A matrix in a loop, rather than having it preallocated as is recommended for better memory management/performance. If the performance mattered you could probably work out how many rows A will have in advance and preallocate it, but the combinatorics were a little daunting :)

[bruno ebel]

Thanks a lot, it's exactly what I want to do.

Actually, with my manual code, I forgot some combinations :-) (a,c,b and some others...)

just a last question about that, do you know if it's possible to have a matrix with the unit names directly in it?

like that :

    'separator 1  seperator 2   0  0 '
    'seperator 2  separator 1   0  0 '

thanks again,

bruno

[Stephen23]

"just a last question about that, do you know if it's possible to have a matrix with the unit names directly in it?"

Use a table:

https://www.mathworks.com/help/matlab/tables.html

[Jon]

Hi Bruno, Glad to hear that this code did exactly what you wanted. Hopefully you can combine it with Stephen's suggestion to use a table to have the unit names directly in it. If this answers your question, when you have a chance it would be good to "accept" the answer. This way others who may have a similar problem will know that an answer is available

[bruno ebel]

Ok thanks a lot, i will test the table.

thanks again,

bruno