Full Factorial Design of Experiments

Hello together,

i am about to write a code that should produce me a txt file with a full factorial combination of the input of vectors. The vectors could have a different length. I know about the matlab function fullfact([,]) but since I will use decimal numbers i needed a differen solution.

I tested the code and it seems to work. But do I make a mistake, that I may have not seen yet? The vectors that i defined in this skript are just for example. Later on I will use a input and the vectors will result in much bigger ones.

clc
clear
pyrz = [1, 2];
pyrx = [1, 2, 3];
pyra = [1, 2];
%I need to know the final count of columns in the resulting matrix
Avert=length(pyrz)*length(pyrx)*length(pyra);

if sum (pyrx) == 0
     pyrx = zeros(1, Avert);
elseif sum (pyrx) ~= 0
     count = Avert/length(pyrx);
     pyrx = repmat(pyrx,1,count);
end

count = Avert/length(pyrz);
pyrz = repmat(pyrz,1,count);
pyrz = sort(pyrz);

count = Avert/length(pyra);
pyra = repmat(pyra,1,count);
pyra = sort(pyra,'descend');

Answer 1

[dpb]

"I know about the matlab function fullfact([,]) but since I will use decimal numbers i needed a differen solution."

There's no reason still to not use fullfact; the levels [1:Nl] are simply placeholders for the actual levels for each factor, not the experimental levels themselves.

If you want to write an array/file that contains the actual levels themselves, just use a lookup table of the level into the values you define for each level. Nothing more is needed.

Small example for brevity; principle holds in general no matter the number of factors and levels...

>> ff=fullfact([3,2])           % design matrix for 3x2 full factorial
ff =
     1     1
     2     1
     3     1
     1     2
     2     2
     3     2
>>
>> LVLS=[4.3*[-1:1];[pi*[-1 1] nan]].'          % array of Levels by column 
LVLS =
   -4.3000   -3.1416
         0    3.1416
    4.3000       NaN
>>

Now build the array of experiment levels

>>FF=cell2mat(arrayfun(@(r)[LVLS(ff(r,1),1) LVLS(ff(r,2),2)],1:size(ff,1),'UniformOutput',false).')
FF =
   -4.3000   -3.1416
         0   -3.1416
    4.3000   -3.1416
   -4.3000    3.1416
         0    3.1416
    4.3000    3.1416
>>

You could, of course, keep separate vector arrays for each factor or a cell array, I used an array with a NaN element for the missing levels to avoid the cell array route as it will never be referenced so it's just a placeholder to make a rectangular array.

[mbyrl]

Thank you, for your advice and work you put into your answer! I now need to think about it.

[Sema Karakus]

Is there any way to implement restrictions for some of the factors?

[dpb]

What kind of restrictions?