Combinations of variables and step sizing for creation of DOE

I'm using matlab to create .txt files containing variables for another program.

I'm trying to create a Design Of Experiments.

An example is, I have 3 variables,v1=5,v2=15 and v3=100

Now each variable also has a step size, v1s=1, v2s=5, v3s=10

and each variable steps by different amounts, so v1a=3,v2a=4,v3a=5

So now I have 3*4*5=60 possible different combinations.

so combination no: 1= 5,15,100 2= 6,15,100 3= 7,15,100 4= 5,20,100 5= 5,25,100 etc....

I'm trying to think of a way that can create all this on the fly for any amount of variables and step sizes but really coming unstuck here.

If anyone has some help it would be greatly appreciated.

Thanks.

Answer 1

[Walter Roberson]

I do not understand about "steps by different amounts" as distinct from "step size" ?

It is not clear from what you posted that there are upper bounds on your variables.

If there are upper bounds on the variables, then for each variable construct the list of valid values and toss it in to a cell array entry, such as

varvals{4} = v1 : v1s : v1end;

When you have them all constructed, then

[valgrids{1:length(varvals)}] = ndgrid(varvals{:});

[Walter Roberson]

Once you have done the above two steps,

tt = cellfun(@(M) reshape(M,[],1), valgrids,'Uniform',0);

combos = horzcat(tt{:}) .';

Answer 2

[Tom Lane]

Do you have the Statistics Toolbox available? It seems like what you want is a full factorial design, but with the variable levels chosen from a set other than {1,2,...,k}. Here's an example creating a two-variable design with every combination of {10,20} for the first variable and {100,200,300} for the second.

>> s1 = [10 20];
>> s2 = [100 200 300];
>> x = fullfact([2 3])
x =
     1     1
     2     1
     1     2
     2     2
     1     3
     2     3
>> x(:,1) = s1(x(:,1));
>> x(:,2) = s2(x(:,2))
x =
    10   100
    20   100
    10   200
    20   200
    10   300
    20   300

This is similar to Walter's ndgrid idea, but for three variables it gives a three-column matrix instead of three separate MATLAB variables.

[Noubara Djimadoumbaye]

Thanks Tom Lane. This answers to my question. Good night!

Answer 3

[Paul]

Let me try and rephrase this again, after reading my first question I don't believe I got my point across very well.

Yes for my variables I will have the lower limit and upper limit so the

varvals{4} = v1 : v1s : v1end;

works perfectly to give the range.

But I still have the problem.

Lets say I have

varvals{1} = 100 : 20 : 200
varvals{2} = 5 : 2 : 11
varvals{3} = 50 : 10 : 70
varvals{4} = 5 : 2 : 11 

length(varvals{1})

length(varvals{2}) 

length(varvals{3})

length(varvals{4}) 
ans =
     6
ans =
     4
ans =
   3
ans =
   4

and now 6*4*3*4=288

Which means out of the 4 variables I can make 288 different combinations.

What my program needs to do is store all these 288 combinations into different files, eg output_1.txt output_2.txt..... output_288.txt

The file writing part is easying, sorting the data into a matrix is now what I'm having trouble with.

In this situation I would need a matrix of size (4,288) so each column is one of the unique 288 combinations, then I can just write each column into my separate file.

Creating this matrix is what I'm now stuck on.

[Walter Roberson]

I added the final two steps to my Answer above.