Unique factorial design or number sequence

Hi,

How would I be able to generate a unique sequence by combining [4 6 8 10 12] and [1 2 3], like the ones below:

4 4 4 4 4 1

4 4 4 4 4 2

4 4 4 4 4 3

4 4 4 4 6 1

4 4 4 4 6 2

4 4 4 4 6 3

. . .. . . . .

12 12 12 12 12 1

12 12 12 12 12 2

12 12 12 12 12 3

However, I do not need repetitions, e.g., I need only one sequence 6 8 8 8 8 1 and NOT 8 6 8 8 8 1

Answer 1

[Andrei Bobrov]

v1 = [4 6 8 10 12]; 
v2 = [1 2 3];
n1 = length(v1);
n2 = length(v2);

ii = flip(fullfact([n2,n1*ones(1,n1)]),2);
ii = ii(all(diff(ii(:,1:end-1),1,2) >= 0,2),:);
out = [v1(ii(:,1:end-1)),v2(ii(:,end))];

or without fullfact:

c = {1:n1,1:n2};
ii = cell(1,numel(v1)+1);
[ii{end:-1:1}] = ndgrid(c{[2,ones(1,n1)]});
ii = cell2mat(cellfun(@(x)x(:),ii,'un',0));
ii = ii(all(diff(ii(:,1:end-1),1,2) >= 0,2),:);
out = [v1(ii(:,1:end-1)),v2(ii(:,end))'];

EDIT

[Fayyaz]

Dear Andrei, many thanks for this.

I tried them without the fullfact but still getting the following;

1 10 12 12 12 12

2 10 12 12 12 12

3 10 12 12 12 12

1 12 12 12 10 12

2 12 12 12 10 12

3 12 12 12 10 12

But I need the first three lines, and not the last three, and manually deleting it is a lengthy job. any thought on this one?

[Andrei Bobrov]

I'm corrected my answer.

[Fayyaz]

Many thanks. That is working perfectly :)

Answer 2

[Image Analyst]

Here's one way:

v1 = [4 6 8 10 12] 
v2 = [1 2 3]
n1 = length(v1)
n2 = length(v2)
row = 1;
output = zeros(n1^5*n2, n1+1);
for k1 = 1 : n1
for k2 = 1 : n1
for k3 = 1 : n1
for k4 = 1 : n1
for k5 = 1 : n1
for k6 = 1 : n2
  vec = [v1(k1), v1(k2), v1(k3), v1(k4), v1(k5), v2(k6)];
  output(row, :) = vec;
  row = row + 1;
end
end
end
end
end
end
% Print to command window:
output

Answer 3

[mounika]

You can start with this:

a = [4 6 8 10 12];
b= [1 2 3];
c = ones(1,6); % initialize to ones
t = randi([1,5],1,1); % to randomly pick a number from 'a'
z = randi([1,3],1,1); % to randomly pick a number from 'a'
c = c.*a(t); 
c(:,end) = b(z); % assign the end value with any no of b
disp(c);

This gives numbers like: 10 10 10 10 10 2 8 8 8 8 8 3 2 2 2 2 2 1 ...

I didn't really understand the last part of your question ' However, I do not need repetitions, e.g., I need only one sequence 6 8 8 8 8 1 and NOT 8 6 8 8 8 1'

You can change the above code for your specifications.