Combinations with a condition

I am trying to create a matrix that list all combinations possible under a certain condition. Right now I am creating all combinations and then filtering but the matrix of combination is too large.

I want to keep only when

Thank you

I am putting an example with smaller vector size

x = [0 0.25 0.5 0.75 1]
x_1 = [0 0.5 1]
x_2 = [0 0.5 1]

[Torsten]

I don't understand your example.

[Les Beckham]

Combinations of what?

[Jan]

I don't either. What are the inputs you want to combine?

[Nicolas Leport]

Sorry I wasn't clear

I want to have all to possible combinations of x, x_1 and x_2 with the condition

I want to end with something like this

Hope it makes more sense

0	    0	 0
0.25	0	 0.5
0.25	0.5	 0
0.5 	0	 1
0.5	    0.5	 0.5
0.5 	1	 0
0.75	0.5	 1
0.75	1	 0.5
1	    1	 1

Answer 1

[Voss]

Maybe something like this?

x = [0 0.25 0.5 0.75 1];
x_1 = [0 0.5 1];
x_2 = [0 0.5 1];

x_12 = (x_1.'+x_2)/2;
[ism,idx] = ismember(x_12,x);
[r,c] = find(ism);
result = [x_1(r); x_2(c); x(idx(ism))].'

result = 9×3

0 0 0 0.5000 0 0.2500 1.0000 0 0.5000 0 0.5000 0.2500 0.5000 0.5000 0.5000 1.0000 0.5000 0.7500 0 1.0000 0.5000 0.5000 1.0000 0.7500 1.0000 1.0000 1.0000

[Nicolas Leport]

Hopefully yes, just with the the 3rd column in an increasing order

[Voss]

x = [0 0.25 0.5 0.75 1];
x_1 = [0 0.5 1];
x_2 = [0 0.5 1];

x_12 = (x_1.'+x_2)/2;
[ism,idx] = ismember(x_12,x);
[r,c] = find(ism);
result = [x_1(r); x_2(c); x(idx(ism))].';

% sort on 3rd column:
[~,idx] = sort(result(:,3));
result = result(idx,:)

result = 9×3

0 0 0 0.5000 0 0.2500 0 0.5000 0.2500 1.0000 0 0.5000 0.5000 0.5000 0.5000 0 1.0000 0.5000 1.0000 0.5000 0.7500 0.5000 1.0000 0.7500 1.0000 1.0000 1.0000

[Nicolas Leport]

Thank you!

[Voss]

You're welcome!

[Nicolas Leport]

How would you modify it if I wanted to add a x_3 and now (x1+x2+x3)/3=x ?

[Walter Roberson]

Voss's solution creates all combinations and filters them, which you had said gets too large for your purposes.

ismember with floating point is risky. This example with exact fractions of powers of 2 gets away with it, but you would have problems with 0.1 and 0.2 for example

[Nicolas Leport]

I actually changed x, x1, x2 to be whole number and then divide the result matrix by the number of data points. It works fine. But I don't know how to modify it to do it with x, x1, x2 and x3