how to build logical relationships between elements of two vectors?

Hi everyone. I have a question that how can i correlate the element in two matrices. For example that suppose i have a matrix A=[a1 a2 a3 a4] and matrix B=[b1 b2], both a1 throught a4 and b1 through b4 are binary decions variables meaning that they can either be 0 or 1.

My question is that I want to put a correlation (or like a constraint) between matrix A and B that b1 turns to 1 when and only when a1 and a2 turn to 1, and b2 turns to 1 when and only when a3 and a4 turns to 1.

thank you!

[Adam]

I'm not aware that you can do this on raw arrays, but you could write a simple function to calculate b from a and call that instead of trying to keep a b-vector permanently updated. Or you could wrap them together in a class and either automatically change b when a changes or make it into a dependent property (which is essentially the same as the first option of making it into a function, except it becomes an implementation detail rather than a visible change code-wise.

[BOWEN LI]

Hi Adam thanks so much for your answer. I tried to put a and b together either as a function or dependent property, but in my case, both a and b are actually my decision variables of my integer optimization problem. I have like many 0-1 type decision varibles (in this case, 6 decision varibles), and A has the first 4 of them (a1-a4) and B has the last 2 (b1-b4). So I am trying to let b be automatically updated if a1 and a2 are simutaneously turn to 1 and for b2 as well, as you mentioned b and a have a dependent property. So I stucked here that this kind of logical relationship i have no exact idea of how to interpret it into codes. Thank you!

[John D'Errico]

You cannot do this with two standard arrays or vectors, that is, have them automatically linked in some way that when one changes, the other does too.

You cam write a function that computes b from a. But you would need to execute that function whenever you were interested in the value of b.

Answer 1

[Shivam Prasad]

Hi BOWEN,

Code for modifying the values of B according to values in A:-

A = [1 0 1 0;1 1 0 0;1 1 1 1;1 1 0 1;0 1 1 1]; % define some nX4 array.
B = [1 1;0 1;1 0;0 0;1 0]; % define some nX2 array. 

if(size(A,1)~=size(B,1))
   error('Dimensions incompatible')    % the number of rows must match. 
end

for i=1:size(A,1)
    if(A(i,1)==1 && A(i,2)==1)    % if both a1 and a2 are 1, turn b1 to 1
        B(i,1)=1;
    end
    if(A(i,3)==1 && A(i,4)==1)    % if both a3 and a4 are 1, turn b2 to 1
        B(i,2)=1;
    end
end

disp(B)

Code for implementing the above constraint:-

A=[1 0 1 0;1 1 0 0;1 1 1 1;1 1 0 1;0 1 1 1]; % define some nX4 array.
B=[1 1;0 1;1 0;0 0;1 0]; % define some nX2 array. 

if(size(A,1)~=size(B,1))
   error('Dimensions incompatible')     % the number of rows must match.
end

for i=1:size(A,1)
    if(A(i,1)==1 && A(i,2)==1) && B(i,1)==0
        error('Constraint a1,a2,b1 failed!')   % if both a1 and a2 are 1, b1 should be 1 
    end
    if(A(i,3)==1 && A(i,4)==1) && B(i,2)==0
        error('Constraint a3,a4,b2 failed!')    % if both a3 and a4 are 1, b2 should be 1
    end
end

disp(B)