how to build logical relationships between elements of two vectors?

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BOWEN LI
BOWEN LI 2019-10-9
编辑： Shivam Prasad 2019-10-14
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!
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BOWEN LI
BOWEN LI 2019-10-9
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
John D'Errico 2019-10-9
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.

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Shivam Prasad
Shivam Prasad 2019-10-14
编辑：Shivam Prasad 2019-10-14
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)

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