How do I multiply 2 1 by 200 vectors and record when a particular answer is achieved?

I need to do some mixer calculations. I have 2 1x200 double vectors. I need to multiply each member of 1 vector by a constant, say 3, and then subtract 2 times the appropriate member of the second vector. In other words, I need to get the solution to 3*a(1)-2*b(1) and get an answer. If the answer is 45, I need to note what a(x) and b(x) produced that result. I need to go through all 200 members of each vector. So, 40,000 calculations. In other words, starting as mentioned, the next problem to be solved would be 3*a(1)-2*b(2). If the answer is 45, record a(1) and b(2). If the answer is not 45, then solve 3*a(1)-2*b(3), etc until 3*a(1)-2*b(200). Then, we would go to 3*a(2)-2*b(1) until we get to 3*a(2)-2*b(200), etc. What is the easiest way to do that in Matlab. I have the latest version?

Answer 1

[Walter Roberson]

[A, B] = ndgrid(a, b);
T = 3*A - 2*B - 45;
ind = find(T(:)==0);
[r, c] = ind2sub(size(A), ind);
sols = [r(:), c(:), A(ind), B(ind)];

This would produce an N x 4 array in which the first column is the entry number in a, the second column is the entry number in b, the third column is the value from a, the fourth column is the value from b.

[Ed Troy]

Thanks to everyone. I suspect all of the answers work, but this one was really nice, quick, and elegant and produced a nice table that I can use.

Answer 2

[Geoff Hayes]

Ed - the easiest (and so not the most efficient) is to use two for loops to iterate over the data. For example,

 A = randi(1000,1,200);
 B = randi(1000,1,200);

 for u=1:200
     for v=1:200
         if 3*A(u)-2*B(v) == 45
             fprintf('%d and %d produce 45 (A(%d),B(%d))\n',A(u),B(v),u,v);
         end
     end
 end

The above code will write out the pair that (according to your equation) produces 45.