how to solve the expression using the loops

p=0;
q=0;
pr=0;
qr=0;
a=0;
b=0;
ar=0;
br=0;

for x=1:1:5
    p=p+P(x,1);
    q=q+Q(x,1);
    pr=pr+P(x,1)*5^(x-1);
    qr=qr+Q(x,1)*5^(x-1);
end

for x=1:1:15
    a=a+A(x,1);
    b=b+B(x,1);
    ar=ar+A(x,1)*5^(x-1);
    br=br+B(x,1)*5^(x-1);
end

Now,how to find this: p*qr*b+p*br*q; combining the two loops.

[Jan]

What are P and Q, A and B? What's wrong with p*qr*b+p*br*q ?

[phoenix]

matrices.if i write in this form p*qr*b+p*br*q ,is it right? how can i combine these two different loops into a single one?

Answer 1

[Jan]

What about:

for x=1:5
  p  = p + P(x,1);
  q  = q + Q(x,1);
  pr = pr + P(x,1)*5^(x-1);
  qr = qr + Q(x,1)*5^(x-1);
  a  = a + A(x,1);
  b  = b + B(x,1);
  ar = ar + A(x,1)*5^(x-1);
  br = br + B(x,1)*5^(x-1);
end

"Combining" seems to be easy, because the two loops are independent from each other. You could even omit the loops:

    c  = 5 .^ (0:4).';     % [EDITED] transposed
    p  = sum(P(1:5, 1));
    q  = sum(Q(1:5, 1));   % [EDITED] trailing parenthesis added
    pr = sum(P(1:5,1) .* c);
    qr = sum(Q(1:5,1) .* c);

And the same for the 2nd loop.

If p*qr*b+p*br*q is correct or not depends on what you want as output. Simply try it. Maybe you want the elementwise products:

p .* qr .* b + p .* br .* q

[phoenix]

It is not working.Any other suggestion? I do not require the elementwise product.

[Jan]

@Phoenix: I cannot run your code, because I do not have your inputs. "It does not work" does not allow to reconsider, what's going on, when you run it. It is not clear, what the problem with "combining" is, because it seems to be trivial to join the bodies of the two independent loops. If you need further help, please explain, what the problem is now.

But when I guess:

P = rand(5, 1);
Q = rand(5, 1);
A = rand(5, 1);
B = rand(5, 1);
p=0; q=0; pr=0; qr=0;
a=0; b=0; ar=0; br=0;

for x = 1:5
  p  = p + P(x,1);
  q  = q + Q(x,1);
  pr = pr + P(x,1) * 5^(x-1);
  qr = qr + Q(x,1) * 5^(x-1);
end

for x = 1:5
  a  = a + A(x,1);
  b  = b + B(x,1);
  ar = ar + A(x,1) * 5^(x-1);
  br = br + B(x,1) * 5^(x-1);
end
R1 = p * qr * b + p * br * q

c  = 5 .^ (0:4).';
p  = sum(P(1:5, 1));
q  = sum(Q(1:5, 1));
pr = sum(P(1:5, 1) .* c);
qr = sum(Q(1:5, 1) .* c);
R2 = p * qr * b + p * br * q

Now R1 and R2 have the same values. Do you want something else?

But a,b,ar,br do not occur in the wanted formula at all. Strange.

[phoenix]

Second loop is different.it ranges from 1:15.can i combine them? Leave aside/delete the term pr,a,ar. I just need to combine using for loop.

[Jan]

@phoenix: Ah, sorry, I've overseen the difference of "5" and "15". Now I see it.

If one loop runs from 1 to 5 and the other from 1 to 15, what does "combining" them mean? I cannot guess, what you want to achieve then. Try to explain, what the actual problem is and why you want to use loops at all. Why not using the sum() commands as shown above?

[phoenix]

@Jan Simon: What does this symbol .' stand for used in c = 5 .^ (0:4).';?

[Jan]

@phoenix: .' is the transpose operator. It is frequently confused with ' , but this is the complex conjugate transposing. See https://www.mathworks.com/help/matlab/ref/transpose.html and https://www.mathworks.com/help/matlab/matlab_prog/matlab-operators-and-special-characters.html