Problem with loop for

Hello

I need to calculate average value using various methods including loop for. I don't know why result using loop is diffrent. Can someone help with that?

N = 1200; 
A = 2; 
fx = 5; 
fp = 1000;  
dt = 1/fp;              
t = dt*(0:N-1);         
x = A*sin(2*pi*fx*t); 

x_sred1 = mean(x);   %average value
x_sred2 = sum(x)/N;

disp(['x_sred1 = ' ,string(x_sred1), 'x_sred2 = ' ,string(x_sred2)])

    "x_sred1 = "    "-1.3414e-16"    "x_sred2 = "    "-1.3414e-16"

%average value loop for
l=length(x);
s_x=0;
for i=1:l
    s_x=s_x+x(i);
end
x_sred3=s_x/N;
disp(['x_sred3 = ' ,string(x_sred3)])

    "x_sred3 = "    "9.142e-17"

[VBBV]

In the loop , you try to add cumulative sum instead of individual sum

[Mathieu NOE]

No , the code is correct in its principle, but your for loop demonstrate that this method is accumulating more errors than the two first methods

with the choosen parameters , your sum should be zero , but you see actually some difference (as tiny numbers) because of round off accumated errors.

now if you can make a small change in your parameters to get a sum that is not (almost) zero , then all 3 computations are very close.

here for example I simply change N from 1200 to 1150 and I get :

"x_sred1 = " "0.056223" "x_sred2 = " "0.056223"

"x_sred3 = " "0.056223"

or N = 1200 and fp = 5000 (to increase time accuracy)

"x_sred1 = " "0.1825" "x_sred2 = " "0.1825"

"x_sred3 = " "0.1825"

[VBBV]

@Joanna Zajac, It is something to do with property of sin function for specific values in input array

N = 1200; 
A = 2; 
fx = 5; 
fp = 1000;  
dt = 1/fp;              
t = dt*(0:N-1);         
x = A*(2*pi*fx*t); 

x_sred1 = mean(x)   %average value

x_sred1 = 37.6677

x_sred2 = sum(x)/N

x_sred2 = 37.6677

disp(['x_sred1 = ' ,string(x_sred1), 'x_sred2 = ' ,string(x_sred2)])

    "x_sred1 = "    "37.6677"    "x_sred2 = "    "37.6677"

%average value loop for
% l=length(x);
s_x=0;
for i=1:numel(x)
    s_x=s_x+x(i);
end
x_sred3=s_x/N;
disp(['x_sred3 = ' ,string(x_sred3)])

    "x_sred3 = "    "37.6677"

Answer 1

[Image Analyst]

This is round-off error, a form of quantization error. See

https://en.wikipedia.org/wiki/Round-off_error

and

https://matlab.fandom.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_(or_similar)_not_equal_to_zero?

for explanations.

They should have taught you this in your numerical analysis class or linear algebra (matrix) class. Hopefully you have taken such a class in college.