How to calculate each result of f(x) in the nested for loop?

This might be a quite simple question but I am really a starter. Hope to get help from you guys, thanks a lot!

I need to calculate different results of f(x) while x equals 1 to 180 to plot a graph.

Firstly , I wrote the nested loop:

j = sqrt(-1);
    for x = 1:180
         for i = 1:5
               f(x)=f(x) + exp((-j).*(i-1).*sin(x))
         end
    end

Then I think I need to do the pre-allocating, so I change the f(x) to :

j = sqrt(-1);
a = zeros(180,5);
    for x = 1:180
         for i = 1:5
              a(x,i)=a(x,i)+ exp((-j).*(i-1).*sin(x))
         end
    end

However, it is still not working, what should I do?

[Jan]

"Still not working" does not clarify, what you consider as problem. The second code is running without an error.

Answer 1

[Jan]

This is correct, but not useful:

j = sqrt(-1);

i and j are defined as imaginary units as default already. But you see the ambiguities with using variables with the same name. So prefer 1j or 1i.

    for x = 1:180
       for i = 1:5
           f(x)=f(x) + exp((-j).*(i-1).*sin(x))
       end
    end    

This fails an error message, because f(x) is undefinde in the first call. So replace it by:

f = zeros(1, 100);
for x = 1:180
    s = 0;
    for i = 1:5
       s = s + exp(-1j .* (i-1) * sin(x));
    end
    f(x) = s;
end

Or convert the inner loop to a vector operation:

f = zeros(1, 100);
for x = 1:180
   f(x) = sum(exp(-1j .* ((1:5)-1) * sin(x)));
   %      sum(exp(-1j .* (0:4) * sin(x)))
end

The outer loop can be vectorized also:

f = sum(exp(-1j .* (0:4).' * sin(1:180)));

[Walter Roberson]

I think it more likely that the user wants sind() instead of sin()

[ZIYI WENG]

Thanks for your help. But after I use the code, s only return as different imaginary values in the command window. What I need to do is draw a graph to state the f(x).

[Walter Roberson]

plot3(1:180, real(f), imag(f)); xlim([0 180])

[ZIYI WENG]

Thank you very much!

Answer 2

[Walter Roberson]

j = 1j;
x = 1:180;
i = (1:5).';

a = sum( exp(-j).*(i-1).*sind(x), 1);
plot(x, real(a), 'k', x, imag(a), 'r')

[ZIYI WENG]

Thank you, but the graph I need to draw is supposed to look like this :

x-axis: x(scale from 1 to 180)

y-axis: a

[Walter Roberson]

j = 1j;
x = 1:180;
i = (1:5).';

a = sum( exp(-j).*(i-1).*sind(x), 1);
plot(x, real(a), 'k', x, imag(a), 'r'); xlim([0 180])Y

Your a is complex-valued, so you cannot use it as the y coordinate. You can use real(a) or imag(a) or abs(a) or angle(a)