Why the I is always a constant

I=zeros(1,1);
f=zeros(1,1);
for ky=-6:1:6
    for kx=-6:1:6
        for n=0:1:2
            for m=0:1:2
                if n==0&&m==0
                    f(ky+7,kx+7)=1
                else
                    f(ky+7,kx+7)=f(ky+7,kx+7)+exp(i*10^(-16)*(2.16*(n+m)*kx+1.245*(n-m)*ky))
                end
            end
            I(ky+7,kx+7)=abs(f(ky+7,kx+7)).^2
        end
    end
end
contourf(-6:1:6,-6:1:6,I,'LineStyle','none');

Why the I doesnot change with kx,ky?

[Adam Danz]

I formatted your code but more importantly, use smart indentation to make your code more readable and easy to manage. To smart-indent, select all of your code from within the editor (ctrl + a) and then press ctrl + i.

[Adam Danz]

In this part of your code, "i" is the imaginary number sqrt(-1). I have a feeling that variable is supposed to represent something else. When 'i' is not defined, matlab uses it to represent the imaginary unit.

exp(i*10^(-16)*(2.16*(n+m)*kx+1.245*(n-m)*ky))
%   ^ here

Answer 1

[KALYAN ACHARJYA]

Befor answering the question, It seems you are messing with code and logic, if yes, figure out.

Now the answer of the question

Why the I is always a constant?

In each iterartion (except one) your code fulfil the "if else" condition and assigned the value of

f(ky+7,kx+7)=f(ky+7,kx+7)+exp(i*10^(-16)*(2.16*(n+m)*kx+1.245*(n-m)*ky))

The "m for loop" have no role to change the I elements value, it pass the last iterration value. Each iteration when the code run with I assignment, it carries the same f(ky+7,kx+7) value and pass the same to I

>> f(ky+7,kx+7)
ans =
   9.0000 + 0.0000i

Hence

I(ky+7,kx+7)=abs(f(ky+7,kx+7)).^2

How 81?

>> f(ky+7,kx+7)
ans =
   9.0000 + 0.0000i
>> ans^2
ans =
  81.0000 + 0.0000i
>> abs(ans)
ans =
    81

Here the issue is not with I, please ensure that f(ky+7,kx+7) is changing during iterations, hence "I" will get different elements as a result.

Good Luck!

[Zhiying Wang]

But the kx ky should change the I elements value, why I does not change?

Answer 2

[Walter Roberson]

>> unique(f(:))
ans =
                          9 +                     0i
                          9 -  4.93038065763132e-32i
                          9 +  4.93038065763132e-32i
                          9 -  9.86076131526265e-32i
                          9 +  9.86076131526265e-32i
                          9 -             3.888e-15i
                          9 +             3.888e-15i
                          9 -             3.888e-15i
                          9 +             3.888e-15i
                          9 -             7.776e-15i
                          9 +             7.776e-15i
                          9 -             7.776e-15i
                          9 +             7.776e-15i
                          9 -            1.1664e-14i
                          9 +            1.1664e-14i
                          9 -            1.1664e-14i
                          9 +            1.1664e-14i
                          9 -            1.5552e-14i
                          9 +            1.5552e-14i
                          9 -            1.5552e-14i
                          9 +            1.5552e-14i
                          9 -             1.944e-14i
                          9 +             1.944e-14i
                          9 -             1.944e-14i
                          9 +             1.944e-14i
                          9 -            2.3328e-14i
                          9 +            2.3328e-14i
                          9 -            2.3328e-14i
                          9 +            2.3328e-14i

Your f is changing -- in the imaginary component.

                          (2.16*(n+m)*kx+1.245*(n-m)*ky)

is not all that large compared to the 10^-16 that you are multiplying it by. Values that are on the order of 1E-16 * sqrt(-1) come out as 1 + small complex component when you exp() them. The complex components do not add up to much, so the real component (1) completely dominates. The result is that you get a matrix full of 9 + varying small complex component. When you take abs(f)^2 the 9^2 dominates and the approximately 1e-16 complex component squared does not contribute numerically to the calculation (too insignificant). Therefore I becomes constant, the non-constant part having underflowed out of the calculation.