Problem with fzero function

I had some troubles in using fzero.

Here is my script: lambda=0.23; T_orb=86400; D=130*1000; omega=2*pi/T_orb; distance=1000*[37700;38400;39000;39600]; for q=1:4 APS.tint(q)=fzero(@(T_int)[distance(q)*lambda/(2*D/2*-(cos(omega*T_int+omega*(T_orb/4-T_int/2))-cos(omega*(T_orb/4-T_int/2))))-2000],100);

end

and it gives me as result tint=[1.527152190882263e-12 1.527032893943011e-12 1.526723991273891e-12 1.527144367230523e-12], but using this values the function has not a zero! Using a bigger first guess (like 1000) it finds the correct first solution (the function is periodical). Why it gives me this result of magnitude 10^-12?

[jgg]

If your function is non-linear, fzero can find local near-zeroes. You will want to trial it from several points.

I can't debug your code further because you didn't include lambda.

Answer 1

[Star Strider]

‘Why it gives me this result of magnitude 10^-12?’

That means that the value of ‘T_int’ it estimates is close to zero.

You left out ‘lambda’, so I created a value for it. I have no idea what its true value should be, so if I chose the wrong value, your function could have true zeros, but it does not for the ‘lambda’ I chose.

However, your function does not have any true zero-crossings in the sense that fzero can locate them. Instead, it has discontinuities with sign-reversals, so you need to search for them. Define the ‘T_int’ vector here to have the range and resolution (number of points) you need to define the sign-reversal points with acceptable accuracy.

The code:

lambda = 1000;                          % <— Insert Correct Value Here
T_orb=86400;
D=130*1000;
omega=2*pi/T_orb;
distance=1000*[37700;38400;39000;39600];

fcn = @(T_int)[distance(q).*lambda./(2*D/2*-(cos(omega*T_int+omega*(T_orb/4-T_int/2))-cos(omega*(T_orb/4-T_int/2))))-2000];

T_int = linspace(0, 5E5, 100);
y = fcn(T_int);

zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);                    % Returns Zero-Crossing Indices Of Argument Vector
zero_cross_idx = zci(y);                                                % Approximate Zero-Crossing Indices Of Your Function

figure(1)
plot(T_int, y)
hold on
plot(T_int(zero_cross_idx), y(zero_cross_idx), '*r')
hold off
grid

[OldCar]

I have wrote the lambda value. I have not understood your answer. Why fzero gives me a value that drives to a big value of the fuction?

[Star Strider]

Even with ‘lambda’ defined, my Answer remains the same. Plot it and you will see the reason.

Your function is periodic, however it periodically goes to +Inf then goes to -Inf and does not cross y=0 between them, so your function has no true zero crossings in the sense that fzero can determine them.

Testing for the +Inf to -Inf sign changes is the only way to detect the periodicity. The plot function connects the +Inf and -Inf values with a line, but that line is not an actual zero-crossing. Your function is not defined between the +Inf and -Inf transitions, so it does not cross zero there.