Find input to function 1 that results in function 2 returning 0

Hello,

I have a function that traces raypaths given input criteria. I then have a second function that solves for error at a given point in space. I am able to find the launch angles that would result in bracketing the target.

My question is this: having solved for launch angles that bracket the point, how do I find the launch angle that results in zero error? An excerpt of the code I am working with is below

rayangle = (-90:.1:90)
nray=length(rayangle)
for ii=1:nray
    theta0=rayangle(ii)
    z_r=raysolver(z0,theta0,cmat,nstep,rstep); %calling the function that traces the rays

    z_r_theta0(ii,:)=z_r(1,:); %Saving the path of each ray in z_r_theta0
end
%% Finding error

%target co-ordinates 
r=50000;
z=1100; 


d_error=deptherror(r,z,z_r_theta0); %gives me depth error for each launch angle

bracket_ray=crossray(d_error)%this gives me all the launch angles that bracket the target. 

%what I need is to find theta0 for each set of bracketing launch angles
%that result in d_error == 0

Answer 1

[Nipun]

Hi Matthew,

I understand that you want to find the launch angle that results in zero error after bracketing the target with launch angles. You can use the fzero function to achieve this.

Here’s how you can modify your script:

rayangle = (-90:.1:90);
nray = length(rayangle);
z_r_theta0 = zeros(nray, 100); % Adjust 100 to match the length of your z_r

for ii = 1:nray
    theta0 = rayangle(ii);
    z_r = raysolver(z0, theta0, cmat, nstep, rstep); % Calling the function that traces the rays
    z_r_theta0(ii,:) = z_r(1,:); % Saving the path of each ray in z_r_theta0
end

% Target coordinates
r = 50000;
z = 1100;

d_error = deptherror(r, z, z_r_theta0); % Gives me depth error for each launch angle
bracket_ray = crossray(d_error); % This gives me all the launch angles that bracket the target.

% Find the launch angle for zero error
theta0_zero_error = fzero(@(theta) deptherror(r, z, raysolver(z0, theta, cmat, nstep, rstep)), [min(bracket_ray), max(bracket_ray)]);

disp(['Launch angle with zero error: ', num2str(theta0_zero_error)]);

Make sure that deptherror and raysolver are defined correctly, and the brackets in fzero cover the range of angles that bracket the target.

Refer to the following MathWorks documentation for "fzero" function in MATLAB: https://www.mathworks.com/help/matlab/ref/fzero.html

Hope this helps.

Nipun