Using fsolve: how to plot fit curve/function to data?

I have some data that I am trying to show that it follows a function (I have the functional form of and solving for here using fsolve) and I want to make a plot of the data with the function fit. How can I do that? Thanks

%Load data from excel sheet
Data = readmatrix('Data.xlsx');
h = Data(:,1); %km height
qE = Data(:,2); %1/vol/s energy deposition
Zenith = 0; %deg solar zenith angle

%Find initial guess from data of star values for solver
qE_star_max_hat = 9192.04; 
h_star_max_hat = 159.602; 
H = 30.45;  %scale height

%Evaluate Chapman prodction func at initial guess
for z = 1:length(h)
    tao(z) = secd(Zenith) *exp(-(h(z) - h_star_max_hat)/H); %optical depth
    ChapmanInitGuess_qE(z,1) = qE_star_max_hat*exp(1- (h(z) - h_star_max_hat)/H - tao(z)); %Energy
end

%Initial Guess vector
StarVars_hat = [qE_star_max_hat; h_star_max_hat; H];

disp('---------Fitted Values --------')
[qE_star_max, h_star_max, H] = GetChapmanFit(Zenith, StarVars_hat, h, qE);

Functions

%This function solves for the qE_star and h_star of a Chapman production
%function to fit a curve of real data
function [qE_star, h_star, H] = GetChapmanFit(Zenith, StarVars_hat, h, qE)
options = optimoptions('fmincon', 'FunctionTolerance', 1E-5, 'OptimalityTolerance', 1E-5, 'MaxIterations', 1000, 'display', 'none', 'Diagnostics', 'off');
ObjectiveFunction = @(StarVars) ChapmanObjectiveFunction(Zenith, StarVars, h, qE);
%
[solution,~] = fsolve(ObjectiveFunction, StarVars_hat, options);


qE_star = solution(1);
h_star = solution(2);
H = solution(3);

and

%This function is the objective of function which minimizes the difference
%b/w the actual qE data and the qE fitted from the Chapman production
%function
function [ErrorNorm] = ChapmanObjectiveFunction(Zenith, StarVars, h, qE)

qE_star_max = StarVars(1);
h_star_max = StarVars(2);
H = StarVars(3);

%Evaluate Chapman Production function at the initial Guess
for z = 1:length(h)
    tao(z) = secd(Zenith) *exp(-(h(z) - h_star_max)/H); %optical depth
    ChapmanFit_qE(z,1) = qE_star_max *exp(1- (h(z) - h_star_max)/H - tao(z)); %Energy
end
Error = abs(qE - ChapmanFit_qE);
ErrorNorm = norm(Error,2);

I also get some warning that I am not sure if it's a problem

MINCON options to FSOLVE. FSOLVE will use the common options and ignore the FMINCON options that do
not apply.

Answer 1

[Torsten]

Call "fmincon", not "fsolve".

"fsolve" is not appropriate to solve your problem.

A better option than "fmincon" for your problem would be "lsqcurvefit".