Confidence interval calculation. Cannot compute confidence interval for imaginary values.

clear; clc

load Steady_State_Data.mat % this contains the wavelength of light and absorbance of substrate and sample

%% Preamble

% Fundamental constants
h = 4.0135667696*10^-15; % units: eV/ Hz
c = 3*10^8; % SI units

% Clean up of data to select range of values
Absorbance = log10(T_substrate./T_sample);
E = (h*c./(Lambda*10^-9));
e = E >= 0 & E <= 2.0; % returns boolean value of the indices that satisfies the logical condition defined above
A = find(e); % gives indices that are non-zero
N = length(A); % no. of elements that are non-zero
n = length(E) + 1;

% Data for fitting
E_p = E(n-N:167);
Abs = Absorbance(n-N:167) – min(Absorbance);
% Abs = Absorbance(n-N:167);

% Fitting function
function F = EM_SS(p, e_p)
for i = 1:numel(e_p)
E_p = e_p(i);
F(i) = p(1)*(2*pi*sqrt(p(4))/E_p)*(1/p(6))*…
(integral(@(E)sech(((E_p – E)./p(6)))*(1 + 10*p(5)*(E – p(3)) + …
126*(p(5))^2*(E – p(3))^2)/(1 – exp(-2*pi*sqrt(p(4)/(E – p(3))))), p(3), Inf, ‘ArrayValued’, 1)) + …
p(2)*(2*pi*p(4)^3/2)*1/p(6)*(…
(1/1^3)*sech((E_p – p(3) + p(4)/1^2)./p(6)) + …
(1/2^3)*sech((E_p – p(3) + p(4)/2^2)./p(6)) + …
(1/3^3)*sech((E_p – p(3) + p(4)/3^2)./p(6)) + …
(1/4^3)*sech((E_p – p(3) + p(4)/4^2)./p(6)) + …
(1/5^3)*sech((E_p – p(3) + p(4)/5^2)./p(6)) + …
(1/6^3)*sech((E_p – p(3) + p(4)/6^2)./p(6)) + …
(1/7^3)*sech((E_p – p(3) + p(4)/7^2)./p(6)));
end
F = F(:);
end

%% Curve fitting options

% Initial parameter guess and bounds
lb = [0,0,0,0,0,0]; ub = [Inf, Inf, 1.65, 0.03, Inf, Inf];
p0 = [0.13, 0.11, 1.4, 0.025, 0.12, 0.035]; % refer to the next line for their order
% p0 = [A1, A2, Eg, Eb, R, g]

% lsqcurvefit and choose between different algorithm that lsqcurvefit employs (3C1, comment those lines that are not choosen and uncomment the line that is choosen, if not, matlab will take the last line of "optim_lsq" by default)
optim_lsq = optimoptions(‘lsqcurvefit’, ‘Algorithm’, ‘levenberg-marquardt’, ‘MaxFunctionEvaluations’,1000, ‘MaxIterations’, 1000, ‘FunctionTolerance’,10^-9, ‘StepTolerance’, 10^-9);
% optim_lsq = optimoptions(‘lsqcurvefit’, ‘Algorithm’, ‘trust-region-reflective’, ‘MaxFunctionEvaluations’,1000, ‘MaxIterations’, ‘FunctionTolerance’,10^-9, ‘StepTolerance’, 10^-9);
% optim_lsq = optimoptions(‘lsqcurvefit’, ‘Algorithm’, ‘interior-point’, ‘MaxFunctionEvaluations’,1000, ‘MaxIterations’, 1000, ‘FunctionTolerance’,10^-9, ‘StepTolerance’, 10^-9);

% Solver for lsqcurvefit
[p, residual, exitflag, output, jacobian] = lsqcurvefit(@EM_SS, p0, E_p, Abs, lb, ub);

%% Standard error calculation
ci = nlparci(p, residual, ‘Jacobian’, jacobian);
lowerbar = p – ci(:,1);
uppperbar = ci(:,2) – p;

if p == real(p)
disp(‘Real’)
else
disp(‘Complex with non-zero imaginary’)
end

if residual == real(residual)
disp(‘Real’)
else
disp(‘Complex with non-zero imaginary’)
end

if J == real(J)
disp(‘Real’)
else
disp(‘Complex with non-zero imaginary’)
end

%% Plot command
plot(E_p, Abs, ‘o’)
hold on
plot(E_p, EM_SS(p, E_p))
xlabel(‘Probe energy (eV)’)
ylabel(‘Absorbance.O.D’)
legend(‘Experimental Data’, ‘Fitted Curve’)
hold off

%% Parameter values (refer to command window)
p1 = p(1,1);
p2 = p(1,2);
p3 = p(1,3);
p4 = p(1,4);
p5 = p(1,5);
p6 = p(1,6);
X1 = [‘ A1 = ‘, num2str(p1)];
X2 = [‘ A2 = ‘, num2str(p2)];
X3 = [‘ Eg = ‘, num2str(p3)];
X4 = [‘ Eb = ‘, num2str(p4)];
X5 = [‘ R = ‘, num2str(p5)];
X6 = [‘ g = ‘, num2str(p6)];
disp(X1);
disp(X2);
disp(X3);
disp(X4);
disp(X5);
disp(X6);
Hi all, I am doing a fitting to my experimental data and I am now trying to calculate the confidence interval. However, it seems like there is something wrong with my code and the computer can’t really calculate it. May I ask where I am wrong? I tried following the instructions on this link but I still can’t get any results.clear; clc

load Steady_State_Data.mat % this contains the wavelength of light and absorbance of substrate and sample

%% Preamble

% Fundamental constants
h = 4.0135667696*10^-15; % units: eV/ Hz
c = 3*10^8; % SI units

% Data for fitting
E_p = E(n-N:167);
Abs = Absorbance(n-N:167) – min(Absorbance);
% Abs = Absorbance(n-N:167);

%% Curve fitting options

% Solver for lsqcurvefit
[p, residual, exitflag, output, jacobian] = lsqcurvefit(@EM_SS, p0, E_p, Abs, lb, ub);

%% Standard error calculation
ci = nlparci(p, residual, ‘Jacobian’, jacobian);
lowerbar = p – ci(:,1);
uppperbar = ci(:,2) – p;

if p == real(p)
disp(‘Real’)
else
disp(‘Complex with non-zero imaginary’)
end

if residual == real(residual)
disp(‘Real’)
else
disp(‘Complex with non-zero imaginary’)
end

if J == real(J)
disp(‘Real’)
else
disp(‘Complex with non-zero imaginary’)
end

%% Plot command
plot(E_p, Abs, ‘o’)
hold on
plot(E_p, EM_SS(p, E_p))
xlabel(‘Probe energy (eV)’)
ylabel(‘Absorbance.O.D’)
legend(‘Experimental Data’, ‘Fitted Curve’)
hold off

load Steady_State_Data.mat % this contains the wavelength of light and absorbance of substrate and sample

%% Preamble

% Fundamental constants
h = 4.0135667696*10^-15; % units: eV/ Hz
c = 3*10^8; % SI units

% Data for fitting
E_p = E(n-N:167);
Abs = Absorbance(n-N:167) – min(Absorbance);
% Abs = Absorbance(n-N:167);

%% Curve fitting options

% Solver for lsqcurvefit
[p, residual, exitflag, output, jacobian] = lsqcurvefit(@EM_SS, p0, E_p, Abs, lb, ub);

%% Standard error calculation
ci = nlparci(p, residual, ‘Jacobian’, jacobian);
lowerbar = p – ci(:,1);
uppperbar = ci(:,2) – p;

if p == real(p)
disp(‘Real’)
else
disp(‘Complex with non-zero imaginary’)
end

if residual == real(residual)
disp(‘Real’)
else
disp(‘Complex with non-zero imaginary’)
end

if J == real(J)
disp(‘Real’)
else
disp(‘Complex with non-zero imaginary’)
end

%% Plot command
plot(E_p, Abs, ‘o’)
hold on
plot(E_p, EM_SS(p, E_p))
xlabel(‘Probe energy (eV)’)
ylabel(‘Absorbance.O.D’)
legend(‘Experimental Data’, ‘Fitted Curve’)
hold off

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