Nonlinear Curve fitting with integrals

I encountered a nonlinear fitting problem, and the fitting formula is shown in Equation (1), which includes two infinite integrals (in practice, the integration range can be set from 0.01E-6 to 200E-6).

In these formulas, except for x and y being vectors, all other variables are scalars, and Rmedian and sigma are the parameters to be fitted.

I found a related post and tried to write the code based on it, but it keeps reporting errors. The error message seems to indicate that the vector dimensions are inconsistent, preventing the operation from proceeding. However, these functions are all calculations for individual scalars.
Error using /
Matrix dimensions must agree.

Error in dsdmain>@(r)1/(2*r*sigma*sqrt(2*pi))*exp(-(log(2*r)-log(2*Rmean)^2)/(2*sigma^2)) (line 13)
gauss = @(r) 1/(2*r*sigma*sqrt(2*pi))* exp( -(log(2*r)-log(2*Rmean)^2)/(2*sigma^2) );
My question is: Can I refer to the content of this post to solve my problem? If yes, what does this error message mean? If not, how should I resolve my problem? (Note: The range of Rmedian is 1E-6 to 5E-6)

After modifying the code according to Walter Roberson and Torsten’s suggestion, the program no longer throws errors. But no matter how I set the initial values on my end, it always prompts:
Initial point is a local minimum.
Optimization completed because the size of the gradient at the initial point
is less than the default value of the optimality tolerance.
<stopping criteria details>
theta = initial point
1.0e-05 *
0.2000
0.1000
Optimization completed: The final point is the initial point.
The first-order optimality measure, 0.000000e+00, is less than
options.OptimalityTolerance = 1.000000e-06.
Optimization Metric Options
relative first-order optimality = 0.00e+00 OptimalityTolerance = 1e-06 (default)

I have checked all the formulas and the units of the variables, and I didn’t find any problems.

————————————– Beblow is my code for issue reproduction ———————————————————-
function testmain()
clc
function Kvec = model(param,xdata)
% Vector of Kd for every xdata:
Kvec = zeros(size(xdata));
Rmean = param(1);
Rstd = param(2);

for i = 1:length(xdata)
model = @(r) unified(xdata(i),r,Rmean,Rstd,delta,Delta,D,lambda);
Kvec(i) = integral(model,0.01E-6,200E-6);
end
end
function s = unified(g,R,Rmean,Rstd,delta,Delta,D,lambda)
%unified Unified fitting model for DSD
% exponentional combined

factor = 1./(2*R*Rstd*sqrt(2*pi)) *2 ; % int(P(r)) = 0.5,1/0.5=2
p1 = -(log(2*R)-log(2*Rmean)).^2/(2*Rstd^2);
c = -2*2.675E8^2*g.^2/D;

tmp = 0;
for il = 1:length(lambda)
a2 = (lambda(il)./R).^2;
an4 = (R/lambda(il)).^4;
Psi = 2+exp(-a2*D*(Delta-delta))-2*exp(-a2*D*delta)-2*exp(-a2*D*Delta)+exp(-a2*D*(Delta+delta));
tmp = tmp+an4./(a2.*R.*R-2).*(2*delta-Psi./(a2*D));
end
p2 = c*tmp;

s = factor.*exp(p1+p2);
end
Delta = 0.075;
delta = 0.002;
D = 0.098E-9;
lambda = [2.0816 5.9404 9.2058 12.4044 15.5792 18.7426 21.8997 25.0528 28.2034 31.3521];

g = [ 0.300616, 0.53884, 0.771392, 1.009616, 1.24784, 1.480392, 1.718616, 1.95684, 2.189392, 2.427616, 2.66584, 2.898392 ];
xdata = g;
ydata = [100, 91.16805426, 80.52955192, 67.97705378, 55.1009735,41.87307917, 30.39638776, 21.13515607, 13.7125649, 8.33083767, 5.146756077, 2.79768609];
ydata = ydata/ydata(1); % normalize

% Inital guess for parameters:
Rmean0 = 2E-6;
Rstd0 = 1E-6;
p0 = [Rmean0;Rstd0];
% lsqcurvefit is in the optimization toolbox.
% fit, from the curve fitting toolbox may be an alternative
theta = lsqcurvefit(@model,p0,xdata,ydata,[0.01E-6;0.1E-6],[10E-6,2E-6])
endI encountered a nonlinear fitting problem, and the fitting formula is shown in Equation (1), which includes two infinite integrals (in practice, the integration range can be set from 0.01E-6 to 200E-6).

In these formulas, except for x and y being vectors, all other variables are scalars, and Rmedian and sigma are the parameters to be fitted.

I have checked all the formulas and the units of the variables, and I didn’t find any problems.

factor = 1./(2*R*Rstd*sqrt(2*pi)) *2 ; % int(P(r)) = 0.5,1/0.5=2
p1 = -(log(2*R)-log(2*Rmean)).^2/(2*Rstd^2);
c = -2*2.675E8^2*g.^2/D;

s = factor.*exp(p1+p2);
end
Delta = 0.075;
delta = 0.002;
D = 0.098E-9;
lambda = [2.0816 5.9404 9.2058 12.4044 15.5792 18.7426 21.8997 25.0528 28.2034 31.3521];

% Inital guess for parameters:
Rmean0 = 2E-6;
Rstd0 = 1E-6;
p0 = [Rmean0;Rstd0];
% lsqcurvefit is in the optimization toolbox.
% fit, from the curve fitting toolbox may be an alternative
theta = lsqcurvefit(@model,p0,xdata,ydata,[0.01E-6;0.1E-6],[10E-6,2E-6])
end I encountered a nonlinear fitting problem, and the fitting formula is shown in Equation (1), which includes two infinite integrals (in practice, the integration range can be set from 0.01E-6 to 200E-6).

In these formulas, except for x and y being vectors, all other variables are scalars, and Rmedian and sigma are the parameters to be fitted.

I have checked all the formulas and the units of the variables, and I didn’t find any problems.

factor = 1./(2*R*Rstd*sqrt(2*pi)) *2 ; % int(P(r)) = 0.5,1/0.5=2
p1 = -(log(2*R)-log(2*Rmean)).^2/(2*Rstd^2);
c = -2*2.675E8^2*g.^2/D;

s = factor.*exp(p1+p2);
end
Delta = 0.075;
delta = 0.002;
D = 0.098E-9;
lambda = [2.0816 5.9404 9.2058 12.4044 15.5792 18.7426 21.8997 25.0528 28.2034 31.3521];

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