Undefined variable when performing nonlinear curve fitting

I have the following code:

clc,clear all,close all

filename='d5D21Re50.csv';
M=csvread(filename,1,0);

d=5e-3; % particle diameter (m)
U0=10e-3; % superficial velocity (m/s)
eps=0.47; % average porosity
Uavg=U0/eps; % average axial velocity (m/s)
C0=6; % inlet tracer concentration (mM)
cellsize=2.5e-4; % grid size (m)
nx=320; % number of cells in the x (axial) direction
ny=86; % number of cells in the y direction
nz=86; % number of cells in the z direction
L=nx*cellsize; % length of the column (m)
R=0.5*(ny-2)*cellsize; % radius of the column (m)
Ri=0.5e-3; % radius of the tracer tube (m)

flag=reshape(M(:,1),[nx,ny,nz]);
Ux=reshape(M(:,2),[nx,ny,nz]);
Uy=reshape(M(:,3),[nx,ny,nz]);
Uz=reshape(M(:,4),[nx,ny,nz]);
C=reshape(M(:,6),[nx,ny,nz]);

N=29; % number of intervals
radp=1:N;
radgrid=[0 radp];

i=20; % index for the axial position
for m=1:N
    jcen=ny/2;
    kcen=nz/2;
    
    centerValue=C(i,jcen,kcen);
    
    r1=radgrid(m);
    conc=0;
    counter=0;
    for j=1:ny
        for k=1:nz
            r=sqrt((j-jcen)^2+(k-kcen)^2);
            r2=radgrid(m+1);
            if r>=r1 && r<=r2 && (flag(i,j,k)==0 || flag(i,j,k)==0.5)
                conc=conc+C(i,j,k);
                counter=counter+1;
            end
        end
    end
    radCprof(m)=conc/counter;
end

radCprof=[centerValue radCprof];

radialpos=R*radp/max(radp);
myArray=[0 radialpos];

roots=30;

z=i*cellsize;

beta=besselzero(1,roots,1);

value=0;
for i=1:roots
    value=value+besselj(1,beta(i)*Ri/R)*besselj(0,beta(i)*r/R)/(beta(i)*(besselj(0,beta(i)))^2)*(z/R)*exp(-beta(i)^2*z/(PeT*R));
end

modelfun=@(PeT,r)C0*(1+(2*R/Ri)*value);
x=lsqcurvefit(modelfun,12,myArray,radCprof);

And I receive the following error when I launch it:

Undefined function or variable 'PeT'.

Error in TransverseDispersionBessel (line 70)

value=value+besselj(1,beta(i)*Ri/R)*besselj(0,beta(i)*r/R)/(beta(i)*(besselj(0,beta(i)))^2)*(z/R)*exp(-beta(i)^2*z/(PeT*R));

How could I solve this problem?

Answer 1

[Geoff Hayes]

mathnewbie - the error message is telling you that PeT is undefined. Nowhere in the code have you tried to define this variable until you use it within the following for loop

for i=1:roots
    value=value+besselj(1,beta(i)*Ri/R)*besselj(0,beta(i)*r/R)/(beta(i)*(besselj(0,beta(i)))^2)*(z/R)*exp(-beta(i)^2*z/(PeT*R));
end

You will need to initialize this variable before you try and use it... Though this is the same input variable in your anonymous function

modelfun=@(PeT,r)C0*(1+(2*R/Ri)*value);

so you may need to clarify what youa are trying to do. It may be that you want to create a nested function like the following

function myMainFunction
    filename='d5D21Re50.csv';
    M=csvread(filename,1,0);  
    d=5e-3; % particle diameter (m)
    % etc.
    function [x] = myNestedFunction(PeT,r)
        value=0;
        for i=1:roots
            value=value+besselj(1,beta(i)*Ri/R)*besselj(0,beta(i)*r/R)/(beta(i)*(besselj(0,beta(i)))^2)*(z/R)*exp(-beta(i)^2*z/(PeT*R));
        end
        x = C0*(1+(2*R/Ri)*value);
    end
    x=lsqcurvefit(@myNestedFunction,12,myArray,radCprof);
end

I haven't tried the above but I hope you get the idea of how your nested function - which has access to all the local variables defined in the main function - can be used for the least squares curve fitting problem...

Answer 2

[Walter Roberson]

Change

value=0;
for i=1:roots
    value=value+besselj(1,beta(i)*Ri/R)*besselj(0,beta(i)*r/R)/(beta(i)*(besselj(0,beta(i)))^2)*(z/R)*exp(-beta(i)^2*z/(PeT*R));
end
modelfun=@(PeT,r)C0*(1+(2*R/Ri)*value);

to

value = @(PeT,r) sum( besselj(1,beta(i)*Ri/R)*besselj(0,beta(i)*r/R)/(beta(i)*(besselj(0,beta(i)))^2)*(z/R)*exp(-beta(i)^2*z/(PeT*R));
end
modelfun=@(PeT,r)C0*(1+(2*R/Ri)*value(PeT,r));