Problem in integration in an array inside integrand

I am getting the error named "Attempted to access R(2); index out of bounds because numel(R)=1." in the below code. can anyone help me? below is my code.

  Nd = 1e24;
  N = 100;
  e  = 12*1e-12;
 % R  = [10e-9,20e-9,30e-9,40e-9];
  R  = [1e-9,2e-9,3e-9,4e-9]
  Et_Ef = -1.01*1.6*1e-19;
  K  = 1.3807e-23;
  T  = linspace(450,600,N);
  Nt = linspace(1e14,1e17,N);
  q  = 1.6e-19;
  Ld = 1.97*10e-9
  for j = 1:numel(R)  
    for i= 1:N 
      funct = @(R,phi0) (4*pi*(Nd-Nd*exp(-phi0))*R.^2);
      equation = @(phi0)integral(@(R)funct(R,phi0),0,R(j))-(4*pi*R(j)^2*Nt(i)/(1+2*exp((Et_Ef + K.*T(i) .*(phi0 + (1/6)*(R(j)/Ld)^2))./(K.*T(i)))));
      %equation = @(phi0)integral(@(r)funct(r,phi0),0,R)-(4*pi*R^2*Nt(i)/(1+2*exp((Et_Ef + K*T *(phi0 + (1/6)*(R/Ld)^2))/(K*T))));
      phi0val(j,i) = fzero(equation,40);
     funneff= @(R)1./(4/3.*pi.*R(j).^3).*(Nd.*exp(-phi0val(j,i))).*R(j).^2
neff(j,i)= (1./(4./3.*pi.*R(j).^3)).*4.*pi.*integral(funneff,0,R(j),'Arrayvalued',true)
    end
  end
plot(neff(1,:),phi0val(1,:))
plot(neff(2,:),phi0val(2,:))
plot(neff(2,:),phi0val(2,:))
plot(neff(2,:),phi0val(2,:))

Answer 1

[Star Strider]

You are using ‘R’ in too many contexts. It is a vector, however it is also an argument to your anonymous functions, and anonymous functions pick up variables from the workspace. Changing the anonymous functions argument ‘R’ to ‘Rv’ allows your code to run:

neff = zeros(numel(R),N);
phi0val = zeros(numel(R),N);
for j = 1:numel(R)
    for i= 1:N
        funct = @(Rv,phi0) (4*pi*(Nd-Nd*exp(-phi0))*Rv.^2);
        equation = @(phi0)integral(@(Rv)funct(Rv,phi0),0,R(j))-(4*pi*R(j)^2*Nt(i)/(1+2*exp((Et_Ef + K.*T(i) .*(phi0 + (1/6)*(R(j)/Ld)^2))./(K.*T(i)))));
        %equation = @(phi0)integral(@(r)funct(r,phi0),0,R)-(4*pi*R^2*Nt(i)/(1+2*exp((Et_Ef + K*T *(phi0 + (1/6)*(R/Ld)^2))/(K*T))));
        phi0val(j,i) = fzero(equation,40);
        funneff= @(Rv)1./(4/3.*pi.*Rv.^3).*(Nd.*exp(-phi0val(j,i))).*Rv.^2;
        neff(j,i)= (1./(4./3.*pi.*R(j).^3)).*4.*pi.*integral(funneff,0,R(j),'Arrayvalued',true);
    end
end
figure
hold all
for k = 1:size(neff,1)
    plot(neff(k,:),phi0val(k,:))
end
hold off
expstr = @(x) [x(:).*10.^ceil(-log10(abs(x(:))))  floor(log10(abs(x(:))))];
Rexp = expstr(R)
hl = legend(sprintfc('$R\\ =\\ %2d\\times10^{%d}$',Rexp));
hl.Interpreter = 'latex';

Check to be certain this does what you want to to do.

The Plot —

EDIT — Added plot image.

[Anil Kumar]

Nicely explained ! thank you sir!

[Star Strider]

As always, my pleasure!