dispersion equation in water waves

I am solving dispersion equation for water waves. I already solved it but with small h now i am using the same code but having different h and it give me incorrect evenscent modes. How i can fix my this code that it works well. Below is my code

clc;
close all;
clear all;


N = 10;        % Terms number used in region I


% --- 2.  Dimensional geometry & environment ---------------------
RI  = 34.5;       % [m] inner / entrance radius  (fully open ⇒ RI = RT)
RE  = 47.5;       % [m] outer hull radius        (used for k0*RE axis)
d   = 38.0;       % [m] draft  = free-surface → rim   (water-column length)
h   = 200;      % [m] total water depth            (free-surface → seabed)
b = h - d;      % [m] clearance rim → seabed  (= 162 m, not usually used)
g=9.81;

k0RE = linspace(5, 35, 200);      % 200 points, dimension-less

I_given_wavenumber = 1;
      % --------------- ① pre-allocate
    for j = 1:length(k0RE)
       if I_given_wavenumber == 1
        wk    = k0RE(j)/RE;                    %wavenumber
        omega = sqrt(g*wk*tanh(wk*h));               %wave radian frequency
        

    fun_alpha = @(x) omega^2 + g*x*tan(x*h);     %dispersion equation for evanescent modes
    
     end
       for n = 1:N
        if n ==1
            k(n) = -1i*wk;
  
        else
            x0_alpha = [(2*n -3)*pi/2./h, (2*n -1)*pi/2./h];  % Narrow interval
        k(n) = fsolve(fun_alpha, mean(x0_alpha));
        end
       end
      
        end

Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved, inaccuracy possible.

The vector of function values is near zero, as measured by the value
of the function tolerance. However, the last step was ineffective.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved, inaccuracy possible.

The vector of function values is near zero, as measured by the value
of the function tolerance. However, the last step was ineffective.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved, inaccuracy possible.

The vector of function values is near zero, as measured by the value
of the function tolerance. However, the last step was ineffective.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values i...

[Torsten]

Don't solve in x, but in y = x*h.

[Javeria]

@Torsten i did not get you. as for h=small number like 10,20,30 we are in intermediate water depth but when i am using for deep water then i do not have the correct evenscent mode. So then for h=200m how i can fix my this code that it give me correct evenscent modes.

[Torsten]

I don't understand your code.

The outer loop goes over j, the inner loop goes over n. But k is only an array that depends on n. That means that you only save the results in k for the last value of omega - all the other results obtained before for omega(1), ..., omega(length(k0RE)-1) are overwritten and lost.

[Javeria]

@Torsten this outerloop is for each j values at the end i need to plot one result for each j and there then i write it like eta(j) .

Answer 1

[Torsten]

I solve in y = x*h. Thus the result has to be divided by h to get x.

k(j,n) = fzero(@(y)fun_alpha(y,omega(j)),y0_alpha)/h;

The results satisfy fun_alpha == 0. If the results don't fit your expectations, the function fun_alpha is most probably wrong.

clc;
close all;
clear all;
N = 10;        % Terms number used in region I
% --- 2.  Dimensional geometry & environment ---------------------
RI  = 34.5;       % [m] inner / entrance radius  (fully open ⇒ RI = RT)
RE  = 47.5;       % [m] outer hull radius        (used for k0*RE axis)
d   = 38.0;       % [m] draft  = free-surface → rim   (water-column length)
h   = 200;      % [m] total water depth            (free-surface → seabed)
b = h - d;      % [m] clearance rim → seabed  (= 162 m, not usually used)
g = 9.81;
k0RE = linspace(5, 35, 200);      % 200 points, dimension-less
I_given_wavenumber = 1;
% --------------- ① pre-allocate
for j = 1:length(k0RE)
  if I_given_wavenumber == 1
    wk    = k0RE(j)/RE;                    %wavenumber
    omega(j) = sqrt(g*wk*tanh(wk*h));               %wave radian frequency        
    fun_alpha = @(y,omega) omega^2 + g*y/h.*tan(y);     %dispersion equation for evanescent modes    
  end
  k(j,1) = -1i*wk;
  yshift(j) = 0.1;
  for n = 2:N 
    while 1
      y0_alpha = [(2*(n-1)-1)*pi/2+yshift(j), (2*(n-1)+1)*pi/2-yshift(j)];  % Narrow interval
      if fun_alpha(y0_alpha(1),omega(j))*fun_alpha(y0_alpha(2),omega(j)) <= 0
        break
      end
      yshift(j) = yshift(j)/2;
    end
    k(j,n) = fzero(@(y)fun_alpha(y,omega(j)),y0_alpha)/h;
  end
end
yshift(1)

ans = 0.0500

yshift(end)

ans = 0.0063

real(k(1,2:end))

ans = 1×9

0.0082 0.0247 0.0411 0.0575 0.0737 0.0899 0.1060 0.1221 0.1381

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real(fun_alpha(k(1,2:end)*h,omega(1)))

ans = 1×9

1.0e-14 * -0.0666 -0.0888 -0.2220 0.1332 0.2665 0.3331 0.0888 -0.3331 0.2220

<mw-icon class=""></mw-icon>

<mw-icon class=""></mw-icon>

[Javeria]

@Torsten I solved the diffraction problem in water waves considering the parameters for deep water. But i didn't get my expected results my output for eta0 give me too much small or large values. one thing i note that my analytical expression is correct but when i used the deep water condition then the argument for the hyperbolic functions is a large number. Also when i increased my turncation number for the system convergence then i get NaN. How to fix this issue in my code i tried pinv solver also. But still i get this isse. Below is my code.

clc;
close all;
clear all;
tic;

N = 20;        % Terms number used in region I
M = 20;        % Terms number used in region II
Q = 20;        % Terms number used in region III P=Q

% --- 2.  Dimensional geometry & environment ---------------------
       
RI  = 34.5;       % [m] inner / entrance radius  (fully open ⇒ RI = RT)
RE  = 47.5;       % [m] outer hull radius        (used for k0*RE axis)
d   = 38.0;       % [m] draft  = free-surface → rim   (water-column length)
h   = 200;      % [m] total water depth            (free-surface → seabed)
b = h - d;      % [m] clearance rim → seabed  (= 162 m, not usually used)
tau = 0.2;               % porosity ratio
g = 9.81;           % gravity
% --- Bessel Function Order ---'l' is the order of the Bessel functions used throughout your system of equations.
l = 0; % You can change this value as desired/required by the problem.
k0RE = linspace(5, 35, 200);      % 200 points, dimension-less
 eta0 = zeros(1,length(k0RE));
I_given_wavenumber = 1;
      % --------------- ① pre-allocate
    for j = 1:length(k0RE)
       if I_given_wavenumber == 1
        wk    = k0RE(j)/RE;                    %wavenumber
        omega = sqrt(g*wk*tanh(wk*h));               %wave radian frequency
        Cg = (g*tanh(wk*h) + g*wk*h*(sech(wk*h)).^2)*omega/(2*g*wk*tanh(wk*h));  %group velocity

    fun_alpha = @(x) omega^2 + g*x*tan(x*h);     %dispersion equation for evanescent modes
    
     end
       for n = 1:N
        if n ==1
            k(n) = -1i*wk;
  %%%%%%%%%%%%% Find derivative of Z0 at z=-d%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      Z0d = (cosh(wk*h) * wk * sinh(wk*b))/(2*wk*h + sinh(2*wk*h));
        else
         x0_alpha = [(2*n -3)*pi/2./h, (2*n -1)*pi/2./h];  % Narrow interval
          k(n) = lsqnonlin(fun_alpha, mean(x0_alpha), (2*n -3)*pi/2./h, (2*n -1)*pi/2./h);
      
       
        Znd(n) = -k(n) * (cos(k(n)*h) * sin(k(n)*b)) / (2*k(n)*h + sin(2*k(n)*h));
 
        
        
    end
       end

           
      
  a1 = 0.93 * (1 - tau) * Cg;  %       
 for m=2:M
     lambda(m) = ((m-1) * pi) / b;
 end
%%%%%%%%%%%%%%%%%%%% Set Matrix A %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    A = zeros(M,N);
    % For first element A00
A(1,1) = (cosh(wk*h) * sinh(wk*b)) / (wk*b * (2*wk*h + sinh(2*wk*h))) ...
         * (besselh(l, 1, wk*RE)) / (dbesselh(l, wk*RE));
% For 2nd Element A0n
for n = 2:N
    A(1,n) =  (cos(k(n)*h) * sin(k(n)*b)) / (k(n)*b * (2*k(n)*h + sin(2*k(n)*h)))...
        * (besselk(l, k(n)*RE) )/(dbesselk(l, k(n)*RE));
end
% % for element Am0
 for m = 2:M
A(m,1) = 2 * (cosh(wk*h) * (-1)^(m-1) * wk * sinh(wk*b))...
    /( b*( (wk^2+lambda(m)^2)*(2*wk*h +sinh(2*wk*h)) ) )  *  (besselh(l,1,wk*RE))/ (dbesselh(l,wk*RE));
 end

%%%%%%%% for element Amn
for m = 2:M
    for n = 2:N

A(m,n) = 2* (cos(k(n)*h) * (-1)^(m-1)* k(n) * sin(k(n)*b)) /(b*((k(n)^2 - (lambda(m))^2)...
    * (2*k(n)*h + sin(2*k(n)*h)))) * (besselk(l, k(n)*RE)) / (dbesselk(l, k(n)*RE));

    end
end

%%%%%%%%%%%%%%%%%% Matrix B %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 B = zeros(N, M); % Or whatever size you require
%%%%% Define B0%%%%%
B(1,1) = (4 * sinh(wk * b)) / (RE* wk*log(RE / RI) * cosh(wk* h));
%%%%%%%% define Bom%%%%
for m = 2:M
    Rml_prime_RE =  lambda(m)*(besselk(l, lambda(m)*RI) * dbesseli(l, lambda(m)*RE) ...
  - besseli(l, lambda(m)*RI) * dbesselk(l, lambda(m)*RE))...
  /(besselk(l, lambda(m)*RI) * besseli(l, lambda(m)*RE) - besselk(l, lambda(m)*RE) * besseli(l, lambda(m)*RI));
     B(1,m) = Rml_prime_RE * (4 * wk * (-1)^(m-1) * sinh(wk*b)) / (cosh(wk*h) * (wk^2 + (lambda(m))^2));
 end
%%%% define Bn0%%%%
for n = 2:N
 B(n,1) = (4* sin(k(n)*b)) / (RE *k(n)* log(RE/RI) * cos(k(n)*h));
end
%%%%%% Define Bnm %%%%%%%%
for n = 2:N
    for m = 2:M
        Rml_prime_RE =  lambda(m)*(besselk(l, lambda(m)*RI) * dbesseli(l, lambda(m)*RE) ...
  - besseli(l, lambda(m)*RI) * dbesselk(l, lambda(m)*RE))...
  /(besselk(l, lambda(m)*RI) * besseli(l, lambda(m)*RE) - besselk(l, lambda(m)*RE) * besseli(l, lambda(m)*RI));
        B(n,m) = Rml_prime_RE * (4* k(n) * (-1)^(m-1) * sin(k(n)*b)) / (cos(k(n)*h) * ((k(n))^2 - (lambda(m))^2));
    end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Define Matrix C %%%%%%%%%%%%%%%%%%%%%%%%
C = zeros(N,M);
C(1,1) = -4 * sinh(wk*b) / (RE * wk*log(RE/RI) * cosh(wk*h));
% %%%%% DEfine C0m%%%%%%
for m = 2:M
     Rml_prime_star_RE =  lambda(m)*(besseli(l, lambda(m)*RE) * dbesselk(l, lambda(m)*RE) ...
  - besselk(l, lambda(m)*RE) * dbesseli(l, lambda(m)*RE))...
  /(besselk(l, lambda(m)*RI) * besseli(l, lambda(m)*RE) - besselk(l, lambda(m)*RE) * besseli(l, lambda(m)*RI));
    C(1,m) = Rml_prime_star_RE * (4 * wk * (-1)^(m-1) * sinh(wk*b)) / (cosh(wk*h) * (wk^2 + (lambda(m))^2));
end
%%%%%%% Define Cn0%%%%%%
for n = 2:N
    C(n,1) = -4 * sin(k(n)*b) / (RE *k(n)* log(RE/RI) * cos(k(n)*h));
end
%%%%%% Define Cnm%%%%%%
for n = 2:N
    for m =2:M

     Rml_prime_star_RE =  lambda(m)*(besseli(l, lambda(m)*RE) * dbesselk(l, lambda(m)*RE) ...
  - besselk(l, lambda(m)*RE) * dbesseli(l, lambda(m)*RE))...
  /(besselk(l, lambda(m)*RI) * besseli(l, lambda(m)*RE) - besselk(l, lambda(m)*RE) * besseli(l, lambda(m)*RI));
    C(n,m) = Rml_prime_star_RE * (4 * k(n) * (-1)^(m-1) * sin(k(n)*b)) / (cos(k(n)*h) * ((k(n))^2 - (lambda(m))^2));  
    end
end
%%%%%%% write Matrix D %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
D = zeros(M,N);
%%%% write D00 %%%%%%
D(1,1) = (cosh(wk*h) * sinh(wk*b)) / (wk*b * (2*wk*h + sinh(2*wk*h))) * (besselj(l, wk*RI) )/ (dbesselj(l, wk*RI));
%%%%% write D0n %%%%%%%%%%
for n =2:N
    D(1,n) = (cos(k(n)*h) * sin(k(n)*b)) / (k(n)*b * (2*k(n)*h + sin(2*k(n)*h))) * (besseli(l, k(n)*RI) )/ (dbesseli(l, k(n)*RI));

end
%%%%%% write Dm0 %%%%%%%%%
for m = 2:M
    D(m,1) = (2 * cosh(wk*h) * (-1)^(m-1) * wk * sinh(wk*b)) /(b * (2*wk*h + sinh(2*wk*h)) * (wk^2 + (lambda(m))^2))...
        *(besselj(l, wk*RI) )/(dbesselj(l, wk*RI));
end
%%%%% Define Dmn%%%%%%%%
for m = 2:M
    for n = 2:N
        D(m,n) = (2 * cos(k(n)*h) * (-1)^(m-1) * k(n) * sin(k(n)*b)) /(b * (2*k(n)*h + sin(2*k(n)*h)) * (k(n)^2 - lambda(m)^2))...
        *(besseli(l, k(n)*RI)) / (dbesseli(l, k(n)*RI));
    end
end

%%%%%%%%%%%%%%%%%%%%%%%%%% Define Matrix E %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
E = zeros(N, M);  % Preallocate the matrix E
%%%%% Define E00%%%%%%%%%%%%
E(1,1) = (4 * sinh(wk*b)) / (RI *wk* log(RE/RI) * cosh(wk*h));
%%%% Define Eom %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for m = 2:M
    Rml_prime_RI = lambda(m)*(besselk(l, lambda(m)*RI) * dbesseli(l, lambda(m)*RI) ...
  - besseli(l, lambda(m)*RI) * dbesselk(l, lambda(m)*RI))...
  / (besselk(l, lambda(m)*RI) * besseli(l, lambda(m)*RE) - besselk(l, lambda(m)*RE) * besseli(l, lambda(m)*RI));
E(1,m) = Rml_prime_RI * (4 * wk * (-1)^(m-1) * sinh(wk*b)) / (cosh(wk*h) * (wk^2 + lambda(m)^2));

end
%%%%%% Define Eno%%%%%%%%%%%%%%
for n = 2:N
    E(n,1) = (4 * sin(k(n)*b)) / (RI *k(n)* log(RE/RI) * cos(k(n)*h));
end
for n = 2:N
    for m = 2:M
        Rml_prime_RI = lambda(m)*(besselk(l, lambda(m)*RI) * dbesseli(l, lambda(m)*RI) ...
  - besseli(l, lambda(m)*RI) * dbesselk(l, lambda(m)*RI))...
  / (besselk(l, lambda(m)*RI) * besseli(l, lambda(m)*RE) - besselk(l, lambda(m)*RE) * besseli(l, lambda(m)*RI));
E(n,m) = Rml_prime_RI * (4 * k(n) * (-1)^(m-1) * sin(k(n)*b)) / (cos(k(n)*h) * (k(n)^2 - lambda(m)^2));
    end 
end
%%%%%%%%%%%%%%%%%%%%%%%% Now write matrix F %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
F = zeros(N,M);
%%%%%%%% Define F00 %%%%%%%%%%
F(1,1) = (-4 * sinh(wk*b)) / (RI * wk*log(RE/RI) * cosh(wk*h));
%%%%%% Define F0m%%%%
for m = 2:M
Rml_star_prime_RE = lambda(m)*(besseli(l, lambda(m)*RE) * dbesselk(l, lambda(m)*RI) ...
  - besselk(l, lambda(m)*RE) * dbesseli(l, lambda(m)*RI))/((besselk(l, lambda(m)*RI) ...
  * besseli(l, lambda(m)*RE) - besselk(l, lambda(m)*RE) * besseli(l, lambda(m)*RI)));
F(1,m) = Rml_star_prime_RE * (4 * wk * (-1)^(m-1) * sinh(wk*b)) / (cosh(wk*h) * (wk^2 + lambda(m)^2));
end
%%%%% Defin Fn0%%%%%%
for n = 2:N
    F(n,1) = (-4 * sin(k(n)*b)) / (RI *k(n)* log(RE/RI) * cos(k(n)*h));
end
%%%%%%% Define Fnm %%%%%%%
for n = 2:N
    for m = 2:M
        Rml_star_prime_RE = lambda(m)*(besseli(l, lambda(m)*RE) * dbesselk(l, lambda(m)*RI) ...
  - besselk(l, lambda(m)*RE) * dbesseli(l, lambda(m)*RI))/((besselk(l, lambda(m)*RI) ...
  * besseli(l, lambda(m)*RE) - besselk(l, lambda(m)*RE) * besseli(l, lambda(m)*RI)));
        F(n,m) = Rml_star_prime_RE * (4 * k(n)* (-1)^(m-1) * sin(k(n)*b)) / (cos(k(n)*h) * (k(n)^2 - lambda(m)^2));
    end
end
% Calling the bessel0j(l,q,option) to find the positive roots of Bessel functions
 roots = bessel0j(l, Q);        % [x_1^l, x_2^l, ..., x_Q^l] (1 x Q vector)
chi = roots./ RI;              % (1 x Q vector) -- only if you need chi_q^l  
% %%%%%%%%%% Write Matrix W %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
W = zeros(N,Q);
%%W_{0q}
for q = 1:Q
    W(1, q) = - (4 * chi(q) / cosh(wk * h)) * (chi(q) * sinh(chi(q) * b) * cosh(wk * b) - wk * sinh(wk * b) * cosh(chi(q) * b)) ...
        / ((chi(q)^2 - wk^2) * sinh(chi(q) * b));
end
% %%% Write W_{nq}
 for n = 2:N
     for q = 1:Q
        W(n, q) =  - (4 * chi(q) / cos(k(n) * h)) * (chi(q) * sinh(chi(q) * b) * cos(k(n) * b) + k(n) * sin(k(n) * b) * cosh(chi(q) * b)) ...
        / ((chi(q)^2 + k(n)^2) * sinh(chi(q) * b));
     end
 end
% %%%%%%%%%%%%%%%%%%%%%%%Find E1_{q}%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for q = 1:Q
f2  = omega^2 / g;            
   E1(q) = ( chi(q)*cosh(chi(q)*h) - f2*sinh(chi(q)*h) ) ...
            / ( f2*cosh(chi(q)*d) - chi(q)*sinh(chi(q)*d) );
end
% 
% find H_{q}
 for q = 1:Q
    % Compute the diagonal value for H at index q
      H(q) = 2 /( sinh(2 *chi(q)*b)) - E1(q)+1i*chi(q)*a1/omega;
% 
%     % % Compute the  value for H at index q, multiplied by the term
%      H(q) = (2 / (sinh(2 * chi(q)*b)) - E1(q) + 1i * a1 *chi(q)/ omega) * (RI^2 *(besselj(l+1, chi(q) * RI))^2 )/ (2 *dbesselj(l, chi(q) * RI));
% 
 end
 %%%%%%%%%%matric G%%%%%%%%%%%%%%%%%%
  G = zeros(Q, N);        % Preallocate
 for q = 1:Q

     G(q, 1) = (2i * a1 / RI*omega*H(q))*(Z0d*chi(q)*besselj(l,wk*RI) ) / ((chi(q)^2-wk^2)*dbesselj(l, wk*RI));
 
 end
% %% G_{qn}
 for q = 1:Q
    for n = 2:N  

     G(q, n) = (2i * a1 / RI*omega*H(q))*(Znd(n)*chi(q)*besseli(l,wk*RI) ) / ((chi(q)^2+wk^2)*dbesseli(l, wk*RI));
    end
  end

% 
%Define the right hand side vector
U = zeros(2*M + 2*N + Q, 1);  % Full vector, M+N+M+N+Q elements

for m = 1:M
    if m == 1
        % Z_0^l term (first entry in Block 1)
        U(m,1) = (besselj(0, wk*RE) * sinh(wk*b)) / (b*wk * cosh(wk*h));
    else
        % Z_m^l terms (m = 2,3,...,M)
        U(m,1) = (2 * besselj(l, wk*RE) * sinh(wk*b) * wk * (-1)^(m-1)) ...
             / (b* cosh(wk*h)*(wk^2 + lambda(m)^2));
    end
end
% Block 2: Y (size N = 3)
for n = 1:N
    if n == 1
        U(n + M, 1) = -dbesselj(l, wk*RE) * (2*wk*h + sinh(2*wk*h)) /(cosh(wk*h)^2);  % Y_0^l
    else
        U(n + M, 1) = 0;  % Y_n^l
    end
end
% Block 3: X (size M)
for m = 1:M
    U(m + M + N, 1) = 0;  % X_0^l, X_m^l
end

% Block 4: W (size N)
for n = 1:N
    U(n + M + N + M, 1) = 0;  % K_0^l, K_n^l
end
% Block 5: linear part
    for q = 1:Q
        U(2*M + 2*N + q) = 0;
     end
ZMM = zeros(M,M); ZMN = zeros(M,N); ZMQ = zeros(M,Q);
ZNM = zeros(N,M); ZNN = zeros(N,N); ZNQ = zeros(N,Q);
ZQM = zeros(Q,M); ZQN = zeros(Q,N);
% % 
    %%%%%%%%%% DEFINE THE MATRIX S%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
S = [ eye(M),   -A,     ZMM,  ZMN,  ZMQ;
     -B,       eye(N),  -C,   ZNN,  ZNQ;
      ZMM,      ZMN,   eye(M), -D,  ZMQ;
     -E,        ZNN,    -F,   eye(N), -W;
      ZQM,      ZQN,    ZQM,  -G,   eye(Q) ];
% % % Solve for the unknowns vector T (which holds [bm; an; cm; dn; eq])
 T = pinv(S) * U;   % If S may be singular or not square
% %   % T = lsqminnorm(S,U);
  % T = S \ U;
% %  % cS = condest(S);    % fast estimate for sparse or dense
% after solving S*T = U
bm = T(1:M);                          %  (M×1)
an = T(M+1:M+N);              %  (N×1)
cm = T(M+N+1:2*M+N);            %  (M×1)
dn = T(2*M+N+1:2*M+2*N);          %  (N×1)
eq = T(2*M+2*N+1:end);              %  (Q×1)
% %%%%%% wave motion inside cylinder %%%%%%%%%%%%
 term1 = dn(1)*cosh(wk*h)^2/(2*wk*h+sinh(2*wk*h))/dbesselj(l,wk*RI);
  sum1 = 0;
 for n =2:N
    sum1 = sum1+dn(n)*cos(k(n)*h)^2/(2*k(n)*h+sin(2*k(n)*h))/dbesseli(l,k(n)*RI);
 end
sum2 = 0;
for q =1:Q
    sum2 = sum2+eq(q)*(E1(q)*cosh(chi(q)*d)/cosh(chi(q)*b)+sinh(chi(q)*h)/cosh(chi(q)*b))*1/(dbesselj(l,chi(q)*RI));
end
 
 eta0(j) =abs(term1+sum1+sum2);

     end

Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.


Local minim...

% 
% 
figure;
plot(k0RE, eta0, 'b-', 'LineWidth', 2); % Plot with blue line, 2px width
% Label axes
xlabel('k0RE');
ylabel('\eta (iA)');
% % Set axis limits
 xlim([5 35]);  % Set x-axis range from 5 to 35

% ylim([1e-7 1e-2]);   % Set y-axis range (adjust this based on your data)   % Set y-axis range with a log scale (you can adjust this based on your data)
% % Set y-axis to log scale
 % set(gca, 'YScale', 'log');
% 
% grid on;   % 
% % Set figure title
% title('Plot of \eta vs. k0RE');
elapsedTime = toc;
disp(['Time consuming =  ', num2str(elapsedTime), ' s']);

Time consuming =  18.3603 s

The Functions which i am calling in my main code is below.

function x = bessel0j(l,q,opt)
% a row vector of the first q roots of bessel function Jl(x), integer order.
% if opt = 'd', row vector of the first q roots of dJl(x)/dx, integer order.
% if opt is not provided, the default is zeros of Jl(x).
% all roots are positive, except when l=0,
% x=0 is included as a root of dJ0(x)/dx (standard convention).
%
% starting point for for zeros of Jl was borrowed from Cleve Moler, 
% but the starting points for both Jl and Jl' can be found in
% Abramowitz and Stegun 9.5.12, 9.5.13. 
%
% David Goodmanson
%
% x = bessel0j(l,q,opt)

k = 1:q;
if nargin==3 && opt=='d'
    beta = (k + l/2 - 3/4)*pi;
    mu = 4*l^2;
    x = beta - (mu+3)./(8*beta) - 4*(7*mu^2+82*mu-9)./(3*(8*beta).^3);
    for j=1:8
        xnew = x - besseljd(l,x)./ ...
            (besselj(l,x).*((l^2./x.^2)-1) -besseljd(l,x)./x);
        x = xnew;    
    end
    if l==0
        x(1) = 0;    % correct a small numerical difference from 0
    end
else
    beta = (k + l/2 - 1/4)*pi;
    mu = 4*l^2;
    x = beta - (mu-1)./(8*beta) - 4*(mu-1)*(7*mu-31)./(3*(8*beta).^3);
    for j=1:8
        xnew = x - besselj(l,x)./besseljd(l,x);
        x = xnew;
    end
end
end

% --- Local helper function for derivative of Bessel function ---
function dJ = besseljd(l, x)
    dJ = 0.5 * (besselj(l - 1, x) - besselj(l + 1, x));
end

function out = dbesselh(l, z)
%DBESSELH  Derivative of the Hankel function of the first kind
%   out = dbesselh(l, z)
%   Returns d/dz [H_l^{(1)}(z)] using the recurrence formula:
%   H_l^{(1)'}(z) = 0.5 * (H_{l-1}^{(1)}(z) - H_{l+1}^{(1)}(z))

    out = 0.5 * (besselh(l-1, 1, z) - besselh(l+1, 1, z));
end

function out = dbesseli(l, z)
%DBESSELI  Derivative of the modified Bessel function of the first kind
%   out = dbesseli(l, z)
%   Returns d/dz [I_l(z)] using the recurrence formula:
%   I_l'(z) = 0.5 * (I_{l-1}(z) + I_{l+1}(z))

    out = 0.5 * (besseli(l-1, z) + besseli(l+1, z));
end

function out = dbesselj(l, z)
%DBESSELJ  Derivative of the Bessel function of the first kind
%   out = dbesselj(l, z)
%   Returns d/dz [J_l(z)] using the recurrence formula:
%   J_l'(z) = 0.5 * (J_{l-1}(z) - J_{l+1}(z))

    out = 0.5 * (besselj(l-1, z) - besselj(l+1, z));
end

function out = dbesselk(l, z)
%DBESSELK  Derivative of the modified Bessel function of the second kind
%   out = dbesselk(l, z)
%   Returns d/dz [K_l(z)] using the recurrence formula:
%   K_l'(z) = -0.5 * (K_{l-1}(z) + K_{l+1}(z))

    out = -0.5 * (besselk(l-1, z) + besselk(l+1, z));
end

[Torsten]

I know too little about the underlying physics and mathematics in order to be of help at this stage of your work. The only thing I did was that I reran your code and noticed that the matrix G has elements in the order of 1e123 for each of the k0RE values. This should not be correct because it will destroy every numerical method.