How could I debug this code?

Hi all,

I am new to MATLAB and I want to formulate the following lease square expression in Matlab. I have some codes that I am typing here. But the optimization problem solution seems not to be correct. Does anyone has an idea why?

First, I want to solve the heat equation T_t(x,t) = - L_x . T(x,t) + F(x,t) where L_x is Laplacian matrix of the graph. then find y from the following least square.

min_y \sum_{j} \sum_{i} (F_j(t_i) - E_j(t_i, y))^2

Thanks in advance!!

Here is my code:

%++++++++++++++++ main ++++++++++++++++++++
 % incidence matrix for original graph
 C_hat = [ 1 -1  0  0  0  0;...
           0  1 -1  0  0 -1;...
           0  0  0  0 -1  1;...
           0  0  0  1  1  0;...
          -1  0  1 -1  0  0];
% initial temperature for each vertex in original graph
T_hat_0 = [0 7 1 9 4];
[M_bar,n,m_bar,T_hat_heat,T_hat_temp] = simulate_temp(T_hat_0,C_hat);
C = [ 1  1 -1 -1  0  0  0  0  0  0;...
     0 -1  0  0  1 -1  1  0  0  0;...
     0  0  1  0  0  1  0 -1 -1  0;...
     0  0  0  1  0  0 -1  0  1 -1;...
    -1  0  0  0 -1  0  0  1  0  1];
%
% initial temperature for each vertex in original graph
T_0 = [0 7 1 9 4];
%
% initial temperature simulation
[l,n,m,T_heat,T_temp] = simulate_temp(T_0,C);
%
% bounds for variables
lb = zeros(m,1);
ub = ones(m,1);
%
% initial edge weights
w0 = ones(m,1);
% optimization problem
%  w = fmincon(@fun, w0, [], [], [], [], lb, ub);

%++++++++++++++++++++ function++++++++++++++++++++++++++++
function [i,n,m,T_heat,T_temp] = simulate_temp(T,C)
%
% initial conditions
 delta_t = 0.1; 
 M = 20; %%number of time steps
 t = 1; 
 [n,m] = size(C);
 I = eye(n); 
 L_w = C * C';
 T_ini = T';
 Temp = zeros(n,1);
 % Computing Temperature
 %
 for i=1:M
     K = 2*I + L_w  * delta_t;
     H = 2*I - L_w  * delta_t;
     %
     if i == 1
         T_heat = (K \ H) * T_ini;
         %
         t = t + delta_t;
     else
         T_heat = (K \ H) * Temp;
         %
         t = t + delta_t;
     end
         % replacing column of T_final with each node temperature in each
         % iteration. It adds one column to the matrix in each step
         T_temp(:,i) = T_heat;
         %
         Temp = T_heat;
 end  
end

%++++++++++++++++++ function+++++++++++++++++++++++++++++++++++++++++
function w_i = fun(w);
%
for r=1:n
    for s=1:M_bar
        w_i = (T_hat_temp(r,s) - T_temp(r,s)).^2;
    end
end

Answer 1

[Image Analyst]

This is a good place to start: http://blogs.mathworks.com/videos/2012/07/03/debugging-in-matlab/