How do I make this sum loop work to fill select matrix elements?

I have a summation loop which is within a nested loop to generate a matrix. I'm not sure how to make it work properly for a start, and then only fill cells which are not on row 1, or column 1.

The code so far is

close all
clear
clc

n = 5;
n_pot = 5;

Vec = [1,1,1,1,1,1,1]
syms k
Sum = sum(Vec,1:n)
Vt = zeros(1,n);
V_sum = zeros(1,n);

A = zeros(n);
for rows = 1:n
    for cols = 1:n      
 
            for i = 1:n_pot
                Vt(i) = Vt(i) + (Vec(i)*(Kron(rows+cols,i) + Kron(abs(cols-rows),i)));
                V_sum = Vt(i);
                A(rows,cols) = V_sum
            end
    end
end

function d = Kron(k,j)

    if k == j
        d = 1;
    else
        d = 0;
    end
end

The Vec vector is only there for ease of manipulation on my part and will be replaced with a regular vector from graph fitting data.

The matrix I'm expecting to get is of the form

Matrix = /  /              /              /              /
         /  /              Vec(1)+Vec(3)  Vec(2)+Vec(3)  Vec(3)+Vec(5)
         /  Vec(1)+Vec(3)  /              Vec(1)+Vec(5)  Vec(2)+Vec(6)
         /  Vec(2)+Vec(3)  Vec(1)+Vec(5)  /              Vec(1)
         /  Vec(3)+Vec(5)  Vec(2)+Vec(6)  Vec(1)         /
         
         

Following this equation, I'm looking to implement the summation portion, and the first term is already worked in.

[Abhishek Gupta]

Can you provide the following clarifications?

1. Your output matrix, i.e., A, contains the value for the second term of the equation, right? If so, then Is 'Vec' in the code corresponds to the 'Sn' in the equation? Also, I don't see any (-1/2) term in your code.
2. What is your final object? Do you want to avoid filling the first row and first column of the matrix?
3. Do you also want to avoid diagonal cells of the matrix? From '/,' you mean NaN?

If you want to solve the second term of the given equation avoiding m and m' corresponding to the first row, first column, and diagonal cells of the matrix, see the answer below.

Answer 1

[Abhishek Gupta]

Hi,

As per my current understanding, you want to solve the second term of the equation, avoiding m and m' corresponding to the first row, first column, and diagonal elements of the matrix.

Here is the implementation of the same: -

A = nan(n);     % output matrix
for rows = 1:n
    for cols = 1:n     
            
        % if statement to avoid filling 1st row, 1st column, and diagonal elements
        if ~((rows == 1) || (cols == 1) || (rows == cols))
            secondTerm = 0; % initialize second term of the equation
            
            % calculate the second term
            for i = 1:n_pot 
                secondTerm = secondTerm + (Vec(i)*(Kron(rows+cols,i) + Kron(abs(cols-rows),i)));
            end
            
            A(rows,cols) = (-1/2)*secondTerm;
        end
            
    end
end

[Domantas Laurinavicius]

I've since worked it out

H_cos = ZeroBased(zeros(n_basis));
for cols = 0:n_basis    
    for rows = 0:n_basis
        
        if         rows == 0 %  Only row 1
               H_cos(rows,cols) = V_rows0(cols+1)*(-(2)^(-0.5)); %  V_rows0 had to be created otherwise V_vals(1) is cut off and the row is wrong.  
                                                                 %  Issue with only the first if statement probably caused by 0 indexed matrix 
         elseif     cols == 0 %  Only column 1
               H_cos(rows,cols) = V_long(rows)*(-(2)^(-0.5));
        

            
        elseif rows == cols
               H_cos(rows,cols) = (rows^2 + sum(V_long))*Kron(rows,cols) - 0.5*V_long(rows+cols);
        else
            
               for i = 1:n_pot
                   Vt(0) = V_vals(1)*(Kron(rows+cols,0) + Kron(abs(cols-rows),0));
                   Vt(i) = Vt(i-1) + V_vals(i)*(Kron(rows+cols,i) + Kron(abs(cols-rows),i));
                   H_cos(rows,cols) = -0.5*Vt(i);       
               end
               
            H_cos(0,0) = sum(V_vals); %  H_cos(0,0) = sum(V_vals) %  Necessary to have an exception statement for 0,0
            
        end
    end
end
H_cos

This works for now, but the ZeroBased() func is incompatible with eig() so I'll have to fix that.