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

조회 수: 4(최근 30일)
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
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
function d = Kron(k,j)
if k == j
d = 1;
d = 0;
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.
  댓글 수: 1
Abhishek Gupta
Abhishek Gupta 2021년 2월 15일
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.

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Abhishek Gupta
Abhishek Gupta 2021년 2월 15일
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)));
A(rows,cols) = (-1/2)*secondTerm;
  댓글 수: 1
Domantas Laurinavicius
Domantas Laurinavicius 2021년 2월 15일
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);
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);
H_cos(0,0) = sum(V_vals); % H_cos(0,0) = sum(V_vals) % Necessary to have an exception statement for 0,0
This works for now, but the ZeroBased() func is incompatible with eig() so I'll have to fix that.

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