# Diagonally Dominant Check & Change for Coefficient Matrix and Result Vector

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Mr.Chandler on 30 Nov 2020
Answered: Stephan Ciobanu on 13 Jan 2021
A is the coefficient matrix of the linear equation system. B is the right hand side vector of the linear equation system (which are results). A and b will be used in Gauss-Seidel method to solve the system. This code checks if A is diagonally dominant or not. If it is not diagonally dominant, it changes row orders of A (of course if it is possible to make it diagonally dominant). However, the problem is, the vector b has also to change in the same order that A was changed. How can I do that?
A=[0.3 0.7 1.3;1.2 0.3 -0.5;0.1 0.5 0.3];
b=[7.6;0.1;2.8];
[maxrow,maxind] = max(abs(A),[],2);
if all(maxrow > (sum(abs(A),2) - maxrow)) && isequal(sort(maxind),(1:numel(maxind))')
A(maxind,:) = A;
else
disp('This matrix can never be made to be diagonally dominant')
A = [];
end

Stephan Ciobanu on 13 Jan 2021
Hi! This code should work for your requests:
By the way, I'd rather calculate
Where is the Gauss-Seidel matrix iteration, are the eigenvalues of and (where n is the size of A)
or check if A is symmetric positive-definite.
[row,col] = size(A);
if row~=col % Checking the size of A
error('A must be square matrix!')
end
Diag = diag(A); % Extracting the main diagonal of A
A_mod = A - Diag.*eye(row); % A_mod is A without the main diagonal
for i=1:row
A_sum_row(i) = sum(abs(A_mod(i,:))); % Calculating the sum of each row and
A_sum_col(i) = sum(abs(A_mod(:,i))); % column
end
% Checking if A is already diagonal dominant
if (all(A_sum_row(:)<abs(Diag(:)))==true && all((A_sum_col(:))<abs(Diag(:)))==true)
fprintf('A is diagonal dominant by rows and column \n')
elseif A_sum_row(:)<abs(Diag(:))
fprintf('A is diagonal dominant by rows \n')
elseif A_sum_col(:)<abs(Diag(:))
fprintf('A is diagonal dominant by column \n')
else
result = false;
end
% Try to convert A in a diagonal dominant matrix
if exist('result','var')
[max_val_row,max_pos_row]=max(abs(A));
if length(unique(max_pos_row))~=length(max_pos_row)
fprintf('A isn''t diagonal dominant by rows or column \n')
else
for i = 1:row
A_diag_dom(i,:) = A(max_pos_row(i),:);
B(i) = b(max_pos_row(i));
end
end
end

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