using matlab you are requested to build your own code, if a matrix is diagonally

Question

using matlab

you are requested to build your own code, if a matrix is diagonally dominated! If it is not diagonally dominated, your code will re-arrange the matrix itself to make it diagonally dominated

The given formula for diagonally dominted is |a_ii| >= sum(|a_ij|) where i~=j.

A helpful code

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% swap i row with all its columns to j with all its columns

A([j i],:) = A([i j],:); % swap

b([j i]) = b([i j]);   % swap i row with j row

---------------------------------------

If you are using GaussSeidel_matlab2.m, your code should be placed between the following

if m ~= n % if m Not equal n, error

error('Matrix A must be square');

end

% Start of checking if diagonally dominant

---------------------------------------

Here

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% end of checking if diagonally dominant

C = A; % copy matrix A into C

Explanation / Answer

Hello Student!

I am happy to help you!

*************** The code goes here ********************

Save it as : dominantMatirx.m

function ans1 = dominantMatirx(Mat)

% Size of matrix

n = size(Mat,1);

% Initialization of variable

xIndex = 1;

yIndex = 1;

% The loop for the row number

for i = 1:n

% The sum value

sum = 0;

% Temp maxi value initialized

maxi = -1000000000;

% The loop for the column number

for j=1:n

% Sum value

sum = sum + abs(Mat(i,j));

% The maximum value is stored in maxi

if maxi < abs(Mat(i,j))

maxi = max(maxi, abs(Mat(i,j)));

xIndex = i;

yIndex = j;

end

end

% sum of the Mat(i,i) is lower than sum then -

if abs(Mat(i,i)) < sum

% if Mat(i,i) is lower than Mat(xIndex, yIndex) then -

if abs(Mat(i,i)) < abs(Mat(xIndex, yIndex))

% swap the elemet

temp = Mat(i,i);

Mat(i,i) = Mat(xIndex, yIndex);

Mat(xIndex, yIndex) = temp;

else

% Error it's not possible

Error('Not possible!');

return;

end

end

end

% return ans1

ans1 = Mat;

end

Save it as : test.m

clc

close all;

clear all;

lower_mat_A = [[1, 0, 0]; [2, 1, 0] ;[3, 4, 1]];

disp(dominantMatirx(lower_mat_A));

*************** The code ends here ********************

Input :

1 0 0
2 1 0
3 4 1

Output :

1 0 0
1 2 0
3 1 4

Thank you. Feel free to ask anything. If you like the answer. Please upvote it. It means a lot. Thank you again.

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