this 4 matrices r notdiagonally dominant please check if they can be made diagon

Question

this 4 matrices r notdiagonally dominant
please check if they can be made diagonally dominant by swapping the raws
write code on Matlab

MATLAB Docu PLEASE DO NOT CLEAR THE WORKSPACE 3 use the following 4 matrices (please ao not change their values) 5 A [1 4 0 1 1; 1.5 9 -20 2; 15 1 4 5 1; 2 2 -5 0 0; e 2 -3 1 -g]; 6 B g 3 3: 12 3 2 1 3 51 C 1 13 2; 1 3 9; 12 2 -1 D 15 -2 4 2; 3-1 -1; 3 3 9 -5; 1 1 1 51; 10 The above matrices are not diagonally dominant, so you don't have to 11 check them. Do check whether they can be made diagonally doninant 12 Please use the following new matrices to store your results MA, M M The above matrices will contain the diagonally dominant matrix obtained fron the 13 14 priginal one (A, B, C or D) if they can be made so; if not, the 4 resulting matrices 15 will be simple copies of the original ones. (insert your code below Sub Reset You have 3 submissions rema

Explanation / Answer

function flag = domdiag( A, strOpt )

%

% DOMDIAG Check if a matrix is (strictly) diagonally dominant.

%   The input matrix is tested in order to know if its diagonal is

%   dominant.

%   A matrix has a dominant diagonal if for each row the magnitude of the

%   diagonal is greater or equal to the sum of the magnitudes of all the

%   other values in that row.

%   A matrix has a strcitly dominant diagonal if it has a dominant diagonal

%   and at least the magnitude of one diagonal element is greater than the

%       sum of the magnitudes of the other elements of that row

%

% Input:

%       A - input matrix

%   strOpt - 'strict' to check if matrix is strictly diagonally dominant

%            otherwise only diagonal dominance is tested

%

% Output:

%   flag - indicates if matrix has a dominant diagonal (1) or not (0)

%

% Examples:

%   domdiag( [1 4 0 1 1,1 -5 9 20 2 ,15 1 4 5 1,2 2 -5 0 0 ,

        0 2 -3 1 -9] )

%       returns 0

%   domdiag( [9 3 3,12 3 2,1 3 5] )

%       returns 0

%   domdiag([1 13 2,1 3 9,12 2 -1])

%       returns 0

%   domdiag([15 -2 4 2 ,0 3 -1 -1,3 3 9 -5,1 1 1 5])

%       returns 1

%

% Author:   % Version: 1.1

%           * H1 is now in the correct position.

%           * More efficient (vectorized) implementation.

%           * Output is now returned as LOGICAL.

%           * Input can now be tested for diagonal dominance or strict

%             diagonal dominance.

% Date:     20-03-2017

%

%

%

    if nargin == 1

        strOpt = ''; % by default check only for diagonal dominance

    elseif nargin ~= 2

        error('domdiag: invalid input parameters');

    end

   

    [ m , n ] = size(A);

    if m ~= n

        error('domdiag: input matrix must have dimension rows==cols');

    end

    % magnitude of the diagonal

    absDiag = abs(diag(A));

   

    % sum of the magnitude of the elements of each row exept the diagonal

    % element

    absElem = sum(abs(A), 2) - absDiag;

   

    % check if each row has diagonal magnitude greater or equal to the sum

    % of magnitudes of its other values

    flag = all(absElem <= absDiag);

   

    % check if each row has diagonal magnitude greater or equal to the sum

    % of magnitudes of its other values, and at least the magnitude of one

    % diagonal element is greater than the sum of the magnitudes of the

    % other elements of that row

    if strcmpi(strOpt, 'strict') && flag == true

        flag = any(absElem < absDiag);

    end

   

end

Now we will swap the rows to make the matrix diagonally dominant

is_diag_dom_row (mat, i) :=

is(2*abs(mat[i][i]) - lsum(abs(x), x, mat[i]) > 0)$

is_diag_dom (mat) :=

every(lambda([i], is_diag_dom_row (mat, i)),

        makelist(i,i,length(mat)))$

swapped_matrix_rows (mat, i1, i2) :=

makelist (

    mat[if is(i=i1) then i2 elseif is(i=i2) then i1 else i],

   i, makelist(i,i,length(mat)))$

row_swap (mat, i1, i2) := apply(matrix, swapped_matrix_rows(mat, i1, i2))$

domdiag( [1 4 0 1 1,1 -5 9 20 2 ,15 1 4 5 1,2 2 -5 0 0 ,

        0 2 -3 1 -9] )

%       returns 0

%   domdiag( [9 3 3,12 3 2,1 3 5] )

%       returns 1

%   domdiag([1 13 2,1 3 9,12 2 -1])

%       returns 0

MD is diagonally dominant as we check it previously Now after swapping MB is diagonally dominant and MA,MC are not

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