How to find the sum of all column vectors of the elements on the kth diagonal of a square matrix in Matlab ?

Hello, sir/madam. I need your help to find a solution to the following case.

n = 3;
A = magic(n)
B = diag(diag(A,0));
C = sum(sum(B))
D = triu(A) + tril(A) + diag(B(B>0)+C) - (2*diag(diag(A,0)))

A =
     8     1     6
     3     5     7
     4     9     2

C =
    15

D =
    23     1     6
     3    20     7
     4     9    17

As can be seen, I found the main diagonal elements and added their sum to each column vector element, as shown in D. But, I can’t do that for following column vector elements (for any n value):

B1 =
     0    1    0          
     0    0    7
     0    0    0

B1 = sum(sum(B1)) = 8

B2 = 
     0    0    6
     0    0    0
     0    0    0

B2 = sum(sum(B2)) = 6

B3 = 
     0    0    0
     3    0    0
     0    9    0

B3 = sum(sum(B3)) = 12

B4 =
     0    0    0
     0    0    0
     4    0    0

B4 = sum(sum(B4)) = 4

Can anyone help me to write a code that can do that so that I can obtain the following output ?

D =
    23     9     6
    15    20    15
    4     21    17

Thank you!

Answer 1

[Massimo Zanetti]

Here it is the code that does the work. Inspect the function diag and partial results at each iteration.

 n = size(A,1);
 for k = -n+1:n-1
    %get kth diagonal sum
    v = sum(diag(A,k));
    %add the sum to the kth diagonal of a
    A = A + diag(v*ones(n-abs(k),1),k)
 end

[Gobert]

Thank you very much, Massimo Zanetti!

[Massimo Zanetti]

You are welcome :) Vote my answer if you liked!

Answer 2

[KSSV]

A = [  8     1     6
     3     5     7
     4     9     2];
 C = 15 ;
 C = C*eye(size(A)) ;
iwant = A+C

[Gobert]

Thanks,Siva, but it does not produce the following:

D =
    23     9     6
    15    20    15
    4     21    17

That's a shortcut to produce the following (I had done).

D =
    23     1     6
     3    20     7
     4     9    17

[KSSV]

Ohk..what I have done only adds to diagonal elements..