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matlabmatrixdiagonal
TYL
TYL

Reputation: 1637

Changing the diagonals beside center diagonal of matrix

Is there a quick way to change the diagonals beside the center diagonal (referring to the 1s below):

m =  
 2     1     0     0     0     0     0     0     0
 1     2     1     0     0     0     0     0     0
 0     1     2     1     0     0     0     0     0
 0     0     1     2     1     0     0     0     0
 0     0     0     1     2     1     0     0     0
 0     0     0     0     1     2     1     0     0
 0     0     0     0     0     1     2     1     0
 0     0     0     0     0     0     1     2     1
 0     0     0     0     0     0     0     1     2

A quick way to change the center diagonal is m(logical(eye(size(m)))) = 2. How about assigning the diagonals beside it to values of 1?

Upvotes: 0

Views: 428

Answers (1)

Dan
Dan

Reputation: 45741

The diag function takes a second parameter, k, which specifies which diagonal to target:

diag([-1,-1,-1,-1],-1) % or diag(-1*ones(4,1),1)

ans = 

     0    0    0    0    0
    -1    0    0    0    0
     0   -1    0    0    0
     0    0   -1    0    0
     0    0    0   -1    0


diag([1,1,1,1],1)

ans = 

     0    1    0    0    0
     0    0    1    0    0
     0    0    0    1    0
     0    0    0    0    1
     0    0    0    0    0

diag([2,2,2],2)

ans = 

     0    0    2    0    0
     0    0    0    2    0
     0    0    0    0    2
     0    0    0    0    0
     0    0    0    0    0

If you already have an existing matrix and you want to change one of the diagonals you could do this:

M = magic(5) % example matrix
v = [1,2,3,4] % example vector that must replace the first diagonal of M, i.e. the diagonal one element above the main diagonal

M - diag(diag(M,1),1) + diag(v,1)

The idea is to first use diag to extract the numbers of the diagonal you want to change, diag(M,1). Then to use diag again to change the vector that the first call to diag created into a matrix, diag(diag(M,1),1). You'll notice that this creates a matrix with the same dimensions as M, the same numbers as M on the 1st diagonal and 0s everywhere else. Thus M - diag(diag(M,1),1) just sets that first diagonal to 0. Now diag(v,1) creates a matrix with the same dimensions as M that is 0 everywhere but with the numbers of v on the first diagonal and so adding diag(v,1) only affects that first diagonal which is all 0s thanks to -diag(diag(M,1),1)

An alternative if you are just applying a constant to a diagonal (for example setting all the values on the first diagonal below the main diagonal to 6):

n = 5;
k = -1;
a = 6;
M = magic(n);
ind = diag(true(n-abs(k),1),k);
M(ind) = a;

Upvotes: 2

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