Creating a tridiagonal matrix

I am currently trying to create a 500*500 matrix in matlab with diagonals a=-1, b=4, c=2. My teacher has said that the best way to go about it is using loops, but is there a coded in function to use?

[David Goodmanson]

Hi Aaron

check out the 'diag' function

[Alex Treat]

coughs you were in the mec 103 class at CSU...

Answer 1

[Stephen23]

"My teacher has said that the best way to go about it is using loops"

Why on earth would they say that? Here are some non-loop aproaches:

1- See @giannit's comment: https://www.mathworks.com/matlabcentral/answers/490368-creating-a-tridiagonal-matrix#comment_1027546

2- Use diag :

>> N = 10;
>> a = -1;
>> b = 4;
>> c = 2;
>> M = diag(a*ones(1,N)) + diag(b*ones(1,N-1),1) + diag(c*ones(1,N-1),-1)
M =
  -1   4   0   0   0   0   0   0   0   0
   2  -1   4   0   0   0   0   0   0   0
   0   2  -1   4   0   0   0   0   0   0
   0   0   2  -1   4   0   0   0   0   0
   0   0   0   2  -1   4   0   0   0   0
   0   0   0   0   2  -1   4   0   0   0
   0   0   0   0   0   2  -1   4   0   0
   0   0   0   0   0   0   2  -1   4   0
   0   0   0   0   0   0   0   2  -1   4
   0   0   0   0   0   0   0   0   2  -1

3- indexing is reasonably simple:

>> M = zeros(N,N);
>> M(  1:1+N:N*N) = a;
>> M(N+1:1+N:N*N) = b;
>> M(  2:1+N:N*N-N) = c
M =
  -1   4   0   0   0   0   0   0   0   0
   2  -1   4   0   0   0   0   0   0   0
   0   2  -1   4   0   0   0   0   0   0
   0   0   2  -1   4   0   0   0   0   0
   0   0   0   2  -1   4   0   0   0   0
   0   0   0   0   2  -1   4   0   0   0
   0   0   0   0   0   2  -1   4   0   0
   0   0   0   0   0   0   2  -1   4   0
   0   0   0   0   0   0   0   2  -1   4
   0   0   0   0   0   0   0   0   2  -1

[Juan Jesús Rocha Cuervo]

How can I stop the output of "M" in this example?

[Jonathan Wharrier]

a semi-colon at the end of the line supresses output

[giannit]

This can be done also using toeplitz

A = toeplitz( [-1 2 zeros(1,498)] , [-1 4 zeros(1,498)] ); % size = 2 MB

and since there are many zeros you can save space using sparse

B = toeplitz( sparse([1 1],[1 2],[-1 2],1,498) , sparse([1 1],[1 2],[-1 4],1,498) ); % size = 28 kB

[Steven Lord]

If you're creating this as a sparse matrix see spdiags.

[Arth Patel]

Can you please explain the second method a bit ? It's not clear to me how you're indexing a matrix using just one argument.

[Stephen23]

"It's not clear to me how you're indexing a matrix using just one argument."

The second example uses linear indexing:

https://www.mathworks.com/help/matlab/math/array-indexing.html

https://www.mathworks.com/company/newsletters/articles/matrix-indexing-in-matlab.html

Answer 2

[Jihen]

function[A]=remplissage(n)
R1=(-4)*ones(n-1,1);
R2=ones(n-2,1);
A=6*eye(n)+diag(R1,-1)+diag(R1,1)+diag(R2,2)+diag(R2,-2);
end

[John D'Errico]

This does not actually answer the question, creating instead a matrix with 5 diagonals, so a penta-diagonal matrix.