tridiagonal matrix with a corner entry from upper diagonal
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ivordes greenleaf
on 22 Apr 2015
Answered: Jacob Lane
on 16 Apr 2019
I am trying a construct a matlab code such that it will solve an almost tridiagonal matrix. The input I want to put in is the main diagonal (a), the upper diagonal (b) and the lower diagonal and the RHS vector (r). The matrix I want to solve looks like this:
| a(1) b(1) |
| c(1) a(2) b(2) |
| c(2) a(3) b(3) |
| . . . |
| . . . |
| . . b(n-1) |
| b(n) c(n) a(n) |
I can construct a code that works for the tridiagonal, but that corner entry got me, especially when it is supposed to come from the original input c.
This is what I got so far:
function y = tridiagonal ( c, a, b, r )
n = length ( a );
for i = 1 : n-1 b(i) = b(i) / a(i); a(i+1) = a(i+1) - c(i) * b(i); end
r(1) = r(1) / a(1); for i = 2 : n r(i) = ( r(i) - c(i-1) * r(i-1) ) / a(i); end
for i = n-1 : -1 : 1 r(i) = r(i) - r(i+1) * b(i); end
if ( nargout == 0 ) disp ( r ) else y = r; end
Thanks for any input!
1 Comment
Guillaume
on 22 Apr 2015
The c entry on the last row should be c(n-1) not c(n). Where does c(n) go? The last column of the first row?
Accepted Answer
Guillaume
on 22 Apr 2015
There is actually a function in matlab to construct tridiagonal matrices. It's well hidden in the gallery function (with the tridiag option). I would construct the matrix this way:
a = 1:10; b = 101:110; c = 201:210; %demo data
m = full(gallery('tridiag', b, [a 0], c));
m(end-1, 1) = m(end-1, end); %move b(n) in first column
m(1, end-1) = m(end, end-1); %move c(n) in first row
m = m(1:end-1, 1:end-1) %get rid of last row and column
I assumed c(n) went in the last column of the first row, since it's c(n-1) that ends up on the last row.
2 Comments
Guillaume
on 22 Apr 2015
No, the coefficients can be anything. a, b and c just have to be vectors (of the same length). For example:
a = rand(1, 20); b = ones(1, 20); c = randperm(20);
work just as well.
More Answers (2)
Ahmet Cecen
on 22 Apr 2015
Check out spdiags and diag functions for a much easier way to do this.
0 Comments
Jacob Lane
on 16 Apr 2019
I am having trouble with trying to write a function for a tridiagonal matrix. I am just trying to prove that one is in fact tridiagonal. Can anyone help me?
0 Comments
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