How to make tridiagonal matrix in matlab?

问题:

How I create matrix below from vector [1 2 3 4 5]

1 0 0 0 0
2 1 0 0 0
3 2 1 0 0
4 3 2 1 0
5 4 3 2 1
0 5 4 3 2
0 0 5 4 3
0 0 0 5 4
0 0 0 0 5

回答1:

This is not tridiagonal, but a variant of pentadiagonal matrix. You can use diag, or sparse, or spdiags, all of which could build it. You could read my blktridiag code, as found on the File Exchange, to learn how I build such a matrix efficiently.

But perhaps the simplest solution is to recognize that your matrix is of a special form, a toeplitz matrix.

>> toeplitz([1:5,zeros(1,4)]',[1, zeros(1,4)])
ans =
     1     0     0     0     0
     2     1     0     0     0
     3     2     1     0     0
     4     3     2     1     0
     5     4     3     2     1
     0     5     4     3     2
     0     0     5     4     3
     0     0     0     5     4
     0     0     0     0     5

回答2:

Not sure exactly what you are trying to do, but you may find diag(v,n) and convmtx(v) useful. In your case

 convmtx([1,2,3,4,5],5)

Produces:

 1     2     3     4     5     0     0     0     0
 0     1     2     3     4     5     0     0     0
 0     0     1     2     3     4     5     0     0
 0     0     0     1     2     3     4     5     0
 0     0     0     0     1     2     3     4     5

回答3:

take a look here: http://www.mathworks.com/help/techdoc/ref/diag.html

Example:

diag(-m:m)+diag(ones(2*m,1),1)+diag(ones(2*m,1),-1)

produces a tridiagonal matrix of order 2*m+1.