(Block) tri-diagonal matrices

Generate (block) tridiagonal matrices

Description

Every once in a while I need to generate a tridiagonal matrix with replicated elements down the diagonals. Sometimes its nice to generate block tridiagonal matrices of the same form.

full(blktridiag(2,-1,-1,5))
ans =
     2 -1 0 0 0
    -1 2 -1 0 0
     0 -1 2 -1 0
     0 0 -1 2 -1
     0 0 0 -1 2

full(blktridiag(ones(2),2*ones(2),3*ones(2),3))
ans =
     1 1 3 3 0 0
     1 1 3 3 0 0
     2 2 1 1 3 3
     2 2 1 1 3 3
     0 0 2 2 1 1
     0 0 2 2 1 1

This can of course be easily extended to handle general blocks, so since I saw an interest from a user, this release does that too.

Amd = reshape(1:16,[2,2,4]);
Asub = reshape(101:112,[2,2,3]);
Asup = reshape(201:212,[2,2,3]);
A = blktridiag(Amd,Asub,Asup);

full(A)
ans =
     1 3 201 203 0 0 0 0
     2 4 202 204 0 0 0 0
   101 103 5 7 205 207 0 0
   102 104 6 8 206 208 0 0
     0 0 105 107 9 11 209 211
     0 0 106 108 10 12 210 212
     0 0 0 0 109 111 13 15
     0 0 0 0 110 112 14 16

I've also seen a request to allow non-square blocks. This too is now accommodated in the latest release.

A = blktridiag([1;2],[3;4],[5;6],4);
full(A)
ans =
     1 5 0 0
     2 6 0 0
     3 1 5 0
     4 2 6 0
     0 3 1 5
     0 4 2 6
     0 0 3 1
     0 0 4 2

• MATLAB release: MATLAB 7.0.1 (R14SP1)
• Other requirements: I've intentionally kept this code accessible to earlier releases of matlab.

[Kong Zuor]

Nice work John. Very usefull indeed. This is a very useful code, especially CFD.

[hicham laanaya]

Thank you John.

[Miguel de Vega]

Wonderful code, and very useful. Thanks John

[Adrian Verhoef]

Very useful code....
Could you please show us the code for the extension too? Thanks in advance.

[Tim Davis]

Great example of the best way to create a sparse matrix. Nice demo (including a demo is very important in a usable submission).

One minor comment: your submission as of May 11 includes ".DS_Store" files in each folder, which only tell a Mac how to size the window when viewing the folders. Those files are visible to the Windows and Unix/Linux users. They can be deleted.

[Antoine Tambue]

Many thank for the function, it work very well for square blocks.
Can you have any idea for tridiagonal matrix with not square blocks?
One again many thanks
Antoine

[Antoine Tambue]

 

[Jun Seo]

Good example for making a sparse matrix.

[Bert Xer]

Nice work! Thanks so much!

[Silvia Sasheva]

Hello, can you help with this error:??? Undefined function or method 'blktridiag' for input arguments of type
'double'.
Probably, it is a stupid question, but I really need help! Thank you in advance!
Best Regards!

[John D'Errico]

It means you have not placed the function in a directory on your search path. Do NOT put it in the matlab toolbox directories, but in some other directory that you should reserve for your own functions. Then make sure that directory is on the search path. Use the functions addpath, savepath and pathtool to set up your search path.

[Silvia Sasheva]

Hello,
can please help me to find out if it's possible, using "blktridiag", to generate a block tridiagonal matrix A, whose main diagonal (Amd) to starts and ends with different copies of Amd. I.e. AmdFirst and AmdLast~= Amd...
example:
[AmdF Asup 0 0 0;
Asub Amd Asup 0 0;
0 Asub Amd Asup 0;
0 0 Asub Amd Asup;
0 0 0 Asub AmdL]

I hope that the explanation was clear enought! Thank you in advance!
Regards

[John D'Errico]

Of course it is possible, since you can supply the individual blocks along the main diagonal. Since the diagonal blocks can be supplied as a pxqxn array in Amd, use repmat to replicate the middle blocks, then replace the first and last blocks in Amd as you wish. Then its just a call to blktridiag.

[Silvia Sasheva]

Thank you for the quick and complete answer. Unfortunately, I'm not familiar with a "repmat" and how to replicate only the middle blocks and replace the first and the last one.
I tried this:
 v = repmat(AmdF(1),n,1);
  v = repmat(Amd(:),n,1);
  v = repmat(AmdL(n),n,1);
but of course it doesn't work....
Have you got a clue how to call it?
Thank you in advance and appreciation again for the code!!!

[Silvia Sasheva]

Hello, John,
I did it in other way. I defined Amdb (A main diag. boundary blocks) in your code and then applied this:
 s=repmat(Amdb(:),1,1);
 v=[s;repmat(Amd(:),n-2,1);s];
It works and now I will try to go further with the solution of the examined problem. Thank you and regards!

[Dany]