Fast Tridiagonal System Solver

A fast tridiagonal system solver.

Description

Solves a tridiagonal system quickly.

• Acknowledgements: This submission has inspired the following:; Fast Pentadiagonal System Solver, Block tridiagonal solver
• MATLAB release: MATLAB 5.2 (R10)

[abhijith bharadwaj]

this programme was very good,super,extraordinary

[Venkata Pradeep Indrakanti]

This code works faster than others using the sparse matrix functions of MATLAB.Although the gain in speed might not be evident for small computations, for the bigger ones, it might save (valuable) time.

[Garner Izru]

Excellent! I was looking for a routine like this, thanks Frederico!

[Bill Armstrong]

The hidden photos were very tastefully done...

[sarava shanmuga]

 

[sebastian swose]

The solving of a linear system with calculating the inverse matrix is faster!!??
I dodnt know why

[Edgar Guevara Codina]

Very fast, it helped me improve the algorithm of a FD-BPM simulation

[Jorge Puebla]

I received a recommendation about this file, is an excelent tool

[Alex Prideaux]

Using Matlab 7.4 and sparse matrices, this code is unfortunately at least 10 times slower than the standard Matlab backslash.

[Tim Davis]

This function is superseded by the tridiagonal solver that is now built into MATLAB (x=A\b). For x=thomas(A,b) where A is sparse and tridiagonal, x=A\b is up to 25,000 times (!) faster than this code. For x=thomas(amain,aup,alo,b), this function is about 30 times slower than x=A\b.

So the only reason for this code is to illustrate the algorithm - for which its still useful. But don't expect to get great performance from it compared to x=A\b in MATLAB 7.5

[Hongjun Zhang]

Excellent algorithm. I tested it on 2000x2000 matrix, it's 10 times faster than back slash and 5 times faster than inv(), on 2.0G Intel Duo Core, 1G ram, on Matlab 8a. (1.2 seconds for thomas, 6.5 s for inv(), and 13.5 for /).

For small matrix, say 100x100, these three are comparable.

I though Tim was right and trusted back slash. But it's not the case for me.

I don't know what kind of sparse matrices Tim and Alex talking about that back slash runs faster for. I would say the 3-diagonal is already sparse and is encounter often in solving pdes.

[Vinesh Rajpaul]

Great script. Easy to use and works very well.

[Xiang]

My test result is the same as Tim's and Alex's. My A matrix is only 20*20 and is strictly diagonally dominant tridiagonal.
It took "thomas(A,B)" 62.7 seconds to complete 4000 time-steps, while "A\B" used only 4.5 seconds.