[R] Solving a tridiagonal system

Thomas W Blackwell
Wed, 01 Oct 2003 14:08:16 -0000

Will  -

Take a look at Roger Koenker's package  SparseMatrix,
available from CRAN.  Look also for some other package
from Roger which depends on SparseMatrix, but has a
different name.  It's a place to look.  I don't recall
whether it will answer your need or not.

-  tom blackwell  -  u michigan medical school  -  ann arbor  -

On Wed, 1 Oct 2003, Will Harvey wrote:

> I need to find solutions to a tridiagonal system. By
> this I mean a set of linear equations Ax = d where A
> is a square matrix containing elements A[i,i-1],
> A[i,i] and A[i,i+1] for i in 1:nrow, and zero
> elsewhere. R is probably not the ideal way to do this,
> but this is part of a larger problem that requires R.
>
> In my application it is much easier (and much faster)
> to generate the diagonal and off-diagonal elements of
> A as vectors, i.e. a = A[i,i-1], b = A[i,i] and c > A[i,i+1]. So I have
three vectors that define A, along
> with a solution vector d. The conventional method of
> solving such systems is to use the so-called "Thomas
> algorithm", see e.g.
>
<http://www.enseeiht.fr/hmf/travaux/CD0001/travaux/optmfn/hi/01pa/hyb74/node24.html>.
> This is very easy to code, but much more difficult to
> "vectorize". Is anyone aware of a library that
> contains a fast implementation of this algorithm?
>
> Another alternative is to use backsolve. I can easily
> eliminate the lower diagonal a, but I'm still left
> with b and c, whereas backsolve requires a matrix.
> Again, I can write a function to read b and c into a
> matrix, but this requires loops, and is too slow. Is
> there a vectorized way of doing it? Of course, the
> diag command works for b, but what about c? In Octave,
> diag allows for an offset, but R apparently does not.
>
> I would appreciate any and all assistance you experts
> can offer. Thanks in advance.
>
> Will Harvey
>
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