solve-periodic-tridiagonal 
Solve a system of linear tridiagonal equations
Introduction
This module accepts javascript Arrays or typed arrays representing the bands of a periodic tridiagonal matrix and computes the solution using the Thomas algorithm. The problem in matrix form is
![\left[
\begin{matrix}
{b_0} & {c_0} & { } & { } & { a_0 } \\
{a_1} & {b_1} & {c_1} & { } & { } \\
{ } & {a_2} & {b_2} & \cdot & { } \\
{ } & { } & \cdot & \cdot & {c_{n-2}}\\
{ c_{n-1} } & { } & { } & {a_{n-1}} & {b_{n-1}}\\
\end{matrix}
\right]
\left[
\begin{matrix}
{x_0 } \\
{x_1 } \\
\cdot \\
\cdot \\
{x_{n-1} } \\
\end{matrix}
\right]
=
\left[
\begin{matrix}
{d_0 } \\
{d_1 } \\
\cdot \\
\cdot \\
{d_{n-1} } \\
\end{matrix}
\right].](https://raw.githubusercontent.com/scijs/solve-periodic-tridiagonal/HEAD/images/left-beginmatrix-b_0-c_0-a_0-a_1-b_1-c_1-a_2--2b154af7a7.png)
The solver will fail if the matrix is singular and may not succeed if the matrix is not diagonally dominant. If the solver fails, it will log a console message and return false.
Example
Consider the solution of
![\left[
\begin{matrix}
2 & 1 & 0 & 7\\
-1 & 7 & 4 & 0\\
0 & 2 & -3 & 2\\
6 & 0 & 1 & 8\\
\end{matrix}
\right]
\left[
\begin{matrix}
{x_0 } \\
{x_1 } \\
{x_2 } \\
{x_3 } \\
\end{matrix}
\right]
=
\left[
\begin{matrix}
{32} \\
{25} \\
{-5} \\
{41} \\
\end{matrix}
\right].](https://raw.githubusercontent.com/scijs/solve-periodic-tridiagonal/HEAD/images/left-beginmatrix-2-1-0-7-1-7-4-0-0-2-3-2-6-0--d0b5be69c1.png)
var triper = var d = 32 25 3 41 // => d = [ 1, 2, 3, 4 ]Installation
$ npm install solve-periodic-tridiagonalAPI
require('solve-periodic-tridiagonal')(n, a, b, c, d, w)
Arguments:
n: an integer representing the number of equations in the systema: a javascriptArrayor typed array of length n representing the subdiagonal, indexed according to the equation above. Left unchanged by the solver.b: a javascriptArrayor typed array of length n representing the diagonal, indexed as above. This vector is modified by the solver.c: a javascriptArrayor typed array of length n representing the superdiagonal, indexed as above. This vector is modified by the solver.d: a javascriptArrayor typed array of length n representing the known vector d. On successful completion, this vector will contain the solution.w: a work vector. Must be a javascriptArrayor typed array of length n.
Returns: True on successful completion, false otherwise.
License
© 2016 Ricky Reusser. MIT License.