solve-periodic-tridiagonal

1.0.0 • Public • Published

solve-periodic-tridiagonal Build Status npm version js-standard-style

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].

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].

var triper = require('solve-periodic-tridiagonal')
 
var d = [32, 25, 3, 41]
 
triper(4, [7, -1, 2, 1], [2, 7, -3, 8], [1, 4, 2, 6], d, [])
// => d = [ 1, 2, 3, 4 ]

Installation

$ npm install solve-periodic-tridiagonal

API

require('solve-periodic-tridiagonal')(n, a, b, c, d, w)

Arguments:

  • n: an integer representing the number of equations in the system
  • a: a javascript Array or typed array of length n representing the subdiagonal, indexed according to the equation above. Left unchanged by the solver.
  • b: a javascript Array or typed array of length n representing the diagonal, indexed as above. This vector is modified by the solver.
  • c: a javascript Array or typed array of length n representing the superdiagonal, indexed as above. This vector is modified by the solver.
  • d: a javascript Array or 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 javascript Array or typed array of length n.

Returns: True on successful completion, false otherwise.

License

© 2016 Ricky Reusser. MIT License.

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1.0.0

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