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# Tridiagonal Matrix Algorithm [![View Tridiagonal Matrix Algorithm (Thomas Alg.) (tridiagonal) on File Exchange](https://www.mathworks.com/matlabcentral/images/matlab-file-exchange.svg)](https://www.mathworks.com/matlabcentral/fileexchange/85438-tridiagonal-matrix-algorithm-thomas-alg-tridiagonal)
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# `tridiagonal_matrix`
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Solves the tridiagonal linear system <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{A}\mathbf{x}=\mathbf{d}"/> for <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{x}\in\mathbb{R}^{n}" title="\mathbf{x}\in\mathbb{R}^{n}" /> using the matrix implementation of the tridiagonal matrix algorithm.
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`x = tridiagonal_matrix(A,d)` solves the tridiagonal linear system <img src="https://latex.codecogs.com/svg.image?\inline&space;\mathbf{A}\mathbf{x}=\mathbf{d}"/> for <img src="https://latex.codecogs.com/svg.image?\inline&space;\mathbf{x}\in\mathbb{R}^{n}" title="\mathbf{x}\in\mathbb{R}^{n}" />, where <img src="https://latex.codecogs.com/svg.image?\inline&space;\mathbf{A}\in&space;{\mathbb{R}}^{n\times&space;n}"/> is a tridiagonal matrix and <img src="https://latex.codecogs.com/svg.image?\inline&space;\mathbf{d}\in&space;{\mathbb{R}}^n"/>.
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# `tridiagonal_vector`
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Solves the tridiagonal linear system <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{A}\mathbf{x}=\mathbf{d}"/> for <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{x}\in\mathbb{R}^{n}" title="\mathbf{x}\in\mathbb{R}^{n}" /> using the vector implementation of the tridiagonal matrix algorithm.
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# Tridiagonal Matrix Convention
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For these implementations, I use the following convention for denoting the elements of the tridiagonal matrix <img src="https://latex.codecogs.com/svg.latex?\inline&space;\mathbf{A}"/>:
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Most other references have <img src="https://latex.codecogs.com/svg.latex?\inline&space;a_i"/>'s ranging from <img src="https://latex.codecogs.com/svg.latex?\inline&space;a_2"/> to <img src="https://latex.codecogs.com/svg.latex?\inline&space;a_n"/> both in the definition of the tridiagonal matrix and in the algorithm used to solve the corresponding linear system. In this implementation, I have the <img src="https://latex.codecogs.com/svg.latex?\inline&space;a_i"/>'s ranging from <img src="https://latex.codecogs.com/svg.latex?\inline&space;a_1"/> to <img src="https://latex.codecogs.com/svg.latex?\inline&space;a_{n-1}"/>; this makes the algorithm slightly more straightforward to implement.
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# Examples and Additional Documentation
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- See "EXAMPLES.mlx" or the "Examples" tab on the File Exchange page for examples.

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