Merge branch 'master' of https://github.com/onezerosix/misc-matlab-scripts

onezerosix · onezerosix · commit 1c08a0de05f3 · 2020-04-12T17:00:44.000-07:00
diff --git a/README.md b/README.md
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+# misc-matlab-scripts
+
+A collection of MATLAB scripts.
+
+### Table of Contents
+
+1. [Tridiagonal LU Decomposition Matrix Solver](#Tridiagonal-LU-Decomposition-Matrix-Solver)  
+  a. [Example](#Example)
+
+### Tridiagonal LU Decomposition Matrix Solver
+
+This script solves `Ax = d` for `x` using LU decomposition for the square tridiagonal matrix `A`.
+
+A square tridiagonal matrix `A` has the following structure:  
+<img src="https://raw.githubusercontent.com/onezerosix/misc-matlab-scripts/master/pictures/tridiag_lu_decomp_A.png" width="40%" alt="matrix A">
+
+The `a`, `b` and `c` variables are used as vector inputs for the script. The values must meet the following criteria for the script to work:  
+<img src="https://raw.githubusercontent.com/onezerosix/misc-matlab-scripts/master/pictures/tridiag_lu_decomp_A_conditions.png" width="50%" alt="matrix A conditions">
+
+The output includes vector `x` and vector `z` such that `z = Ux`. It also includes vectors `alpha` and `beta` such that:  
+<img src="https://raw.githubusercontent.com/onezerosix/misc-matlab-scripts/master/pictures/tridiag_lu_decomp_LU.png" width="70%" alt="L and U matrices">
+
+##### Example
+```
+>> [alpha, beta, z, x] = tridiag_lu_decomp([2;2;2;2;2], [1;1;1;1;1], [1;1;1;1;1], [3;4;4;4;3])
+
+alpha =
+    2.0000    1.5000    1.3333    1.2500    1.2000
+
+beta =
+         0    0.5000    0.6667    0.7500    0.8000
+         
+z =
+    3.0000    2.5000    2.3333    2.2500    1.2000
+
+x =
+     1     1     1     1     1
+```
