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

Author: onezerosix

README.md

@@ -2,10 +2,14 @@
 
 A collection of MATLAB scripts.
 
+The input values for each function are generally not validated other than their lengths. If an error such as division by 0 occurs, it will propagate. Please refer to each function's help documentation for additional information.
+
 ### Table of Contents
 
 1. [Tridiagonal LU Decomposition Matrix Solver](#Tridiagonal-LU-Decomposition-Matrix-Solver)  
-  a. [Example](#Example)
+  a. [Example 1](#Example)
+2. [Least-Square Plot Using QR Decomposition](#Least-Square-Plot-Using-QR-Decomposition)  
+  b. [Example 2](#Example-1)
 
 ### Tridiagonal LU Decomposition Matrix Solver
 
@@ -36,3 +40,27 @@ z =
 x =
      1     1     1     1     1
 ```
+### Least-Square Plot Using QR Decomposition
+
+This script solves `Ax = y` for the n x 1 vector `x` in the least-square sense using QR decomposition. It also plots the least-square fit function along with the input coordinates for comparison.
+
+The input n x 1 `basis` functions (with m x 1 input `t`) are used to form the m x n matrix `A`. For example, for n = 2 basis functions `b_1(t) = e^-t` and `b_2(t) = e^-2t` with m = 3 input coordinates given by `t = [0; 1; 2]` and `y = [0; 2; 1.06]`, we get the following 3 x 2 matrix:
+
+```
+    [ e^0   e^0  ]
+A = [ e^-1  e^-2 ]
+    [ e^-2  e^-4 ]
+```
+
+Two assumptions made for the script are: `A` has rank n and m >= n.
+
+##### Example
+
+```
+>> [x] = lsquare_plot_with_qr([0;.5;1;1.3;2;3], [0;1.6;2;1.93;1.06;0.38], {@(t)exp(-t), @(t)exp(-2*t)})
+
+x =
+    8.3282
+   -8.4245
+```
+<img src="https://raw.githubusercontent.com/onezerosix/misc-matlab-scripts/master/pictures/lsquare_plot_with_qr_example_graph.png" width="45%" alt="example plot">