MATLAB Examples

## 1D Example

This example shows the behavior of regularizeNd in 1D.

```clc; clear; close all; ```

## Define Some Test Points

```x = [0;0.55;1.1;2.6;2.99]; y = [1;1.1;1.5;2.5;1.9]; ```

## setup 2 different grids. One course. One fine.

```xGrid1 = {[-0.50,0,0.50,1,1.50,2,2.50,3,3.30,3.60]}; xGrid2 = {-0.5:0.1:3.6}; ```

## Regularize

Try other smoothness values to see how they affect the fit. Change the values by a factor of 10 or more.

```smoothness = 5e-3; % smoothness = 1e-9; % smoothness = 1e-1; % smoothness = 1e-10; the problem is ill-conditioned for this value and the % output is garbage. yGrid1 = regularizeNd(x, y, xGrid1, smoothness); % Alternative equivalent calls to regularizeNd % yGrid1 = regularizeNd(x, y, xGrid1, smoothness, 'linear', 'normal'); % yGrid1 = regularizeNd(x, y, xGrid1, smoothness, [], 'normal'); % yGrid1 = regularizeNd(x, y, xGrid1, smoothness, [], []); % yGrid1 = regularizeNd(x, y, xGrid1, smoothness, 'inear', []); yGrid2 = regularizeNd(x, y, xGrid2, smoothness); ```

## Plot the Regularized Lookup Table and Test Data

plot test data screenSize = get(0,'screensize'); figure('position', [screenSize(3:4)*0.2, screenSize(3:4)*0.6])

```plot(x,y,'rx', 'MarkerSize', 20, 'DisplayName', 'Test Points') xlabel('x') ylabel('y') grid on; hold all; ```

plot the lookup table

```plot(xGrid1{1}, yGrid1, 'DisplayName', 'Course Grid') plot(xGrid2{1}, yGrid2, 'DisplayName', 'Fine Grid') legend('show', 'location', 'best') title('1D Regularization Example') ```