Contents

Runge Function Example

Author(s): Paul R. Miles & Ralph C. Smith

Date Created: April 10, 2019

Exampled created using MATLAB2018a. Certain features may not be compatible with previous versions of MATLAB.

The Lagrange Polynomial toolbox is available for download on the File Exchange of MATLAB Central: https://www.mathworks.com/matlabcentral/fileexchange/13151-lagrange-interpolator-polynomial?focused=5083678&tab=function

% Setup workspace
close all; clear; clc;

% Add path to Lagrange Polynomial toolbox
% Note: I assume the uncompressed folder has been placed in the current
% working directory.
addpath('lagrangepoly');

High-Fidelity Model or "Data"

f = @(q) 1./(1+25*q.^2);

Grid Choice 1

M1 = 11;
j = 1:1:M1;
x1 = -1 + (j-1)*2/M1;
y1 = f(x1);
[P1, R1, S1] = lagrangepoly(x1, y1);

Grid choice 2: Clenshaw-Curtis

M2 = 10;
j = 1:1:M2;
x2 = -cos(pi*(j-1)/(M2-1));
y2 = f(x2);
[P2, R2, S2] = lagrangepoly(x2, y2);

Plot

xx = -1:0.01:1;

% Plot Grid Choice 1
subplot(1, 2, 1);
hold on
h3 = plot(xx, f(xx), '-k', 'linewidth', 2);
h1 = plot(xx, polyval(P1, xx), '--r', 'linewidth', 2);
h2 = plot(x1, y1, 'or', 'linewidth', 2, 'markersize', 10);
hold off
xlabel('q');
ylabel('f');
legh = legend([h1, h2, h3], ...
    {'L', 'QP', 'HFM'});
set(legh, 'location', 'best');
box on
title(sprintf('Grid Choice 1: M = %i', M1));
set(gca, 'FontSize', 22);

% Plot Grid Choice 2
subplot(1, 2, 2);
hold on
h3 = plot(xx, f(xx), '-k', 'linewidth', 2);
h1 = plot(xx, polyval(P2, xx), '--b', 'linewidth', 2);
h2 = plot(x2, y2, 'sb', 'linewidth', 2, 'markersize', 10);
hold off
xlabel('q');
ylabel('f');
legh = legend([h1, h2, h3], ...
    {'L', 'QP', 'HFM'});
set(legh, 'location', 'best');
box on
title(sprintf('Grid Choice 2: M = %i\nClenshaw-Curtis', M2));
set(gca, 'FontSize', 22);
set_figure_dimensions(12, 6)

Support Functions

function set_figure_dimensions(width, height)
% adjust figure dimensions
set(gcf,'units','inches');
pos = get(gca, 'pos');
set(gcf, 'Position', [pos(1) pos(2) width height]);
end

Published with MATLAB® R2018a