% IAP2007 Introduction to MATLAB: Interface and Basics
% Instructor: Violeta Ivanova, violeta@mit.edu

% EXERCISE 2 Curve Fitting
% MATLAB vectors, polynomials, matrix operations, curve fitting, plotting. 

% The coordinates (x1,y1), (x2,y2), (x3,y3) and (x4,y4) of four points are
% given: (1, 54), (5, 82), (8, 40), and (10, 10).
% Find a cubic equation y(x) that passes through the four points i.e.:
% y = c1*x^3 + c2*x^2 + c3*x + c4
% Fit also a straight line and a quadratic curve to the points.

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% A. VECTORS

% A1. Define column vectors X and Y from the points' coordinates such that
% X = (x1, x2, x3, x4) and Y = (y1, y2, y3, y4)

% Create a column vector X by transposing a row vector:
X = [1 5 8 10]; X=X'

% Create a column vector Y by entering its elements row by row:
Y = [54; 82; 40; 10]

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% B. CURVE FITTING
% Compute straight line, quadratic, and cubic fits with function POLYFIT.

% B1. Straight line fit:
C1 = polyfit(X, Y, 1);

% B2 Quadratic fit:
C2 = polyfit(X, Y, 2);

% B2 Cubic fit:
C3 = polyfit(X, Y, 3);

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% C. POLYNOMIALS

% C1. Compute a cubic curve, a quadratic curve, and a straight line over an
% x interval from 0 to 10 at a step of 0.1. Hint: use function POLYVAL.

x = [0 : 0.1 : 10];
y1 = polyval(C1, x);
y2 = polyval(C2, x);
y3 = polyval(C3, x);

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% D. PLOTTING

% D1. Plot the cubic curve, quadratic curve, straight line, and four points
% on the same figure. Note: use different colors and/or markers.
% Hint: use functions PLOT, HOLD ON, and HOLD OFF.

p = plot (x, y1, 'r-');
hold on;
p2 = plot (x, y2, 'g-');
hold on;
p1 = plot (x, y3, 'k-');
hold on;
P = plot (X, Y, 'bo');
hold off;

% D2. Add a title, X and Y labels, and a legend to the figure.
% Hint: Use functions TITLE, XLABEL, YLABEL, and LEGEND. 

xlabel('X', 'FontSize', 12);
ylabel('Y', 'FontSize', 12);
title('CURVE FITTING TO POINTS', ...
       'FontSize', 12, ...
       'FontWeight', 'bold');
legend ('Cubic Fit', 'Quadratic Fit', 'Straight Line Fit', 'Data Points');

% D3. Customize the figure using the PROPERTY EDITOR.

% D4. Save the figure in a JPEG file.