Detailed Explanation of Matlab Fitting

Polynomial Fitting

p = 1×3      -0.7630    8.5343   25.9050

clear
x = linspace(0,4*pi,10)';
y = sin(x);
p = polyfit(x,y,7);
x1 = linspace(0,4*pi);
y1 = polyval(p,x1);
figure

plot(x,y,'o')
hold onplot(x1,y1)
hold off

If you want to make predictions, look at the trend of some points afterwards

x2=linspace(0,4.2*pi,120);

y2=sin(x2);
x3=x2;
y3=polyval(p,x3);
figure
plot(x,y,'o')
hold onplot(x2,y2,'r')
plot(x3,y3,'--g')
hold off

More powerfulfit function

One-dimensional polynomial fitting (curve)

figure

plot(f,x,y)

Two-dimensional polynomial fitting (surface)

plot(sf,[x,y],z)

Specify fitting parameters and types

clear
load censusplot(cdate,pop,'o')
fo = fitoptions('Method','NonlinearLeastSquares',...

    'Lower',[0,0],...    'Upper',[Inf,max(cdate)],...    'StartPoint',[1 1]);

ft = fittype('a*(x-b)^n','problem','n','options',fo);
[curve2,gof2] = fit(cdate,pop,ft,'problem',2)

[curve3,gof3] = fit(cdate,pop,ft,‘problem’,3)

hold onplot(curve2,'m')
plot(curve3,'c')
legend('Data','n=2','n=3')
hold off

Define a function to fit based on the specified function file

x = [0.81;0.91;0.13;0.91;0.63;0.098;0.28;0.55;...

    0.96;0.96;0.16;0.97;0.96];
y = [0.17;0.12;0.16;0.0035;0.37;0.082;0.34;0.56;...

    0.15;-0.046;0.17;-0.091;-0.071];
ft = fittype( 'piecewiseLine( x, a, b, c, d, k )' )

f = fit( x, y, ft, ‘StartPoint’, [1, 0, 1, 0, 0.5] )

plot( f, x, y )

Fit after excluding individual points

clear
[x, y] = titanium;
gaussEqn = 'a*exp(-((x-b)/c)^2)+d'

startPoints = [1.5 900 10 0.6]

f1 = fit(x’,y’,gaussEqn,‘Start’, startPoints, ‘Exclude’, [1 10 25])

f2 = fit(x’,y’,gaussEqn,‘Start’, startPoints, ‘Exclude’, x < 800)

plot(f1,x,y)
title('Fit with data points 1, 10, and 25 excluded')

figure
plot(f2,x,y)
title('Fit with data points excluded such that x < 800')

Exclude some points in surface fitting and mark them in the graph

clear
load frankef1 = fit([x y],z,'poly23', 'Exclude', [1 10 25]);
f2 = fit([x y],z,'poly23', 'Exclude', z > 1);

figure
plot(f1, [x y], z, 'Exclude', [1 10 25]);
title('Fit with data points 1, 10, and 25 excluded')

figure
plot(f2, [x y], z, 'Exclude', z > 1);
title('Fit with data points excluded such that z > 1')

Curve Fitting app

Curve Fitting 3 Order and5Order Polynomial Fitting

Moving Average

clear
x = (0:0.1:15)';
y = sin(x) + 0.5*(rand(size(x))-0.5);
y([90,110]) = 3;
yy0 = smooth(x,y,5);
yy1 = smooth(x,y,0.1,'loess');
yy2 = smooth(x,y,0.1,'rloess');
subplot(3,1,1)
plot(x,y,'b.',x,yy0,'r-')
set(gca,'YLim',[-1.5 3.5])
legend('5')
subplot(3,1,2)
plot(x,y,'b.',x,yy1,'g-')
set(gca,'YLim',[-1.5 3.5])
legend('loess')  % Local regression
subplot(3,1,3)
plot(x,y,'b.',x,yy2,'y-')
set(gca,'YLim',[-1.5 3.5])

Smoothing Spline

p=0 Least Squares Linear Fitting

p=1 Cubic Spline Interpolation

Usingfit function for smoothing

f = fit(x,y,'smoothingspline');

figure
plot(f,x,y)

f = fit(x,y,'smoothingspline','SmoothingParam',0.4);

figure
plot(f,x,y)

[f,gof,out]= fit(x,y,‘smoothingspline’,‘SmoothingParam’,0.4)

options = fitoptions('Method','Smooth','SmoothingParam',0.3);
[f,gof,out] = fit(x,y,'smooth',options)

Interpolation

One-dimensional data interpolation

strlb={'(a)method=nearest','(b)method=linear',...

Two-dimensional data interpolation

Usingfit function for interpolation

figure
clear
load carbon12alphaf1 = fit(angle,counts,'nearestinterp');
f2 = fit(angle,counts,'pchip');

p1 = plot(f1,angle,counts);
xlim([min(angle),max(angle)])
hold on

p2 = plot(f2,'b');
hold offlegend([p1;p2],'Counts per Angle','Nearest Neighbor','pchip',...

    'Location','northwest')

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Introduction to MATLAB Functions, Features, and Advantages

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