How to extend curve fit beyond data points?

Question

Nicholas Pfaff 2018-7-10

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/409693-how-to-extend-curve-fit-beyond-data-points

评论： Gamra Samha 2020-7-10

image.png

I have plotted my data and fitted a curve onto it. However, I am not able to extend my fit beyond my data points (I want it to go through my points and through the axis).

My code:

function [fitresult, gof] = createFit(diameter, time)
%%Fit: 'Raw Data'.
[xData, yData] = prepareCurveData( diameter, time );
% Set up fittype and options.
ft = fittype( 'power1' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [155.522818446907 -1.88432816467686];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );
% Plot fit with data
figure( 'Name', 'Raw Data' );
h = plot( fitresult,'b', xData, yData, '.k' );
h(1).MarkerSize = 12;
h(2).LineWidth = 1;
legend( h, 'time vs. diameter', 'Raw Data', 'Location', 'NorthEast' );
% Label axes
xlabel diameter
ylabel time
grid on
hold on;
axis([0 22 0 41]);

Produced graph through my code:

How I want it to look:

%

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Answer 1

jonas 2018-7-10

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/409693-how-to-extend-curve-fit-beyond-data-points#answer_328310

编辑：jonas 2018-7-11

在 MATLAB Online 中打开

You have the coefficients of the 'power1' function stored in fitresult. It probably looks something like this:

fitresult =

       General model Power1:
       f(x) = a*x^b
       Coefficients (with 95% confidence bounds):
         a =        1.46  (1.22, 1.69)
         b =      0.40  (0.38, 0.43)

with 1.46 and 0.40 being the coefficients. Just create new bounds by

x=linspace(xmin,xmax,n)

and plug it into the equation

y=(fitresult.a).*x.^(fitresult.b)
plot(x,y)

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jonas 2018-7-11

编辑：jonas 2018-7-11

在 MATLAB Online 中打开

untitled5.jpg

Here is an example code with some made-up data. I suspect that the issue was that I wrote fitresults instead of fitresult? I've fixed the answer.

xData=1:.5:20;
yData=(2.*Xdata.^-1.5)+0.02.*rand(size(Xdata));
%%Fit: 'Raw Data'.
[xData, yData] = prepareCurveData( xData, yData );
% Set up fittype and options.
ft = fittype( 'power1' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [155.522818446907 -1.88432816467686];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );
% Plot fit with data
figure( 'Name', 'Raw Data' );
%h = plot( fitresult,'b', xData, yData, '.k' );
x=linspace(0,25,100);
y=(fitresult.a).*x.^(fitresult.b);
h=plot(xData,yData,'.k',...
    x,y,'b');
h(1).MarkerSize = 12;
h(2).LineWidth = 1;
legend( [h(2) h(1)], 'time vs. diameter', 'Raw Data', 'Location', 'NorthEast' );
% Label axes
xlabel diameter
ylabel time
grid on
hold on;
axis([0 25 0 3])

Nicholas Pfaff 2018-7-11

Thank you!

Gamra Samha 2020-7-10

Hi,

I am having some sort of a similar problem. I have x and y values and I need to fit them expoentially. Below is my code.

xData = [0.9,2,3,4.1,5.2,6.2,7.3,8.4,9.5,10.5,11.6,12]';

yData = [216.4684,153.2911,108.3671,82.3165,58.4557,47.2278,40.1013,36.9241,32.3291,31.3671,30.0000,27.9747]';

[xData, yData] = prepareCurveData (xData, yData);

ft = fittype( 'exp1' );

opts = fitoptions( 'Method', 'NonlinearLeastSquares' );

opts.Algorithm = 'Levenberg-Marquardt';

opts.Display = 'Off';

opts.StartPoint = [200.802517208848 -0.198913568004103];

[f1,gof,output] = fit(xData,yData,ft,opts);

% Plot fit with data.

figure

h_1 = plot(f1, x, y );

legend( h_1, 'y vs. x', 'untitled fit 1', 'Location', 'NorthEast' );

% Label axes

xlabel x

ylabel y

grid on

I am not able though to make the curve meet the first point of the y values well. The curve as well does not meet the y axis as it should be.

I have also used your suggested code above, but for some reason the data points and curve do not meet, even when I change the values in linspace. Also the curve does not meet the y-axis.

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