quadratic curvature doesn't went smoothly

Question

nirwana 2023-10-24

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2037901-quadratic-curvature-doesn-t-went-smoothly

编辑： John D'Errico 2023-10-24

采纳的回答： John D'Errico

steam.mat

在 MATLAB Online 中打开

Anyone can help me?

I am trying to fit my data with first and second order polynomial, but the result of quadratic curvature doesn't smoothly, seems it repeat several time in certain point. Here is my code

%Loads the vectors x and y.
load steam
% Fit a first degree polynomial to the data.
[p s]= polyfit(x,y,2);
y1=polyval(p,x);
% PLOTTING DATA
plot(x,y,'o',MarkerFaceColor='k',MarkerEdgeColor='none')
hold on
plot(x,y1,'--')

steam data is

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Answer 1

John D'Errico 2023-10-24

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2037901-quadratic-curvature-doesn-t-went-smoothly#answer_1339591

编辑：John D'Errico 2023-10-24

在 MATLAB Online 中打开

steam.mat

load steam

% Fit a first degree polynomial to the data.

[p s]= polyfit(x,y,2);

y1=polyval(p,x);

% PLOTTING DATA

plot(x,y,'o',MarkerFaceColor='k',MarkerEdgeColor='none')

hold on

plot(x,y1,'--')

What is the problem? You are confused by the line that is plotted, I know. That just means your data was not sorted. Plot connects the dots. But if the dots are not in sequential order for x, then it back tracks.

diff(x)
ans = 1×24
   -5.6000    1.1000   28.0000    2.6000    9.9000    3.1000    2.3000   -6.0000  -13.2000  -11.1000  -17.5000   -0.8000   11.0000    7.7000    1.7000   10.8000   10.7000         0    4.5000   -2.4000  -14.0000  -13.5000  -11.2000   -4.8000

Do you see some the elements of x are not uniformly increasing? The negative elements in the diff tell you that.

[xs,tags] = sort(x);

ys = y(tags);

yshat = polyval(p,xs);

figure

plot(x,y,'o',MarkerFaceColor='k',MarkerEdgeColor='none')

hold on

plot(xs,yshat,'--')

There is no problem when you plot only the points as dots, but when you connect the dots, watch out!!!!!!!