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Why do my coeffvalues not produce a sensible result?

Nicholas Turton 님이 질문을 제출함. 28 Aug 2019
최근 활동 Torsten 님이 댓글을 추가함. 28 Aug 2019
I have a script that uses the fit fuction on some data using a poly55 fit type. I then use this to get the coeffvalues for the fittted curve and try to replot the surface using the coeffvalues but the result produced is orders of magnitude different from the original data.
Script attached as well as some example data.
Can anyone explain what is happening or recommend a way forward?

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Torsten 님의 답변 28 Aug 2019
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If you use the 'Normalize','on' fitting option, your polynomial has powers of (x-meanx)/stdx and (y-meany)/stdy instead of x and y.

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Hi Torsten,
Can you elaborate. I am new to matlab and not following fully what you mean
I have used
[Psi_d_xData, Psi_d_yData, Psi_d_zData] = prepareSurfaceData( id_ind, iq_ind, Psi_d);
[Psi_d_fitresult, Psi_d_gof] = fit( [Psi_d_xData, Psi_d_yData], Psi_d_zData, ft, 'Normalize', 'on' );% Fit model to data.
Psi_d_coeffvals = coeffvalues(Psi_d_fitresult);
curvefit.png
which when produced numel(Psi_d_coeffvals) = 21
Using the poly55 eqation
f(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 + p30*x^3 + p21*x^2*y
+ p12*x*y^2 + p03*y^3 + p40*x^4 + p31*x^3*y + p22*x^2*y^2
+ p13*x*y^3 + p04*y^4 + p50*x^5 + p41*x^4*y + p32*x^3*y^2
+ p23*x^2*y^3 + p14*x*y^4 + p05*y^5
...I have then called up each of these coeffvals as well as my desired x and y values to try and reproduce the curve but only could manage the following
reproduced curve.png
Are you saying I need to calculate the mean and std values of x and y and use these in the calculation?
if you switch the mentioned option off, you can use the polynomial you defined in the calculation.
Otherwise you will have to insert (x-meanx)/stdx for x and (y-meany)/stdy for y in the calculation for your polynomial value:
f(x,y) = p00 + p10*(x-meanx)/stdx + p01*(y-meany)/stdy + p20*((x-meanx)/stdx))^2 + ...

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Thanks Torsten, it worked perfectly
function output_fit = fittingcurve(x_data, y_data, coeffvals)
x_mean = mean(x_data(1,:));
x_std = std(x_data(1,:));
y_mean = mean(y_data(:,1));
y_std = std(y_data(:,1));
output_fit = ...
coeffvals(1) ...
+ coeffvals(2).*((x_data-x_mean)./x_std) ...
+ coeffvals(3).*((y_data-y_mean)./y_std) ...
+ coeffvals(4).*((x_data-x_mean)./x_std).^2 ...
+ coeffvals(5).*((x_data-x_mean)./x_std).*((y_data-y_mean)./y_std) ...
+ coeffvals(6).*((y_data-y_mean)./y_std).^2 ...
+ coeffvals(7).*((x_data-x_mean)./x_std).^3 ...
+ coeffvals(8).*((x_data-x_mean)./x_std).^2.*((y_data-y_mean)./y_std) ...
+ coeffvals(9).*((x_data-x_mean)./x_std).*((y_data-y_mean)./y_std).^2 ...
+ coeffvals(10).*((y_data-y_mean)./y_std).^3 ...
+ coeffvals(11).*((x_data-x_mean)./x_std).^4 ...
+ coeffvals(12).*((x_data-x_mean)./x_std).^3.*((y_data-y_mean)./y_std) ...
+ coeffvals(13).*((x_data-x_mean)./x_std).^2.*((y_data-y_mean)./y_std).^2 ...
+ coeffvals(14).*((x_data-x_mean)./x_std).*((y_data-y_mean)./y_std).^3 ...
+ coeffvals(15).*((y_data-y_mean)./y_std).^4 ...
+ coeffvals(16).*((x_data-x_mean)./x_std).^5 ...
+ coeffvals(17).*((x_data-x_mean)./x_std).^4.*((y_data-y_mean)./y_std) ...
+ coeffvals(18).*((x_data-x_mean)./x_std).^3.*((y_data-y_mean)./y_std).^2 ...
+ coeffvals(19).*((x_data-x_mean)./x_std).^2.*((y_data-y_mean)./y_std).^3 ...
+ coeffvals(20).*((x_data-x_mean)./x_std).*((y_data-y_mean)./y_std).^4 ...
+ coeffvals(21).*((y_data-y_mean)./y_std).^5;
reproduced curve.png

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