MATLAB: Dont know what Polyval is here doing :-/

polyval

Hello Together, i dont know what polyval is doing here with the blue lines:
What i want is a line through all points (like the black one).
untitled.jpg
Code for it is at end.
  • As you can see, the black line with polyval is plotted correct.
  • The points yd1 for xd1 and yd2 for xd2 are plotted correct
  • What is not plotted correct, is the polyval for xd1 and xd2 -> What have i done wrong here?
Thanks a lot!
%Black line

xml1 = [ -0.3,  0.4];
yml1 = [-0.15, -0.15];
xml2 = 0.4 + 0.7 * cos(0:pi/50:pi/2) ;
yml2 = -0.85 +0.7 * sin(0:pi/50:pi/2);
xml3 = [1.1, 1.1];
yml3 = [-0.85, -1.15];
load ('xdata310519.mat')
%xd1 =  0    0.3906    0.7430    1.0227    1.2022    1.2641    1.2022
%yd1 =  0   -0.0619   -0.2414   -0.5211   -0.8735   -1.2641   -1.6547
%xd2 =  0    0.1943    0.3696    0.5087    0.5980    0.6288    0.5980
%yd2 =  0   -0.0308   -0.1201   -0.2592   -0.4345   -0.6288   -0.8231
grad = 5;
p1 = polyfit( xd1, yd1, grad);
p2 = polyfit( xd1, yd2, grad);
f1 = polyval( p1, xd1);
f2 = polyval( p2, xd2);
hold on
%Black line
plot(xml1, yml1, '--k');
plot(xml2, yml2,'--k');
plot(xml3, yml3, '--k');
%points
plot(xd1, yd1,'s', xd2, yd2,'s');
plot(xd1,  f1,'b', xd2, f2,'b');

Best Answer

You fit yd2 vs xd1 but then plotted against xd2. One presumes the fit should be against xd2 as well.
BUT: A perfect illustration why higher order polynomials are rarely the right fitting function--what your fit really is is shown below--
untitled.jpg
where this was generated from
p2 = polyfit( xd2, yd2, grad);               % fit against intended variable
figure
plot(xd2,yd2,'bx')                           % plot the data points
hold on
plot(xd2,f2,'b-')                            % and the fit at only those points (linear between)
x2=linspace(min(xd2),max(xd2));              % fill in 100 points between first, last
plot(x2,polyval(p2,x2),'r-')                 % and plot those as well...
legend('Data','5th Order at X','5th Order at 100X')
A polynomial is an exceedingly bad choice for such data; use an interpolating spline instead or something similar.
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