Fit-Curve through certain start point

How can I define a fit function out of an array, that goes through a defined start point and end point? Also, if there is a point out of zeros, it should not be considered. I tried it with the fit function and chose the "NonLinearLeastSquares" Method.

data = [0 1 2 3 4 5 6 0 8 9 ; 3 5 4 6 8 6 5 0 5 2]

xdata = data(1,:);
ydata = data(2,:);

start = [xdata(1) ydata(1)];
exclude = [0 0]

options = fitoptions('Method','NonlinearLeastSquares','Startpoint',start,'Exclude',exclude)
fit_xy = fit(xdata',ydata','poly5',options);

ydata_fitted = feval(fit_xy,xdata);

figure
plot(xdata,ydata,'-ob');
hold on
plot(xdata,ydata_fitted,'-or');
plot(fit_xy);

Thanks a lot!

Answer 1

[dpb]

The easiest way is to use one of John D'Errico's inestimably-valuable tools from the FEX; in this case <LSE> which was written expressly for the purpose.

N=2;                         % choose poly power (quadratic)
iC=[1 length(X)];            % pick points indices for constraints (first, last here)
A=X.^[0:N];                  % build a LS model matrix for the chosen power
C=A(iC,:);                   % and the constrained points subset
b=lse(A,Y,C,Y(iC))           % call John's magic...
b =
    3.0000
    1.6417
   -0.1948
>> C*b                       % see that constraints were satisfied
ans =
    3.0000
    2.0000
>> yh=A*b           % evaluate model at input points; observe constraints satisfied
yh =
    3.0000
    4.4470
    5.5044
    6.1723
    6.4507
    6.3396
    5.8390
    3.6692
    2.0000
>>

To evaluate the model at any other points, simply build the appropriate A including the desired points in the vector.

ADDENDUM Oh, forgot to address the question of missing data (0-valued); had already done that in the above...

data = [0 1 2 3 4 5 6 0 8 9 ; 3 5 4 6 8 6 5 0 5 2];  % original
data=data.';                % columns are generally more convenient
data=data(any(data,2),:);   % eliminate rows that have both columns 0

[Ilja Verspohl]

Thanks a lot!!

[John D'Errico]

:)

[dpb]

Double and triple :) !!!

This most-excellent tool has bailed me out numerous times over the past rather than having to relearn/reinvent the wheel; there's no way to express the level of appreciation that you took the time and effort to build such tools and submit them via FEX...

ERRATUM I see I didn't capitalize the 'D'...didn't recall that; will fix--dpb

GEEZER TALE ALERT Once upon a time when a much younger pup about 45 year ago now, had issues with a 2D surface fit of Rh-emitter incore detectors to estimate power distribution across the 177 fuel assembly locations from the 52 (very strangely distributed; I didn't have anything to do with that; happened and was cast in stone long before I ever got to the vendor) instrumented locations. Compute-power was extremely limited so was a quadratic polynomial in XY when I inherited the software with no constraints. As with all polynomials the fit was very sensitive to noise, especially at the boundary locations for larger XY. I was sure that adding a boundary condition of zero power/flux around the outer edge of the core periphery would help.

I was able to use SAS to model a number of cases for "proof of principle" that was a viable and probable improvement but I hadn't at the time the mathematical prowess to figure out how to code the solution. Fortunately, there was on staff a Senior Mathematician who was available for such problems and Dr. Clark showed me how to solve the problem and it made a big improvement in the overall results in computing local power peaking. He is now long deceased but I learned much from him that was also of absolute critical importance over the next 30 years...