Using polifit in matlab

Hi,

I'm processing some data collected of charges and discharges curves of a battery. To do so, I'm fitting the data to a polynomial using polifit. what I'm doing is the following:

    t=time(line,colomn);
                         V=volt(line,colomn);

                          sz=size(t,1);
                          l=150;
                          n=3;
                          tab=[];

                          %charge
                           for k1=(1+l/2):sz-l/2
                              x=t((k1-l/2):(k1+l/2),1);
                              y=V((k1-l/2):(k1+l/2),1);
                              poly=polyfit(x,y,n);
                              yf=polyval(pply,t(k1,1));
                              tab=[tab;t(k1,1) yf];

           %But it takes a lot of time doing it. It exist any other way to do the same thing in less time?
           %I think that part of the problem come from doing vertcat of each value. 

          thank you

Answer 1

[Jan]

Using the center point of a polynomial fitted to the surrounding points is a Savitzky-Golay filter. Either use Matlab's sgolayfilt or the C-Mex function https://www.mathworks.com/matlabcentral/fileexchange/5661-fsgolayfilt. Then the loop is not required:

tab = fSGolayFilt(V, 3, 151);  % or sgolayfilt, about 50% slower

This works only, if t is equidistant. If not think about a linear interpolation at first. Or replace the polyfit function by a faster version:

function p = fPolyFit(x, y, n)
% Construct Vandermonde matrix:
x = x(:);
V = ones(length(x), n + 1);
for j = n:-1:1
   V(:, j) = V(:, j + 1) .* x;
end

% Solve least squares problem:
[Q, R] = qr(V, 0);
p      = transpose(R \ (transpose(Q) * y(:)));  % Same as: (V \ y)'

Note that omitting the validity checks of the inputs is not a good idea in general. But here it helps.

You are right: The iterative growing of the array is a severe problem. A "pre-allocation" helps - serach in the forum for this term to learn the details.

len  = sz - l;
tab  = zeros(1, len);
iTab = 0;
for k1 = (1+l/2):sz-l/2
  ...
  iTab      = iTab + 1;
  tab(iTab) = yf;
end

Join the time afterwards.

Answer 2

[Image Analyst]

How much data do you have? Billions of elements? Otherwise it should be really fast. Since the (badly named) l is 150, it looks like the fits are done over only a minuscule 150 points, so that should be blazingly fast to do just a single fit.

It looks like you're trying to fit lots of polynomials in a window sliding along your data. If so, that's basically a Savitzky-Golay filter and can be done efficiently using the function sgolayfilt() in the Signal Processing Toolbox.