Polyfit with odd powers only?

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Nathan Kennedy
Nathan Kennedy 2018-5-8
评论： Rik 2018-5-8
Hi,
I am trying to get a polyfit with only odd powers - so polyfit will not work because it has odd and even.
I do not have the curve fitting toolbox.
Is there another function of lines of code that will do this? I've searched around and read topics but cant seem to get it working...
x = [-50 -49.9 -49.7 -49.6 -49.4 -49.3 -49.1 -49 -48.8 -48.7 -48.6 -48.4 -48.3 -48.1 -48 -47.8 -47.7 -47.5 -47.4 -47.2 -47.1 -47 -46.8 -46.7 -46.5 -46.4 -46.2 -46.1 -45.9 -45.8 -45.7 -45.5 -45.4 -45.2 -45.1 -44.9 -44.8 -44.6 -44.5 -44.3 -44.2 -44.1 -43.9 -43.8 -43.6 -43.5 -43.3 -43.2 -43 -42.9 -42.8 -42.6 -42.5 -42.3 -42.2 -42 -41.9 -41.7 -41.6 -41.4 -41.3 -41.2 -41 -40.9 -40.7 -40.6 -40.4 -40.3 -40.1 -40 -39.9 -39.7 -39.6 -39.4 -39.3 -39.1 -39 -38.8 -38.7 -38.5 -38.4 -38.3 -38.1 -38 -37.8 -37.7 -37.5 -37.4 -37.2 -37.1 -37 -36.8 -36.7 -36.5 -36.4 -36.2 -36.1 -35.9 -35.8 -35.6 -35.5 -35.4 -35.2 -35.1 -34.9 -34.8 -34.6 -34.5 -34.3 -34.2 -34.1 -33.9 -33.8 -33.6 -33.5 -33.3 -33.2 -33 -32.9 -32.7 -32.6 -32.5 -32.3 -32.2 -32 -31.9 -31.7 -31.6 -31.4 -31.3 -31.2 -31 -30.9 -30.7 -30.6 -30.4 -30.3 -30.1 -30 -29.8 -29.7 -29.6 -29.4 -29.3 -29.1 -29 -28.8 -28.7 -28.5 -28.4 -28.3 -28.1 -28 -27.8 -27.7 -27.5 -27.4 -27.2 -27.1 -26.9 -26.8 -26.7 -26.5 -26.4 -26.2 -26.1 -25.9 -25.8 -25.6 -25.5 -25.4 -25.2 -25.1 -24.9 -24.8 -24.6 -24.5 -24.3 -24.2 -24 -23.9 -23.8 -23.6 -23.5 -23.3 -23.2 -23 -22.9 -22.7 -22.6 -22.5 -22.3 -22.2 -22 -21.9 -21.7 -21.6 -21.4 -21.3 -21.1 -21];
y = [-24.75097 -24.67164 -24.4801 -24.3577 -24.16221 -24.07226 -23.8446 -23.74222 -23.54947 -23.44198 -23.34674 -23.1479 -23.02214 -22.84665 -22.73298 -22.54093 -22.42616 -22.22016 -22.12129 -21.92824 -21.83178 -21.72892 -21.51621 -21.42578 -21.21406 -21.11511 -20.91655 -20.82348 -20.60448 -20.51302 -20.41675 -20.21547 -20.11611 -19.92628 -19.81589 -19.62125 -19.51582 -19.31288 -19.21443 -19.01194 -18.91046 -18.82235 -18.62306 -18.52276 -18.31691 -18.21565 -18.01884 -17.91986 -17.7219 -17.62982 -17.53392 -17.32261 -17.22725 -17.02708 -16.92875 -16.72639 -16.62719 -16.42994 -16.32574 -16.12839 -16.03569 -15.93901 -15.73049 -15.62979 -15.44024 -15.33308 -15.14062 -15.04554 -14.83767 -14.74988 -14.64451 -14.44684 -14.34319 -14.14475 -14.05439 -13.85229 -13.75652 -13.55815 -13.45882 -13.25949 -13.17189 -13.06923 -12.8671 -12.77876 -12.57822 -12.48735 -12.29286 -12.19462 -12.00186 -11.91447 -11.81787 -11.63201 -11.54073 -11.34952 -11.27196 -11.0899 -11.00039 -10.82415 -10.74487 -10.57193 -10.49104 -10.40562 -10.24737 -10.16286 -10.00381 -9.92581 -9.77272 -9.70086 -9.53765 -9.47072 -9.39156 -9.24676 -9.17277 -9.02883 -8.96238 -8.82083 -8.75691 -8.62635 -8.5598 -8.44304 -8.38449 -8.32837 -8.21934 -8.16412 -8.05312 -8.00186 -7.90721 -7.85077 -7.74586 -7.69695 -7.63831 -7.53163 -7.48072 -7.37289 -7.32272 -7.21067 -7.15707 -7.05749 -7.01419 -6.9207 -6.88097 -6.84193 -6.77068 -6.74107 -6.6824 -6.65511 -6.60911 -6.58551 -6.54557 -6.51723 -6.503 -6.46382 -6.44574 -6.39763 -6.38649 -6.34661 -6.33092 -6.29201 -6.27877 -6.2389 -6.22502 -6.20754 -6.17015 -6.15153 -6.11958 -6.10592 -6.06368 -6.05479 -6.023 -6.00659 -5.99346 -5.96016 -5.94925 -5.9124 -5.90166 -5.87321 -5.85589 -5.82928 -5.82597 -5.7912 -5.77671 -5.76612 -5.73985 -5.731 -5.71439 -5.70532 -5.67559 -5.66804 -5.6418 -5.63944 -5.63151 -5.61857 -5.60494 -5.58464 -5.58045 -5.55205 -5.54998 -5.52862 -5.52516 -5.50865 -5.50969];
Please can someone assist

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采纳的回答

Torsten
Torsten 2018-5-8
编辑：Torsten 2018-5-8
x = [ ... ];
y = [ ... ];
x = x.';
y = y.';
n = 5; % degree of polynomial p ; n must be odd
A = [];
for i = 1:2:n
A = [A x.^i];
end
coeff = A\y % Polynomial is given by p(z)=coeff(1)*z + coeff(2)*z^3 + ... + coeff((n+1)/2)*z^n
Best wishes
Torsten.
  2 个评论
Guillaume
Guillaume 2018-5-8
You can construct A more simply:
A = x(:) .^ (1:2:n); %R2016b or later
A = bsxfun(@power, x(:), 1:2:n); %pre-R2016b
Rik
Rik 2018-5-8
Wow, I was really overdoing it with my answer.

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更多回答（1 个）

Rik
Rik 2018-5-8
%set initial estimate
intial_b_vals=[1 5];
x = rand(10,1);%x-values
yx = rand(10,1);%measured y(x)
%create function (must support vector input)
a=(1:(2*length(intial_b_vals)-1));
a(2,1==mod(a,2))=1:length(intial_b_vals);
str=sprintf('b(%d)*x.^%d+',a([2 1],:));
str=strrep(str,'b(0)','0');
str(end)='';
fun=eval(['@(b,x) ' str]);
%set options and perform actual fit
%Ordinary Least Squares cost function
OLS = @(b) sum((y(b,x) - yx).^2);
opts = optimset('MaxFunEvals',50000, 'MaxIter',10000);
%Use 'fminsearch' to minimise the 'OLS' function
fit_output = fminsearch(OLS, intial_b_vals, opts);

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