Polyfit with odd powers only?

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

Answer 1

[Torsten]

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.

[Guillaume]

You can construct A more simply:

A = x(:) .^ (1:2:n);  %R2016b or later
A = bsxfun(@power, x(:), 1:2:n);  %pre-R2016b

[Rik]

Wow, I was really overdoing it with my answer.

Answer 2

[Rik]

%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);