Trying to find best fit for cosine curve

Hello,

I have 4 data points that I have plotted and are supposed to yield a cosine wave. How do I go about finding the best fit for this cosine wave? I understand 4 points is not a lot but am trying to get the best fit I can.

data = [1 4.2101; 2 -33.0595; 3 -5.6488; 4 76.2462]

Thank you for your help!

Answer 1

[Star Strider]

This works:

data = [1 4.2101; 2 -33.0595; 3 -5.6488; 4 76.2462];
x = data(:,1);
y = data(:,2);

yu = max(y);
yl = min(y);
yr = (yu-yl);                               % Range of ‘y’
yz = y-yu+(yr/2);
zx = x(yz(:) .* circshift(yz(:),[1 0]) <= 0);     % Find zero-crossings
per = 2*mean(diff(zx));                     % Estimate period
ym = mean(y);                               % Estimate offset

fit = @(b,x)  b(1).*(sin(2*pi*x./b(2) + 2*pi/b(3))) + b(4);    % Function to fit
fcn = @(b) sum((fit(b,x) - y).^2);                              % Least-Squares cost function
s = fminsearch(fcn, [yr;  per;  -1;  ym])                       % Minimise Least-Squares

xp = linspace(min(x),max(x));

figure(1)
plot(x,y,'b',  xp,fit(s,xp), 'r')
grid

[Matthew]

Thanks! How do I find the r^2 between the best fit cosine line and the points though?

[Star Strider]

You didn’t say you wanted that.

I would just use:

rsq = (corrcoef(y, fit(s,xp))).^2;

[Matthew]

An error pops us if I use rsq = (corrcoef(y, fit(s,xp))).^2;

'X and Y must have the same number of elements.'

Any way around this?

[Star Strider]

Typo. It should be:

rsq = corrcoef(y, fit(s,x)).^2;

With four parameters and four data, the fit should be perfect (as it is here).

[Tien Tran]

Hi Star How to get b constans and fit function?

[Star Strider]

The parameters (that I assume you refer to as ‘b’ constants, since they are called β in most textbooks and in the literature) are ‘s’ in my code here. The rest I hope is self-explanatory.

[Tien Tran]

I substitute constant in ' s ' and x =1 into 'fit', the result = 138.7373 is different with y value. Why is it not fit?

[Star Strider]

I have no idea. Yours should be a new Question anyway, since this one is resolved. You can refer to and link to this one for reference. You need to post all your code in your NEW POST so we can deal with it appropriateluy I usually do not respond to additional Questions posted to resolved Questions, and I am stopping with this one.

[Abi sek]

In the fit you are using sine function but how ccome it becomes cosine one

[Star Strider]

Since the sine and cosine are related by a phase difference of pi/2, the phase term here will allow the function to fit both. This is basic trigonometry.

[Ali Alamri]

How can I constrain this fit to 2pi?