MATLAB: Polynomial fitting with dependent variables

multivariablepolyfit

How can I obtain a polynomial fitting in Matlab having coefficients depending on another variable ? e.g I have variables X1 and Y and I want to find the line (polynomial of degree 1) that fits Y=f(X1)=p0+p1*X1. That would result in the two polynomial coefficients p0,p1 with the function polyfit. Now, I would like to obtain a fitting for which the coefficients p0,p1 depend (linearly) on another variable X2 so p0=f1(X2)=a*X2+b, p1=f2(X2)=c*X2+d.

That would finally result in Y=f1(X2)+f2(X2)*X1.

How to do that ?

Thanks in advance.

Best Answer

In this case, your model is of the form

Y=c*X1*X2+d*X1+a*X2+b

and you have to estimate the coefficients a,b,c and d.

Since this model is also linear in the coefficients, you can use the same method as for the model

Y=p0+p1*X1

Best wishes

Torsten.

Related Solutions

MATLAB: Polynominal Fitting Constrained in 1 Coefficient

f(0) = 1 exactly implies that p(1) = 1 exactly. So subtract that 1 from each y value.

y1 = y - 1;

Now, hand-waving time: subtract the p(1) from the polynomial, and factor the x. You get x * (p(6) * x^4 + p(5) * x^3 + p(4) * x^2 + p(3) * x + p(2)). So (wave, wave) divide your y1 by x,

y1divx = y1(2:end) ./ x(2:end);   %remove the (0,1) pair

leaving (wave, wave) p(6) * x^4 + p(5) * x^3 + p(4) * x^2 + p(3) * x + p(2) to be fit by a 4th order polynomial:

p1divx = polyfit(x(2:end), y1div, 4);
y1divx_hat = polyval(p1divx, x);
y1_hat = y1divx_hat .* x + 1;   %undo division by x and subtraction of 1

MATLAB: How to fit data to the customized form automatically

Since you're already using Curve Fitting Toolbox, use the underlying functions: fitttype and fit.

Example:

f = fittype('a-b*x^3', 'independent', 'x', 'coefficients', {'a', 'b'});
fitobj =  fit(rand(10,1), rand(10,1), f)

Alternatively, you can generate MATLAB code from cftool.

Best Answer

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MATLAB: Polynominal Fitting Constrained in 1 Coefficient

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