Convert interpolation function to symbolic
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Hello,
I have a Nx2 .dat file which I import to Matlab as a Nx2 matrix. This .dat file is roughly a collection of [x,y] coordinates of a curve.
What I am trying to do is to obtain not only the curve that intepolates those point but also its form in symbolic code.
My code is the following
clc
clear all
%Importing .dat file and converting to a nx2 matrix
f = fopen('GITT_bi1g20.dat');
data = textscan(f, '%f %f');
data = cell2mat(data); % convert to matrix from cell array
fclose(f);
%Comparison between different interpolation functions
%Polynomial
x = data(:,1);
y = data(:,2);
p = polyfit(x,y,9);
y1 = polyval(p,x);
%pchip() - Hermitian
xx = x;
p = pchip(x,y,xx);
figure(1)
hold on
plot(data(:,1),data(:,2),'m')
plot(xx,p,'--black')
hold off
My biggest wish is actually write the pchip() that intepolates the data points as a symbolic function. (So I can do some Calculus stuff with it and other symbolic functions I am using)
Thanks in advance.
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Bjorn Gustavsson
2020년 2월 10일
You already get a piecewise polynomial out of pchip. That is a symbolic function - though not on the form expected by the symbolic functions of matlab so not the format you want. Bot look at the form of your final p and you should be able to figure out what to do next.
HTH
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Bjorn Gustavsson
2020년 2월 13일
Cheers. I thought that since they are polynomials it would be "reasonably" straight-forward to integrate and differentiate - D(a*x^n) = n*a*x^(n-1) etc. I must admit that I spent no time at all thinking about exactly how the polynomials were represented, so it might get tricky in practice. Then on the other hand polynomials are reasonably well suited for numerical integration so you could wihtout much loss turn to that.
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