Different polyfit / polyval

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Furkan Kocaman
Furkan Kocaman 2019-6-22
评论： Walter Roberson 2019-6-22
I want to understand the functions polyval and polyfit. At First I programming in Matlab the following lines:
cooefs = [-15.3800,74.8008, -53.3701, 346.3550, 0]
x = (0:.01:95)/180*pi;
y = polyval(cooefs(end:-1:1), x);
[p,~,mu] = polyfit(y, x, 5);
My first question is: The result from polyfit is not the same if I write this line:
p = polyfit(y, x, 5);
Why? The Variable p must be the same. The next question is, are any possibility to convert an matlab script with polyval / polyfit to C or python. The Matlab coder cant do this.

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回答（1 个）

Walter Roberson
Walter Roberson 2019-6-22
The two results do not need to be same. When you use the version that outputs mu then you would pass mu in to polyval.
The version with mu does a linear shift and scaling.
polyfit without the scaling can be written in terms of constructing a vandermode matrix and using the \ operator. Those can have code generation.
  2 个评论
Furkan Kocaman
Furkan Kocaman 2019-6-22
And how can I use the scaling in Python or in C?
Walter Roberson
Walter Roberson 2019-6-22
The help documentation phrases it as
[P,S,MU] = polyfit(X,Y,N) finds the coefficients of a polynomial in
XHAT = (X-MU(1))/MU(2) where MU(1) = MEAN(X) and MU(2) = STD(X). This
centering and scaling transformation improves the numerical properties
of both the polynomial and the fitting algorithm.
This should provide sufficient clue as to how to create XHAT yourself.

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