Different polyfit / polyval

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.

Answer 1

[Walter Roberson]

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.

[Furkan Kocaman]

And how can I use the scaling in Python or in C?

[Walter Roberson]

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.