SqrtParabolicFit1D

class SqrtParabolicFit1D(rawData)

Bases: FitData1D

SqrtParabolicFit1D fits y = sqrt(A*(x - x0)^2 + C) to 1D data.

Fits a square-root parabolic model commonly used where the dependent variable scales with the absolute distance from a center with an offset. Automatically estimates amplitude, center, and offset from the data.

• Formula: \(y = \sqrt{A\,(x-x_0)^2 + C}\)

• Coefficients: \(A\) (scale), \(x_0\) (center), \(C\) (offset)

Example1:

% Fit sqrt-parabolic model to data
x = linspace(-5,5,101)';
y = sqrt(0.2*(x-0.7).^2 + 0.05) + 0.01*randn(size(x));
data = [x, y];
fitObj = SqrtParabolicFit1D(data);
fitObj.do();
fitObj.plot();

Example2:

% Access fitted parameters
A     = fitObj.Coefficient(1);
x0    = fitObj.Coefficient(2);
C     = fitObj.Coefficient(3);

Constructor Summary

SqrtParabolicFit1D(rawData)

Construct a SqrtParabolicFit1D.

Parameters:

rawData (double array) – Input data as n x 2 matrix [x, y]

Method Summary

guessCoefficient()

Automatically estimate initial fit parameters from data.

Estimates center from the minimum of \(y^2\), offset from end regions, and scale from edge points.

setFormula()

Set the sqrt-parabolic fit formula.