qspec.analyze.york_fit  (  x ,  y ,  sigma_x = None ,  sigma_y = None ,  corr = None ,  iter_max = 200 ,  report = False ,  show = False ,  ** kwargs  )[source]

A linear regression algorithm to find the best straight line through points $\vec{\mu}_i\in\mathbb{R}^2$ with covariances $\mathbf{\Sigma}_i\in\mathbb{R}^{2\times 2}$, assuming $2$-dimensional multivariate normal distributions $\mathcal{N}(\vec{\mu}_i, \mathbf{\Sigma}_i)$. The data points and covariances are given by $$\vec{\mu} = \begin{pmatrix}x\\y\end{pmatrix},\quad \mathbf{\Sigma} = \begin{pmatrix} \sigma_x^2 & \rho_{xy}\sigma_x\sigma_y \\ \rho_{xy}\sigma_x\sigma_y & \sigma_y^2 \end{pmatrix}.$$ The algorithm is described in [York et al., Am. J. Phys. 72, 367 (2004)].

Parameters:

xarray_like

The $x$ data.

yarray_like

The $y$ data.

sigma_xarray_like | None

The standard deviation $\sigma_x$ of the x data.

sigma_yarray_like | None

The standard deviation $\sigma_y$ of the y data.

corrarray_like | None

The correlation coefficients $\rho_{xy}$ between the x and y data.

iter_maxint

The maximum number of iterations to find the best slope.

reportbool

Whether to print the result of the fit.

showbool

Whether to plot the fit result.

kwargsNone

Additional keyword arguments.

Returns:

(popt, pcov)tuple[ndarray, ndarray]

The best y-intercept and slope and their covariance matrix.