flystar.fit_velocity
====================

.. py:module:: flystar.fit_velocity


Attributes
----------

.. autoapisummary::

   flystar.fit_velocity.x


Functions
---------

.. autoapisummary::

   flystar.fit_velocity.linear
   flystar.fit_velocity.linear_fit
   flystar.fit_velocity.calc_chi2
   flystar.fit_velocity.fit_velocity


Module Contents
---------------

.. py:function:: linear(x, k, b)

.. py:function:: linear_fit(x, y, sigma=None, absolute_sigma=True)

   Weighted linear regression (See https://en.wikipedia.org/wiki/Weighted_least_squares#Solution). Recommended for low-dimension, non-degenerate data. Otherwise, please use scipy.curve_fit.

   Parameters
   ----------
   x : array-like
       x data
   y : array-like
       y data
   sigma : array-like, optional
       Weighted by 1/sigma**2. If not provided, weight = 1, by default None
   absolute_sigma : bool, optional
       If True (default), sigma is used in an absolute sense and the estimated parameter uncertainty reflects these absolute values. If False, only the relative magnitudes of the sigma values matter, by default True

   Returns
   -------
   result : dictionary
       Dictionary with keys 'slope', 'e_slope', 'intercept', 'e_intercept', and 'chi2' if return_chi2=True.


.. py:function:: calc_chi2(x, y, sigma, slope, intercept)

.. py:function:: fit_velocity(startable, weighting='var', use_scipy=False, absolute_sigma=True, epoch_cols='all', art_star=False)

   Fit proper motion with weighted linear regression equations (see https://en.wikipedia.org/wiki/Weighted_least_squares#Solution).
   Assumes that all data are valid.

   Parameters
   ----------
   startable : StarTable
       StarTable object
   weighting : str, optional
       Weighting by variance (1/ye**2) or standard deviation (1/ye), by default 'var'
   use_scipy : bool, optional
       Use scipy.curve_fit or flystar.fit_velocity.linear_fit, by default False
   absolute_sigma : bool, optional
       If True (default), sigma is used in an absolute sense and the estimated parameter uncertainty reflects these absolute values. If False, only the relative magnitudes of the sigma values matter, by default True
   epoch_cols : str or list of intergers, optional
       List of indicies of columns to use. If 'all', use all columns, by default 'all'
   art_star : bool, optional
       Artificial star catalog or not. If True, use startable['x'][:, epoch_ols, 1] as the location, by default False.

   Returns
   -------
   result : pd.DataFrame
       Proper motion dataframe with keys vx, vxe, vy, vye, x0, x0e, y0, y0e

   Raises
   ------
   ValueError
       If weighting is neither 'std' nor 'var'


.. py:data:: x