pastas.solver.LeastSquares.get_covariances
==========================================

.. py:method:: pastas.solver.LeastSquares.get_covariances(jacobian: pastas.typing.ArrayLike, cost: float, method: Literal['trf', 'dogbox', 'lm'] = 'trf', absolute_sigma: bool = False) -> pastas.typing.ArrayLike
   :staticmethod:


   
   Method to get the covariance matrix from the jacobian.

   :param jacobian: The jacobian matrix with dimensions nobs, npar.
   :type jacobian: ArrayLike
   :param cost: The cost value of the scipy.optimize.OptimizeResult which is half
                the sum of squares. That's why the cost is multiplied by a factor
                of two internally to get the sum of squares.
   :type cost: float
   :param method: Algorithm with which the minimization is performed. Default is "trf".
   :type method: Literal["trf", "dogbox", "lm"], optional
   :param absolute_sigma: If True, `sigma` is used in an absolute sense and the estimated
                          parameter covariance `pcov` reflects these absolute values. If
                          False (default), only the relative magnitudes of the `sigma` values
                          matter. The returned parameter covariance matrix `pcov` is based on
                          scaling `sigma` by a constant factor. This constant is set by
                          demanding that the reduced `chisq` for the optimal parameters
                          `popt` when using the *scaled* `sigma` equals unity. In other
                          words, `sigma` is scaled to match the sample variance of the
                          residuals after the fit. Default is False.
                          Mathematically, ``pcov(absolute_sigma=False) =
                          pcov(absolute_sigma=True) * chisq(popt)/(M-N)``
   :type absolute_sigma: bool, optional

   :returns: **pcov** -- numpy array with the covariance matrix.
   :rtype: array_like

   .. rubric:: Notes

   This method is copied from Scipy:
   https://github.com/scipy/scipy/blob/92d2a8592782ee19a1161d0bf3fc2241ba78bb63/scipy/optimize/_minpack_py.py
   Please refer to the SciPy optimization module::
   https://docs.scipy.org/doc/scipy/reference/optimize.html















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