microcalorimetry.math.fitting
=============================

.. py:module:: microcalorimetry.math.fitting

.. autoapi-nested-parse::

   Analsysis functions for performing fitting using DataArrays.

   ..
       !! processed by numpydoc !!


Functions
---------

.. autoapisummary::

   microcalorimetry.math.fitting.polyderive
   microcalorimetry.math.fitting.polyval
   microcalorimetry.math.fitting.polyfit
   microcalorimetry.math.fitting.polyval2
   microcalorimetry.math.fitting.polyfit2
   microcalorimetry.math.fitting.polysolve2
   microcalorimetry.math.fitting.ordinary_least_squares


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

.. py:function:: polyderive(coeffs: xarray.DataArray, degree_dim: str = 'deg') -> xarray.DataArray

   
   Derive polynomial coefficients.


   :Parameters:

       **coeffs** : xr.DataArray
           Coefficients along dim
           'degree' as last dimension.



   :Returns:

       **derivative** : xr.DataArray
           Derivative of the derived coefficients











   ..
       !! processed by numpydoc !!

.. py:function:: polyval(coord: xarray.DataArray, coeffs: xarray.DataArray, degree_dim: str = 'deg')

   
   Evaluate a polynomial.


   :Parameters:

       **coord** : xr.DataArray
           Array to evaluate

       **coeffs** : xr.DataArray
           Coefficients along dim
           'deg' as last dimension.

       **degree_dim** : str, optional
           Dimension that stores the degrees. The default is 'deg'.



   :Returns:

       **val** : xr.DataArray
           Array of results of evaluated polynomial.











   ..
       !! processed by numpydoc !!

.. py:function:: polyfit(xarr: xarray.DataArray, dim: str, deg: int)

   
   Polynomial fit a dataset.


   :Parameters:

       **xarr** : xr.DataArray
           Data to fit.

       **dim** : str
           dimension to fit along.

       **deg** : int
           degree of fit.



   :Returns:

       **coeffs** : xr.DataArray
           Coefficients along dim
           'degree' as last dimension.











   ..
       !! processed by numpydoc !!

.. py:function:: polyval2(coeffs: xarray.DataArray, x: xarray.DataArray)

   
   Evaluate polynomial coefficients on x and y.

   coeffs x assumed to have dimension 'deg' with index corresponding
   to the power. I.E. deg = 2  is the coeffcient for c_2*x**2.

   :Parameters:

       **coeffs** : xr.DataArray
           Coefficients along dimension 'deg'. Index of 'deg' corresponds
           to power of polynomial coefficient.
           coeffs should have shape (..., m) where m is the number of
           coefficients and (...) is the same shape as x.

       **x** : xr.DataArray.
           (..., n) shape, last dimension is the fit dimension.



   :Returns:

       **y** : xr.DataArray
           x evaluated at polynomial coefficients shape (..., n)











   ..
       !! processed by numpydoc !!

.. py:function:: polyfit2(x: xarray.DataArray, y: xarray.DataArray, deg: int, constrain_zero: bool = False, yunc: xarray.DataArray = None)

   
   Fit polynominal coefficients c_n for y = Sum(c_n * x^n) for n<=deg.


   :Parameters:

       **x** : xr.DataArray.
           (..., n) shape, last dimension is the fit dimension.

       **y** : xr.DataArray.
           (..., n) shape, last dimension is the fit dimension.
           Must be same shape as x.

       **deg** : int
           Degree of polynomial fit.

       **constrain_zero** : bool
           Constrain fit to cross zero.

       **yunc: xr.DataArray, optional**
           (n,) 1d-array. Uncertainty on the yvalues that is diagonalized
           and used as weighting in the ordinary least squares. If not
           provided, no weighting is used.



   :Returns:

       **coeffs** : xr.DataArray
           Coefficients along dimension 'deg'. Index of 'deg' corresponds
           to power of polynomial coefficient.











   ..
       !! processed by numpydoc !!

.. py:function:: polysolve2(coeffs: xarray.DataArray, y: xarray.DataArray)

   
   Solve's for solution to polynomial.

   Solve for x in y = Sum( c_n * x^n).

   :Parameters:

       **coeffs: xr.DataArray,**
           Coefficients with along last dimension called deg. Index
           is integer with ineteger value corresponding to coefficient
           degree. Shape (..., m) for degree m polynomial. The 0th
           degree coefficient can optionally be omitted.

       **y** : xr.DataArray, optional
           Value to solve for solutions to polynomial at (if provided).
           Shape (..., n) where (...) matches the dimensions (...) in coeffs.
           Assumed to be zero if not provided.



   :Returns:

       result: xr.DataArray
           Shape (..., n, m-1) solutions to polynomial equation at y.











   ..
       !! processed by numpydoc !!

.. py:function:: ordinary_least_squares(X: xarray.DataArray, Y: xarray.DataArray, W: xarray.DataArray = None) -> xarray.DataArray

   
   Perform ordinary least squares on observation M and results y.

   This function is designed to operate on stacks of arrays,where the
   Last 2 dimensions of M are treated as regressor array and last 2 dimensions
   of Y are treated as the response matrix. Formulation follows the linear
   matrix formulation outlined in:

   https://en.wikipedia.org/wiki/Ordinary_least_squares.

   All dimensions '...' in (...,n,m) are treates as copies/stacks. It is
   assmued y has the same dimensions (...).

   Weight matrix defined as follows:
   https://online.stat.psu.edu/stat501/lesson/13/13.1

   Typically a diagonal matrix of the uncertainties.

   :Parameters:

       **X** : xr.DataArray
           With shape (...,n,m)

       **Y** : xr.DataArray
           With shape (...,n,1).

       **W** : xr.DataArray, optional
           Weight matrix with shape (..., n,m). If none is provide, identity
           matrix is used (i.e. no weighting).



   :Returns:

       **coeff** : xr.DataArray
           Array of coefficiencts with dimensions (...,m) corresponding
           to the columns along dimension m in X.











   ..
       !! processed by numpydoc !!