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.

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

   :returns: **derivative** -- Derivative of the derived coefficients
   :rtype: xr.DataArray















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

   
   Evaluate a polynomial.

   :param coord: Array to evaluate
   :type coord: xr.DataArray
   :param coeffs: Coefficients along dim
                  'deg' as last dimension.
   :type coeffs: xr.DataArray
   :param degree_dim: Dimension that stores the degrees. The default is 'deg'.
   :type degree_dim: str, optional

   :returns: **val** -- Array of results of evaluated polynomial.
   :rtype: xr.DataArray















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

   
   Polynomial fit a dataset.

   :param xarr: Data to fit.
   :type xarr: xr.DataArray
   :param dim: dimension to fit along.
   :type dim: str
   :param deg: degree of fit.
   :type deg: int

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















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.. 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.

   :param coeffs: 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.
   :type coeffs: xr.DataArray
   :param x: (..., n) shape, last dimension is the fit dimension.
   :type x: xr.DataArray.

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















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.. 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.

   :param x: (..., n) shape, last dimension is the fit dimension.
   :type x: xr.DataArray.
   :param y: (..., n) shape, last dimension is the fit dimension.
             Must be same shape as x.
   :type y: xr.DataArray.
   :param deg: Degree of polynomial fit.
   :type deg: int
   :param constrain_zero: Constrain fit to cross zero.
   :type constrain_zero: bool
   :param yunc: (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.
   :type yunc: xr.DataArray, optional

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















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.. 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).

   :param coeffs: 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.
   :type coeffs: xr.DataArray,
   :param y: 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.
   :type y: xr.DataArray, optional

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















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.. 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.

   :param X: With shape (...,n,m)
   :type X: xr.DataArray
   :param Y: With shape (...,n,1).
   :type Y: xr.DataArray
   :param W: Weight matrix with shape (..., n,m). If none is provide, identity
             matrix is used (i.e. no weighting).
   :type W: xr.DataArray, optional

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















   ..
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