microcalorimetry.math.fitting

Analsysis functions for performing fitting using DataArrays.

Functions

polyderive(→ xarray.DataArray)

Derive polynomial coefficients.

polyval(coord, coeffs[, degree_dim])

Evaluate a polynomial.

polyfit(xarr, dim, deg)

Polynomial fit a dataset.

polyval2(coeffs, x)

Evaluate polynomial coefficients on x and y.

polyfit2(x, y, deg[, constrain_zero, yunc])

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

polysolve2(coeffs, y)

Solve's for solution to polynomial.

ordinary_least_squares(→ xarray.DataArray)

Perform ordinary least squares on observation M and results y.

Module Contents

microcalorimetry.math.fitting.polyderive(coeffs: xarray.DataArray, degree_dim: str = 'deg') → xarray.DataArray[source]

Derive polynomial coefficients.

Parameters:

coeffs (xr.DataArray) – Coefficients along dim ‘degree’ as last dimension.

Returns:

derivative – Derivative of the derived coefficients

Return type:

xr.DataArray

microcalorimetry.math.fitting.polyval(coord: xarray.DataArray, coeffs: xarray.DataArray, degree_dim: str = 'deg')[source]

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 – Array of results of evaluated polynomial.

Return type:

xr.DataArray

microcalorimetry.math.fitting.polyfit(xarr: xarray.DataArray, dim: str, deg: int)[source]

Polynomial fit a dataset.

Parameters:

  • xarr (xr.DataArray) – Data to fit.

  • dim (str) – dimension to fit along.

  • deg (int) – degree of fit.

Returns:

coeffs – Coefficients along dim ‘degree’ as last dimension.

Return type:

xr.DataArray

microcalorimetry.math.fitting.polyval2(coeffs: xarray.DataArray, x: xarray.DataArray)[source]

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 – x evaluated at polynomial coefficients shape (…, n)

Return type:

xr.DataArray

microcalorimetry.math.fitting.polyfit2(x: xarray.DataArray, y: xarray.DataArray, deg: int, constrain_zero: bool = False, yunc: xarray.DataArray = None)[source]

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 – Coefficients along dimension ‘deg’. Index of ‘deg’ corresponds to power of polynomial coefficient.

Return type:

xr.DataArray

microcalorimetry.math.fitting.polysolve2(coeffs: xarray.DataArray, y: xarray.DataArray)[source]

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 – Shape (…, n, m-1) solutions to polynomial equation at y.

Return type:

xr.DataArray

microcalorimetry.math.fitting.ordinary_least_squares(X: xarray.DataArray, Y: xarray.DataArray, W: xarray.DataArray = None) → xarray.DataArray[source]

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 – Array of coefficiencts with dimensions (…,m) corresponding to the columns along dimension m in X.

Return type:

xr.DataArray