xarray_polyfit

PlasmaCalcs.tools.xarray_tools.xarray_sci.xarray_polyfit(array, coord, degree, *, stddev=False, full=False, cov=False, eval=False, **kw_polyfit): returns array.polyfit(coord, degree, **kw_polyfit), after swapping coord to be a dimension, if needed.

E.g. for an array with dimension ‘snap’ and associated non-dimension coordinate ‘t’,

xarray_polyfit(array, ‘t’, 1) is equivalent to array.swap_dims(dict(snap=’t’)).polyfit(‘t’, 1).

stddev: bool

whether to also return the standard deviations of each coefficient in the fit.

if True, assign the variable ‘polyfit_stddev’ = diagonal(polyfit_covariance)**0.5,

mapping the diagonal (across ‘cov_i’, ‘cov_j’) to the dimension ‘degree’.

if cov False when stddev True, do not keep_cov in the result.

Not compatible with full=True.

full: bool

passed into polyfit; see below.

cov: bool

passed into polyfit; see below.

Note: if stddev=True when cov=False, still use cov=True during array.polyfit,

however then remove polyfit_covariance & polyfit_residuals from result.

eval: bool

whether to also return the fit, evaluated at array.coords[coord]

if True, assign the variable ‘polyfit_eval’ = sum(coeff * coord**degree, ‘degree’).

if stddev=True too, assign ‘polyfit_eval-stddev’ and ‘polyfit_eval+stddev’ too,

using similar formula but using coeffs +/- stddev.

Docs for xr.DataArray.polyfit copied below:

——————————————-

Least squares polynomial fit.

This replicates the behaviour of numpy.polyfit but differs by skipping

invalid values when skipna = True.

Parameters

———-

dim : Hashable

Coordinate along which to fit the polynomials.

deg : int

Degree of the fitting polynomial.

skipna : bool or None, optional

If True, removes all invalid values before fitting each 1D slices of the array.

Default is True if data is stored in a dask.array or if there is any

invalid values, False otherwise.

rcond : float or None, optional

Relative condition number to the fit.

w : Hashable, array-like or None, optional

Weights to apply to the y-coordinate of the sample points.

Can be an array-like object or the name of a coordinate in the dataset.

full : bool, default: False

Whether to return the residuals, matrix rank and singular values in addition

to the coefficients.

cov : bool or “unscaled”, default: False

Whether to return to the covariance matrix in addition to the coefficients.

The matrix is not scaled if cov='unscaled'.

Returns

——-

polyfit_results : Dataset

A single dataset which contains:

polyfit_coefficients

The coefficients of the best fit.

polyfit_residuals

The residuals of the least-square computation (only included if full=True).

When the matrix rank is deficient, np.nan is returned.

[dim]_matrix_rank

The effective rank of the scaled Vandermonde coefficient matrix (only included if full=True)

[dim]_singular_value

The singular values of the scaled Vandermonde coefficient matrix (only included if full=True)

polyfit_covariance

The covariance matrix of the polynomial coefficient estimates (only included if full=False and cov=True)

See Also

——–

numpy.polyfit

numpy.polyval

xarray.polyval

DataArray.curvefit