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

———-

dimHashable

Coordinate along which to fit the polynomials.

degint

Degree of the fitting polynomial.

skipnabool 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.

rcondfloat or None, optional

Relative condition number to the fit.

wHashable, 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.

fullbool, default: False

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

to the coefficients.

covbool 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_resultsDataset

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