bluemira.utilities.fit_tools

Fitting tools

Functions

surface_fit(→ tuple[numpy.ndarray, numpy.ndarray, ...)

Fit a polynomial surface to a 3-D data set.

powers_arange(→ list[int])

Reorder powers index to order by power from 1st to nth index.

Module Contents

bluemira.utilities.fit_tools.surface_fit(x: numpy.ndarray, y: numpy.ndarray, z: numpy.ndarray, order: int = 2, n_grid: int = 30) → tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, list[float], float]

Fit a polynomial surface to a 3-D data set.

Parameters:

  • x (numpy.ndarray) – The x values of the data set

  • y (numpy.ndarray) – The y values of the data set

  • z (numpy.ndarray) – The z values of the data set

  • order (int) – The order of the fitting polynomial

  • n_grid (int) – The number of gridding points to use on the x and y data

Returns:

  • x2d – The gridded x data (i, j indexed)

  • y2d – The gridded y data (i, j indexed)

  • zz – The gridded z fit data (i, j indexed)

  • coeffs – The list of polynomial coefficents

  • r2 – The R^2 score of the fit

Raises:

ValueError – x, y and z are not of equal length

Return type:

tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, list[float], float]

Notes

The coefficients are ordered by power, and by x and y. For an order = 2 polynomial, the resultant equation would be:

\(c_{1}x^{2}+c_{2}y^{2}+c_{3}xy+c_{4}x+c_{5}y+c_{6}\)

bluemira.utilities.fit_tools.powers_arange(powers: numpy.ndarray) → list[int]

Reorder powers index to order by power from 1st to nth index.

Parameters:

powers (numpy.ndarray) – array of powers

Return type:

index to rearrange array