numpy.polynomial.legendre.Legendre.fit

classmethod Legendre.fit(x, y, deg, domain=None, rcond=None, full=False, w=None, window=None)

Least squares fit to data.

Return a series instance that is the least squares fit to the data y sampled at x. The domain of the returned instance can be specified and this will often result in a superior fit with less chance of ill conditioning.

Parameters:

x : array_like, shape (M,)

x-coordinates of the M sample points (x[i], y[i]).

y : array_like, shape (M,) or (M, K)

y-coordinates of the sample points. Several data sets of sample points sharing the same x-coordinates can be fitted at once by passing in a 2D-array that contains one dataset per column.

deg : int

Degree of the fitting polynomial.

domain : {None, [beg, end], []}, optional

Domain to use for the returned series. If None, then a minimal domain that covers the points x is chosen. If [] the class domain is used. The default value was the class domain in NumPy 1.4 and None in later versions. The [] option was added in numpy 1.5.0.

rcond : float, optional

Relative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. The default value is len(x)*eps, where eps is the relative precision of the float type, about 2e-16 in most cases.

full : bool, optional

Switch determining nature of return value. When it is False (the default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned.

w : array_like, shape (M,), optional

Weights. If not None the contribution of each point (x[i],y[i]) to the fit is weighted by w[i]. Ideally the weights are chosen so that the errors of the products w[i]*y[i] all have the same variance. The default value is None.

New in version 1.5.0.

window : {[beg, end]}, optional

Window to use for the returned series. The default value is the default class domain

New in version 1.6.0.

Returns:

new_series : series

A series that represents the least squares fit to the data and has the domain specified in the call.

[resid, rank, sv, rcond] : list

These values are only returned if full = True

resid – sum of squared residuals of the least squares fit rank – the numerical rank of the scaled Vandermonde matrix sv – singular values of the scaled Vandermonde matrix rcond – value of rcond.

For more details, see linalg.lstsq.