numpy.polynomial.chebyshev.Chebyshev.fit¶

Chebyshev.fit(x, y, deg, domain=None, rcond=None, full=False, w=None, window=None)[source]¶

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:

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 or 1-D array_like Degree(s) of the fitting polynomials. If deg is a single integer all terms up to and including the deg‘th term are included in the fit. For NumPy versions >= 1.11.0 a list of integers specifying the degrees of the terms to include may be used instead. 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.

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 or 1-D array_like

Degree(s) of the fitting polynomials. If deg is a single integer all terms up to and including the deg‘th term are included in the fit. For NumPy versions >= 1.11.0 a list of integers specifying the degrees of the terms to include may be used instead.

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.