numpy.polynomial.legendre.Legendre.fit¶

Legendre.
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: x : array_like, shape (M,)
xcoordinates of the M sample points
(x[i], y[i])
.y : array_like, shape (M,) or (M, K)
ycoordinates of the sample points. Several data sets of sample points sharing the same xcoordinates can be fitted at once by passing in a 2Darray that contains one dataset per column.
deg : int or 1D 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 andNone
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 2e16 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 productsw[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.