numpy.polynomial.chebyshev.chebfit#

polynomial.chebyshev.chebfit(x, y, deg, rcond=None, full=False, w=None)[source]#

Least squares fit of Chebyshev series to data.

Return the coefficients of a Chebyshev series of degree deg that is the least squares fit to the data values y given at points x. If y is 1-D the returned coefficients will also be 1-D. If y is 2-D multiple fits are done, one for each column of y, and the resulting coefficients are stored in the corresponding columns of a 2-D return. The fitted polynomial(s) are in the form

\[p(x) = c_0 + c_1 * T_1(x) + ... + c_n * T_n(x),\]

where n is deg.

Parameters:

xarray_like, shape (M,): x-coordinates of the M sample points (x[i], y[i]).
yarray_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.
degint 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.
rcondfloat, 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.
fullbool, 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.
warray_like, shape (M,), optional: Weights. If not None, the weight w[i] applies to the unsquared residual y[i] - y_hat[i] at x[i]. Ideally the weights are chosen so that the errors of the products w[i]*y[i] all have the same variance. When using inverse-variance weighting, use w[i] = 1/sigma(y[i]). The default value is None.

Returns:

coefndarray, shape (M,) or (M, K)

Chebyshev coefficients ordered from low to high. If y was 2-D, the coefficients for the data in column k of y are in column k.

[residuals, rank, singular_values, rcond]list

These values are only returned if full == True

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

For more details, see numpy.linalg.lstsq.

Warns:

RankWarning

The rank of the coefficient matrix in the least-squares fit is deficient. The warning is only raised if full == False. The warnings can be turned off by

>>> import warnings
>>> warnings.simplefilter('ignore', np.exceptions.RankWarning)