numpy.polynomial.chebyshev.Chebyshev

class numpy.polynomial.chebyshev.Chebyshev(coef, domain=[-1, 1], window=[-1, 1])

A Chebyshev series class.

Chebyshev instances provide the standard Python numerical methods ‘+’, ‘-‘, ‘*’, ‘//’, ‘%’, ‘divmod’, ‘**’, and ‘()’ as well as the listed methods.

Parameters:

coef : array_like

Chebyshev coefficients, in increasing order. For example, (1, 2, 3) implies P_0 + 2P_1 + 3P_2 where the P_i are a graded polynomial basis.

domain : (2,) array_like, optional

Domain to use. The interval [domain[0], domain[1]] is mapped to the interval [window[0], window[1]] by shifting and scaling. The default value is [-1,1].

window : (2,) array_like, optional

Window, see domain for its use. The default value is [-1,1]. .. versionadded:: 1.6.0

Notes

It is important to specify the domain in many cases, for instance in fitting data, because many of the important properties of the polynomial basis only hold in a specified interval and consequently the data must be mapped into that interval in order to benefit.

Attributes

domain
window

coef

(N,) ndarray

Chebyshev coefficients, from low to high.

Methods

basis(deg[, domain, window])	Chebyshev polynomial of degree deg.
cast(series[, domain, window])	Convert instance to equivalent Chebyshev series.
convert([domain, kind, window])	Convert to different class and/or domain.
copy()	Return a copy.
cutdeg(deg)	Truncate series to the given degree.
degree()	The degree of the series.
deriv([m])	Differentiate.
fit(x, y, deg[, domain, rcond, full, w, window])	Least squares fit to data.
fromroots(roots[, domain, window])	Return Chebyshev instance with specified roots.
has_samecoef(other)	Check if coefficients match.
has_samedomain(other)	Check if domains match.
has_sametype(other)	Check if types match.
has_samewindow(other)	Check if windows match.
identity([domain, window])	Identity function.
integ([m, k, lbnd])	Integrate.
linspace([n, domain])	Return x,y values at equally spaced points in domain.
mapparms()	Return the mapping parameters.
roots()	Return list of roots.
trim([tol])	Remove small leading coefficients
truncate(size)	Truncate series to length size.