numpy.polynomial.chebyshev.Chebyshev

class documentation

class Chebyshev(ABCPolyBase):

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A Chebyshev series class.

The Chebyshev class provides the standard Python numerical methods '+', '-', '*', '//', '%', 'divmod', '**', and '()' as well as the methods listed below.

Parameters

coef : array_like
Chebyshev coefficients in order of increasing degree, i.e., (1, 2, 3) gives 1*T_0(x) + 2*T_1(x) + 3*T_2(x).
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].

New in version 1.6.0.
Class Method interpolate Interpolate a function at the Chebyshev points of the first kind.
Class Variable basis​_name Undocumented
Class Variable domain Undocumented
Class Variable window Undocumented

Inherited from ABCPolyBase:

Class Method basis Series basis polynomial of degree deg.
Class Method cast Convert series to series of this class.
Class Method fit Least squares fit to data.
Class Method fromroots Return series instance that has the specified roots.
Class Method identity Identity function.
Class Method ​_repr​_latex​_term Undocumented
Class Method ​_str​_term​_ascii String representation of a single polynomial term using ** and _ to represent superscripts and subscripts, respectively.
Class Method ​_str​_term​_unicode String representation of single polynomial term using unicode characters for superscripts and subscripts.
Static Method ​_add Undocumented
Static Method ​_der Undocumented
Static Method ​_div Undocumented
Static Method ​_fit Undocumented
Static Method ​_fromroots Undocumented
Static Method ​_int Undocumented
Static Method ​_line Undocumented
Static Method ​_mul Undocumented
Static Method ​_pow Undocumented
Static Method ​_repr​_latex​_scalar Undocumented
Static Method ​_roots Undocumented
Static Method ​_sub Undocumented
Static Method ​_val Undocumented
Method __add__ Undocumented
Method __call__ Undocumented
Method __divmod__ Undocumented
Method __eq__ Undocumented
Method __floordiv__ Undocumented
Method __format__ Undocumented
Method __getstate__ Undocumented
Method __init__ Undocumented
Method __iter__ Undocumented
Method __len__ Undocumented
Method __mod__ Undocumented
Method __mul__ Undocumented
Method __ne__ Undocumented
Method __neg__ Undocumented
Method __pos__ Undocumented
Method __pow__ Undocumented
Method __radd__ Undocumented
Method __rdiv__ Undocumented
Method __rdivmod__ Undocumented
Method __repr__ Undocumented
Method __rfloordiv__ Undocumented
Method __rmod__ Undocumented
Method __rmul__ Undocumented
Method __rsub__ Undocumented
Method __rtruediv__ Undocumented
Method __setstate__ Undocumented
Method __str__ Undocumented
Method __sub__ Undocumented
Method __truediv__ Undocumented
Method ​_generate​_string Generate the full string representation of the polynomial, using term_method to generate each polynomial term.
Method ​_get​_coefficients Interpret other as polynomial coefficients.
Method ​_repr​_latex​_ Undocumented
Method convert Convert series to a different kind and/or domain and/or window.
Method copy Return a copy.
Method cutdeg Truncate series to the given degree.
Method degree The degree of the series.
Method deriv Differentiate.
Method has​_samecoef Check if coefficients match.
Method has​_samedomain Check if domains match.
Method has​_sametype Check if types match.
Method has​_samewindow Check if windows match.
Method integ Integrate.
Method linspace Return x, y values at equally spaced points in domain.
Method mapparms Return the mapping parameters.
Method roots Return the roots of the series polynomial.
Method trim Remove trailing coefficients
Method truncate Truncate series to length size.
Class Variable __array​_ufunc__ Undocumented
Class Variable __hash__ Undocumented
Class Variable ​_subscript​_mapping Undocumented
Class Variable ​_superscript​_mapping Undocumented
Class Variable ​_use​_unicode Undocumented
Class Variable maxpower Undocumented
Instance Variable __dict__ Undocumented
Instance Variable coef Undocumented
@classmethod
def interpolate(cls, func, deg, domain=None, args=()):

Interpolate a function at the Chebyshev points of the first kind.

Returns the series that interpolates func at the Chebyshev points of the first kind scaled and shifted to the domain. The resulting series tends to a minmax approximation of func when the function is continuous in the domain.

New in version 1.14.0.

Parameters

func : function
The function to be interpolated. It must be a function of a single variable of the form f(x, a, b, c...), where a, b, c... are extra arguments passed in the args parameter.
deg : int
Degree of the interpolating polynomial.
domain : {None, [beg, end]}, optional
Domain over which func is interpolated. The default is None, in which case the domain is [-1, 1].
args : tuple, optional
Extra arguments to be used in the function call. Default is no extra arguments.

Returns

polynomial : Chebyshev instance
Interpolating Chebyshev instance.

Notes

See numpy.polynomial.chebfromfunction for more details.

basis_name: str =
overrides numpy.polynomial._polybase.ABCPolyBase.basis_name

Undocumented

domain =
overrides numpy.polynomial._polybase.ABCPolyBase.domain

Undocumented

window =
overrides numpy.polynomial._polybase.ABCPolyBase.window

Undocumented