numpy.polynomial.legendre.Legendre

classnumpy.polynomial.legendre.Legendre(coef, domain=None, window=None, symbol='x')[source]

A Legendre series class.

The Legendre class provides the standard Python numerical methods ‘+’, ‘-’, ‘*’, ‘//’, ‘%’, ‘divmod’, ‘**’, and ‘()’ as well as the attributes and methods listed below.

Parameters:

coefarray_like

Legendre coefficients in order of increasing degree, i.e., (1, 2, 3) gives 1*P_0(x) + 2*P_1(x) + 3*P_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.].

symbolstr, optional

Symbol used to represent the independent variable in string representations of the polynomial expression, e.g. for printing. The symbol must be a valid Python identifier. Default value is ‘x’.

New in version 1.24.

Attributes:

symbol

Methods

__call__(arg)	Call self as a function.
basis(deg[, domain, window, symbol])	Series basis polynomial of degree deg.
cast(series[, domain, window])	Convert series to series of this class.
convert([domain, kind, window])	Convert series to a different kind and/or domain and/or window.
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, ...])	Least squares fit to data.
fromroots(roots[, domain, window, symbol])	Return series instance that has the 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, symbol])	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 the roots of the series polynomial.
trim([tol])	Remove trailing coefficients
truncate(size)	Truncate series to length size.