class numpy.polynomial.legendre.Legendre(coef, domain=[-1, 1], window=[-1, 1])[source]

A Legendre series class.

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

Parameters :

coef : array_like

Legendre 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


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.


coef ((N,) ndarray) Legendre coefficients, from low to high.
domain ((2,) ndarray) Domain that is mapped to window.
window ((2,) ndarray) Window that domain is mapped to.


basis(deg[, domain, window]) Legendre polynomial of degree deg.
cast(series[, domain, window]) Convert instance to equivalent Legendre 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 Legendre 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.