archimedes.measure.LegendreMeasure

class archimedes.measure.LegendreMeasure

Measure for the Legendre polynomial family.

Weight \(w(x) = 1\) on \([-1, 1]\).

__init__()

Methods

__init__()
affine_params([a, b])	Map the reference interval \([-1, 1]\) onto \([a, b]\).
mass(*args, **kwargs)	Total mass of the measure mapped by affine_params(*args, **kwargs).
weight(x)	Reference weight function \(w(x) = 1\), evaluated at x.

Attributes

reference_mass	\(\int_{-1}^1 1 \, dt = 2\).
support	Support \([-1, 1]\).
uniform_weight	True if the weight is constant (weight(x) == weight(y)) for every x, y in support -- e.g. true for Legendre, false for Jacobi (singular at the endpoints) or Hermite/Laguerre (unbounded support).