choreo.segm.quad.QuadTable#

class QuadTable(w, x, wlag, th_cvg_rate=None)#

Numerical integration and approximation.

This class implements useful methods for the approximate integration (or quadrature) of regular functions on a segment, as well as other related numerical methods.

(1)#\[\int_{0}^{1} f(x) \dd x \approx \sum_{i=0}^{n-1} w_i f(x_i)\]

Class Constructor

__init__()

Builds a QuadTable from input node and weight arrays.

Parameters:

w (numpy.ndarray(shape = (n), dtype = np.float64)) – Quadrature weights.
x (numpy.ndarray(shape = (n), dtype = np.float64)) – Quadrature nodes on \([0,1]\).
wlag (numpy.ndarray(shape = (n), dtype = np.float64)) – Barycentric Lagrange interpolation weights.
th_cvg_rate (int, optional) – Theoretical convergence rate of the quadrature formula, by default None.

Methods Summary

`__init__`	Builds a `QuadTable` from input node and weight arrays.
`is_symmetric`	Returns `True` if the integration method is symmetric.
`is_symmetric_pair`	Returns `True` if the pair of integration methods is symmetric.
`symmetric_adjoint`	Computes the symmetric adjoint of a `QuadTable`.
`symmetry_default`	Computes the symmetry default of a single / a pair of `QuadTable`.

Attributes

`nsteps`	Number of steps of the method.
`th_cvg_rate`	Theoretical convergence rate of the quadrature for smooth functions.
`w`	Integration weights of the method on \([0,1]\).
`wlag`	Barycentric Lagrange interpolation weights relative to the nodes.
`x`	Nodes of the method in \([0,1]\).