choreo.segm.quad.QuadTable

class QuadTable

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 \([0,1]\).