GenzKeisterOriginalQR

About the GenzKeisterOriginalQR class

The WaveBlocks Project

@author: R. Bourquin @copyright: Copyright (C) 2010, 2011, 2012, 2013, 2014, 2015, 2016 R. Bourquin @license: Modified BSD License

Inheritance diagram

Inheritance diagram of GenzKeisterOriginalQR

Class documentation

class WaveBlocksND.GenzKeisterOriginalQR(dimension, level, options={})[source]

This class implements a Genz-Keister quadrature rule. The quadrature is not transformed to exclude the exponential weight factor \exp(-x^2).

__init__(dimension, level, options={})[source]

Initialize a new Genz-Keister quadrature rule.

Parameters:
  • dimension – The dimension D of the Genz-Keister quadrature.
  • level – The level K of the Genz-Keister quadrature.
Raise:

ValueError if the K is not in the range [1, \ldots, 18].
[1]Alan Genz: “Fully Symmetric Interpolatory Rules for Multiple Integrals”, SIAM J. Num. Analysis. 23(6) (1986), pp. 1273-1283.
[2]Alan Genz and Bradley Keister: “Fully Symmetric Interpolatory Rules for Multiple Integrals over Infinite Regions with Gaussian Weight”, J. Comp. Appl. Math. 71 (1996), pp. 299-309.
construct_rule(K)[source]

Compute a Genz-Keister quadrature rule.

Parameters:K – The level K of the Genz-Keister construction.

Note

This is an internal method and there should be no reason to explicitely call it manually.

Warning

This method can be expensive and may take some time to finish. Also, the quadrature nodes may use large amounts of memory depending on the dimension and level parameters.

get_description()[source]

Return a description of this quadrature rule object. A description is a dict containing all key-value pairs necessary to reconstruct the current instance. A description never contains any data.

get_dimension()
Returns:The space dimension D of the quadrature rule.
get_nodes()[source]

Returns the quadrature nodes \{\gamma_i\}_i.

Returns:An array containing the quadrature nodes \{\gamma_i\}_i.
get_number_nodes()
Returns:The number of quadrature nodes denoted by |\Gamma| that are part of this quadrature rule \Gamma = (\gamma, \omega).
get_weights()[source]

Returns the quadrature weights \{\omega_i\}_i.

Returns:An array containing the quadrature weights \{\omega_i\}_i.