HomogeneousQuadrature

About the HomogeneousQuadrature class

The WaveBlocks Project

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

Inheritance diagram

Class documentation

class WaveBlocks.HomogeneousQuadrature(QR=None, order=None)

build_matrix(packet, operator=None)

Calculate the matrix representation of .

Parameters:

• packet – The wavepacket .
• operator – A function with two arguments .

Returns:

A square matrix of size .

build_qr(qorder)

Create a quadrature rule of the given order.

Parameters:qorder – The order of the quadrature rule.

get_qr()

Return the GaussHermiteQR instance used for quadrature.

Returns:The current instance of the quadrature rule.

quadrature(packet, operator=None, summed=False, component=None, diag_component=None)

Performs the quadrature of for a general .

Parameters:

• packet – The wavepacket .
• operator – A real-valued function .
• summed – Whether to sum up the individual integrals .
• component – Request only the i-th component of the result. Remember that .
• diag_component – Request only the i-th component from the diagonal entries, here

Returns:

The value of . This is either a scalar value or a list of scalar elements.

Note

‘component’ takes precedence over ‘diag_component’ if both are supplied. (Which is discouraged)

set_qr(QR)

Set the GaussHermiteQR instance used for quadrature.

Parameters:QR – The new GaussHermiteQR instance.

transform_nodes(Pi, eps, QR=None)

Transform the quadrature nodes such that they fit the given wavepacket.

Parameters:

• Pi – The parameter set of the wavepacket.
• eps – The epsilon of the wavepacket.
• QR – An optional quadrature rule providing the nodes.