InhomogeneousQuadrature¶

About the `InhomogeneousQuadrature` class¶

The WaveBlocks Project

Inheritance diagram¶

Inheritance diagram of InhomogeneousQuadrature

Class documentation¶

class WaveBlocks.InhomogeneousQuadrature(QR=None, order=None)¶

build_matrix(pacbra, packet, operator=None)¶

Calculate the matrix representation of $\langle\Psi|f|\Psi\rangle$ .

Parameters:	pacbra – The wavepacket $<\Psi\|$ from the bra with $Nbra$ components and basis size of $Kbra$ . packet – The wavepacket $\|\Psi>$ from the ket with $Nket$ components and basis size of $Kket$ . operator – A function with two arguments $f:(q, x) \rightarrow R^{Nbra \times Nket}$ .
Returns:	A square matrix of size $\sum_i Kbra_i \times \sum_j Kket_j$ .

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.

mix_parameters(Pibra, Piket)¶

Mix the two parameter sets $Pi_bra$ and $Pi_ket$ from the bra and the ket wavepacket.

Parameters:	Pibra – The parameter set $Pi$ from the bra. Piket – The parameter set $Pi$ from the ket.
Returns:	The mixed parameters $q0$ and $QS$ . (See the theory for details.)

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

Performs the quadrature of $\langle\Psi|f|\Psi\rangle$ for a general $f$ .

Parameters:

pacbra – The wavepacket $<\Psi|$ from the bra with $Nbra$ components and basis size of $Kbra$ .
packet – The wavepacket $|\Psi>$ from the ket with $Nket$ components and basis size of $Kket$ .
operator – A real-valued function $f(x):R \rightarrow R^{Nbra \times Nket}$ .
summed – Whether to sum up the individual integrals $\langle\Phi_i|f_{i,j}|\Phi_j\rangle$ .
component – Request only the i-th component of the result. Remember that $i \in [0, Nbra*Nket-1]$ .
diag_component – Request only the i-th component from the diagonal entries, here $i \in [0, Nket-1]$

Returns:

The value of $\langle\Psi|f|\Psi\rangle$ . This is either a scalar value or a list of $Nbra*Nket$ 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(Pibra, Piket, eps, QR=None)¶

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

Parameters:	Pibra – The parameter set $Pi$ from the bra. Piket – The parameter set $Pi$ from the ket. eps – The epsilon of the wavepacket. QR – An optional quadrature rule providing the nodes.

InhomogeneousQuadrature¶

About the `InhomogeneousQuadrature` class¶

Inheritance diagram¶

Class documentation¶

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InhomogeneousQuadrature¶

About the InhomogeneousQuadrature class¶

Inheritance diagram¶

Class documentation¶

Table Of Contents

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About the `InhomogeneousQuadrature` class¶