LinearCombinationOfHAWPs¶

About the `LinearCombinationOfHAWPs` class¶

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class WaveBlocksND.LinearCombinationOfHAWPs(dimension, number_components, eps, number_packets=0)[source]¶

This class represents linear combinations of compatible Hagedorn wavepackets.

__init__(dimension, number_components, eps, number_packets=0)[source]¶

Initialize a new linear combination of Hagedorn wavepackets. This object represents $\Upsilon := \sum_{j=0}^{J-1} c_j \Psi_j$ . All $J$ wavepackets $\Psi_j$ have the same number $N$ components and are defined in the $D$ dimensional space.

Parameters:	dimension – The space dimension $D$ the packets have. ncomponents – The number $N$ of components the packets have.
Returns:	An instance of `LinearCombinationOfHAWPs`.

__str__()[source]¶

Returns:	A string describing the linear combination of Hagedorn wavepackets $\Upsilon = \sum_{j=0}^J c_j \Psi_j$ .

add_wavepacket(packet, coefficient=1.0)[source]¶

Add a new wavepacket to the linear combination.

Parameters:	packet (A `HagedornWavepacket` instance.) – The new Hagedorn wavepacket $\Psi_j$ to add. coefficient – The corresponding coefficient $c_j$ , default is 1.0.

add_wavepackets(packetlist, coefficients=None)[source]¶

Add a list of new wavepackets to the linear combination.

Parameters:	packetlist (A list of `HagedornWavepacket` instances.) – A list of new Hagedorn wavepackets $\{\Psi_j\}$ . coefficients – The corresponding coefficient vector $c$ , default is a vector of all 1.0.

clone()¶

Raise:	`NotImplementedError` Abstract interface.

evaluate_at(grid, packetindex=None, prefactor=False)[source]¶

Evaluate the linear copmbination $\Upsilon = \sum_{j=0}^J c_j \Psi_j$ of Hagedorn wavepackets $\Psi_j$ at the given nodes $\gamma$ .

Parameters:	grid (A class having a `get_nodes(...)` method.) – The grid $\Gamma$ containing the nodes $\gamma$ . packetindex – The index $j$ of a single packet $\Psi_j$ to evaluate. (Defaults to `None` for evaluating all wavepackets.) prefactor (Boolean, default is `False`.) – Whether to include a factor of $\frac{1}{\sqrt{\det(Q_j)}}$ .
Returns:	A list of arrays or a single array containing the values of the $\Psi_j$ at the nodes $\gamma$ .

evaluate_basis_at(grid, prefactor=False)[source]¶

Evaluate all the individual Hagedorn wavepackets $\Psi_j$ of $\Upsilon = \sum_{j=0}^J c_j \Psi_j$ at the given nodes $\gamma$ .

Parameters:	grid (A class having a `get_nodes(...)` method.) – The grid $\Gamma$ containing the nodes $\gamma$ . prefactor (Boolean, default is `False`.) – Whether to include a factor of $\frac{1}{\sqrt{\det(Q_j)}}$ .
Returns:	A two-dimensional ndarray $H$ of shape $(\|\Gamma\|, J)$ where the entry $H[i, j]$ is the value of $\Psi_j(\gamma_i)$ .

get_basis_shapes(packetindex=None)[source]¶

Retrieve the basis shapes $\mathfrak{K}_j$ for each packet $\Psi_j$ .

Parameters:	component (int) – The component $i$ whose basis shape we request. (Default is `None` which means to return the basis shapes for all components.
Returns:	The basis shape for an individual component or a list with all shapes.

get_basis_shapes_hashes(packetindex=None)[source]¶

Retrieve the hashes of all basis shapes $\mathfrak{K}_j$ for each packet $\Psi_j$ .

Parameters:	component (int) – The component $i$ whose basis shape we request. (Default is `None` which means to return the basis shapes for all components.
Returns:	The basis shape for an individual component or a list with all shapes.

get_basis_sizes(packetindex=None)[source]¶

Retrieve the basis sizes $|\mathfrak{K}_j|$ for each packet $\Psi_j$ .

Parameters:	component (int) – The component $i$ whose basis shape we request. (Default is `None` which means to return the basis shapes for all components.
Returns:	The basis shape for an individual component or a list with all shapes.

get_coefficient(packetindex)[source]¶

Get the coefficient $c_j$ of the wavepacket $\Psi_j$ .

Parameters:	packetindex – The index $0 \leq j < J$ of the coefficient to retrieve.
Returns:	The coefficient $c_j$ .

get_coefficients()[source]¶

Get the vector with all coefficients $c_j$ of all wavepackets $\Psi_j$ .

Returns:	The vector $c$ of all coefficients $c_j$ . The vector is of shape $(J, 1)$ .
Type:	An `ndarray`

get_description()[source]¶: Return a description of this linear combination 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 all the wavepackets $\Psi_j$ .

get_eps()[source]¶

Retrieve the semi-classical scaling parameter $\varepsilon$ of the wavepacket.

Returns:	The value of $\varepsilon$ .

get_number_components()¶

Returns:	The number $N$ of components all the wavepackets $\Psi_j$ have.

get_number_packets()¶

Returns:	The number $J$ of wavepackets in the linear combination $\Upsilon := \sum_{j=0}^{J-1} c_j \Psi_j$ .

get_wavepacket(packetindex)[source]¶

Get the wavepacket $\Psi_j$ from the linear combination.

Parameters:	index – The index $0 \leq j < J$ of the packet to retrieve.
Returns:	The wavepacket $\Psi_j$ .
Type:	A `HagedornWavepacket` instance.

get_wavepacket_coefficient(packetindex, index)[source]¶

Retrieve a single coefficient $c^i_k$ of the specified component $\Phi_i$ of $\Psi$ .

Parameters:	component – The index $i$ of the component $\Phi_i$ we want to update. index (A tuple of $D$ integers.) – The multi-index $k$ of the coefficient $c^i_k$ we want to update.
Returns:	A single complex number.
Raise:	`ValueError` For invalid indices $i$ or $k$ .

get_wavepacket_coefficients(packetindex=None)[source]¶

Retrieve a single coefficient $c^i_k$ of the specified component $\Phi_i$ of $\Psi$ .

Parameters:	component – The index $i$ of the component $\Phi_i$ we want to update. index (A tuple of $D$ integers.) – The multi-index $k$ of the coefficient $c^i_k$ we want to update.
Returns:	A single complex number.
Raise:	`ValueError` For invalid indices $i$ or $k$ .

get_wavepacket_parameters(packetindex=None, key=('q', 'p', 'Q', 'P', 'S'))[source]¶

Get the Hagedorn parameter set $\Pi$ of the wavepacket $\Psi_j$ .

Parameters:	packetindex – The index $0 \leq j < J$ of the packet whose parameter set $Pi$ we want.
Returns:	The Hagedorn parameter set $\Pi = (q, p, Q, P, S)$ in this order.

get_wavepackets()[source]¶

Get all the wavepackets $\Psi_j$ from the linear combination $\Upsilon$ .

Warning

This method potentially generates a large number of wavepacket instances.

Returns:	A list of `HagedornWavepacket` instances.

remove_wavepacket(packetindex)[source]¶

Remove a wavepacket $\Psi_j$ from the linear combination.

Parameters:	packetindex – The index $0 \leq j < J$ of the packet to remove.

set_coefficient(packetindex, coefficient)[source]¶

Set the coefficient $c_j$ of the wavepacket $\Psi_j$ .

Parameters:	packetindex – The index $0 \leq j < J$ of the coefficient to retrieve. coefficient – The coefficient $c_j$ .

set_coefficients(coefficients)[source]¶

Update all the coefficients $c$ of $\Upsilon$ .

Parameters:	coefficients (An `ndarray`) – The vector $c$ .

set_wavepacket_coefficient(packetindex, index, value)[source]¶

Set a single coefficient $c^i_k$ of the specified component $\Phi_i$ of $\Psi$ .

Parameters:	component – The index $i$ of the component $\Phi_i$ we want to update. index (A tuple of $D$ integers.) – The multi-index $k$ of the coefficient $c^i_k$ we want to update. value – The new value of the coefficient $c^i_k$ .
Raise:	`ValueError` For invalid indices $i$ or $k$ .

set_wavepacket_coefficients(coefficients, basisshapes=None, packetindex=None)[source]¶

Retrieve a single coefficient $c^i_k$ of the specified component $\Phi_i$ of $\Psi$ .

Warning: make sure the coefficients and basis shapes stay in sync!

Parameters:	component – The index $i$ of the component $\Phi_i$ we want to update. index (A tuple of $D$ integers.) – The multi-index $k$ of the coefficient $c^i_k$ we want to update.
Returns:	A single complex number.
Raise:	`ValueError` For invalid indices $i$ or $k$ .

set_wavepacket_parameters(Pilist, packetindex=None, key=('q', 'p', 'Q', 'P', 'S'))[source]¶

Set the Hagedorn parameters $\Pi$ of the wavepacket $\Psi_j$ .

Parameters:	Pilist – The Hagedorn parameter set $\Pi = (q, p, Q, P, S)$ in this order.

set_wavepackets(packetlist)¶

Raise:	`NotImplementedError` Abstract interface.

slim_recursion(grid, packetindex, prefactor=False)[source]¶

Evaluate the Hagedorn wavepacket $\Psi$ at the given nodes $\gamma$ . This routine is a slim version compared to the full basis evaluation. At every moment we store only the data we really need to compute the next step until we hit the highest order basis functions.

Parameters:	grid (A class having a `get_nodes(...)` method.) – The grid $\Gamma$ containing the nodes $\gamma$ . component – The index $i$ of a single component $\Phi_i$ to evaluate. prefactor (Boolean, default is `False`.) – Whether to include a factor of $\frac{1}{\sqrt{\det(Q)}}$ .
Returns:	A list of arrays or a single array containing the values of the $\Phi_i$ at the nodes $\gamma$ .

Note that this function does not include the global phase $\exp(\frac{i S}{\varepsilon^2})$ .

LinearCombinationOfHAWPs¶

About the `LinearCombinationOfHAWPs` class¶

Inheritance diagram¶

Class documentation¶

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LinearCombinationOfHAWPs¶

About the LinearCombinationOfHAWPs class¶

Inheritance diagram¶

Class documentation¶

About the `LinearCombinationOfHAWPs` class¶