Mesh Interpolator¶
- class torchpme.lib.MeshInterpolator(cell: Tensor, ns_mesh: Tensor, interpolation_nodes: int, method: str)[source]¶
Class for handling all steps related to interpolations in the context of a mesh based Ewald summation.
In particular, this includes two core functionalities: 1. “forwards” interpolation, in which the “charges” or more general “particle weights” of atoms are assigned to grid points of a mesh. This is done in the
points_to_mesh()function. 2. “backwards” interpolation, in which values defined on a mesh are interpolated to arbitrary positions typically lying between mesh points. This is done in themesh_to_points()function.Since the computation of the interpolation weights for both of the above types of calculations is identical, this is performed in a separate function called
compute_weights().See also the Examples of the MeshInterpolator class for a demonstration of the functionalities of this class.
- Parameters:
cell (Tensor) – torch.tensor of shape
(3, 3), wherecell[i]is the i-th basis vector of the unit cellns_mesh (Tensor) – toch.tensor of shape
(3,)Number of mesh points to use along each of the three axesinterpolation_nodes (int) – int The number
nof nodes used in the interpolation per coordinate axis. The total number of interpolation nodes in 3D will ben^3. In general, fornnodes, the interpolation will be performed by piecewise polynomials of degreen - 1(e.g.n = 4for cubic interpolation). For Lagrange interpolation, only the values3, 4, 5, 6, 7are supported. For P3M interpolation, only the values1, 2, 3, 4, 5are supported.method (str) – str The interpolation method to use. Either “Lagrange” or “P3M”.
- update(cell: Tensor | None = None, ns_mesh: Tensor | None = None) None[source]¶
Update buffers and derived attributes of the instance.
Call this to reuse a
MeshInterpolatorobject when thecellparameters or the mesh resolution changes. If neithercellnorns_meshare passed there is nothing to be done.
- get_mesh_xyz() Tensor[source]¶
Returns the Cartesian positions of the mesh points.
- Returns:
torch.tensor of shape
(nx, ny, nz, 3)containing the positions of the grid points- Return type:
- compute_weights(positions: Tensor)[source]¶
Compute the interpolation weights of each atom for a given cell (specified during initialization of this class). The weights are not returned, but are used when calling the forward (
points_to_mesh()) and backward (mesh_to_points()) interpolation functions.- Parameters:
positions (Tensor) – torch.tensor of shape
(N, 3)Absolute positions of atoms in Cartesian coordinates
- points_to_mesh(particle_weights: Tensor) Tensor[source]¶
Generate a discretized density from interpolation weights. It assumes that
compute_weights()has been called before to compute all the necessary weights and indices.- Parameters:
particle_weights (Tensor) – torch.tensor of shape
(n_points, n_channels)particle_weights[i,a]is the weight (charge) that point (atom) i has to generate the “a-th” potential. In practice, this can be used to compute e.g. the Na and Cl contributions to the potential separately by using a one-hot encoding of the types.- Returns:
torch.tensor of shape
(n_channels, n_mesh, n_mesh, n_mesh)Discrete density- Return type:
- mesh_to_points(mesh_vals: Tensor) Tensor[source]¶
Take a function defined on a mesh and interpolate its values on arbitrary positions.
- Parameters:
mesh_vals (Tensor) – torch.tensor of shape
(n_channels, nx, ny, nz)The tensor contains the values of a function evaluated on a three-dimensional mesh.(nx, ny, nz)are the number of points along each of the three directions, whilen_channelsprovides the number of such functions that are treated simulateously for the present system.- Returns:
interpolated_values: torch.tensor of shape
(n_points, n_channels)Values of the interpolated function.- Return type:
