Cells

DataPoints(seeds, source[, bc, box_size])

Main class for seeds/source data points.

Cells(seeds, source, vol_x[, extra_space, ...])

Main class for particles with a volume.
class iceshot.cells.DataPoints(seeds, source, bc=None, box_size=[1.0, 1.0])

Bases: object

Main class for seeds/source data points.

Variables:

  • device – default device for all the tensors (same as seeds device)

  • dtype – data type

  • d – dimenstion

  • x – seeds positions

  • y – source positions

  • bc – boundary conditions

  • L – box size as tensor

__init__(seeds, source, bc=None, box_size=[1.0, 1.0])

Initialize

Parameters:

  • seeds ((N,d) Tensor) – seed points

  • source ((M,d) Tensor) – source points

  • bc (optional) – boundary condition. Defaults to None.

  • box_size (list, optional) – Defaults to [1.0,1.0].

lazy_XY()

Return the XY matrix as a LazyTensor.

The XY matrix is the matrix \((y_j - x_i)_{ij}\) where \(y\) and \(x\) are respectively the source and seed points.

Returns:

(N,M) LazyTensor

class iceshot.cells.Cells(seeds, source, vol_x, extra_space=None, fluid_size=None, orientation=None, axis=None, ar=None, bc=None, box_size=[1.0, 1.0], jct_method='Kmin')

Bases: DataPoints

Main class for particles with a volume.

Variables:

  • N_cells – initial number of cells

  • N_crystals – current number of cells

  • M_grid – number of source points

  • vol_grid – volume of a source point (equal to 1/M_grid)

  • axis – (N,d) Tensor of axes

  • ar – (N,) Tensor of aspect ratios

  • orientation – (N,d,d) Tensor of orientations

  • f_x – (N,) Tensor of Kantorovich potentials

  • g_y – (M,) Tensor of Kantorovich potentials

  • labels – (M,) Tensor of labels

__init__(seeds, source, vol_x, extra_space=None, fluid_size=None, orientation=None, axis=None, ar=None, bc=None, box_size=[1.0, 1.0], jct_method='Kmin')

Initialize

Parameters:

  • seeds ((N,d) Tensor) – seed points

  • source ((M,d) Tensor) – source points

  • vol_x (N Tensor) – volumes of the particles

  • extra_space (str, optional) – TBI. Defaults to None.

  • fluid_size (float) – TBI. Defaults to None.

  • orientation ((N,d,d) Tensor, optional) – Orientation matrices. Defaults to None (automatically computed from axis and aspect ratio).

  • axis ((N,d) Tensor, optional) – Orientation axis. Defaults to None (random axis).

  • ar (N tensor, optional) – Aspect ratios. Defaults to 1.

  • bc (optional) – boundary condition. Defaults to None.

  • box_size (list, optional) – Defaults to [1.0,1.0].

  • jct_method (string, optional) – The method used to compute junction points. Can be ‘linear’ (faster on CPU) or ‘Kmin’ (faster on GPU). Defaults to ‘linear’.

orientation_from_axis()

Compute the orientation matrices from the axes and aspect ratios.

Raises:

NotImplementedError – Only in 2D and 3D

Returns:

Orientation matrices

Return type:

Tensor

covariance_matrix(vols=None, bsr=False, **kwargs)

Compute the covariance matrices of a particle configuration.

Parameters:

  • vols (_type_, optional) – Input volumes. Defaults to None (automatically computed).

  • bsr (bool, optional) – Use Block-Sparse-Reduction (faster). Defaults to False.

Raises:

NotImplementedError – Only in 2D and 3D

Returns:

Covariance matrix

Return type:

(N,d,d) Tensor

allocation_matrix(type='lazy')

Compute the allocation matrix

Parameters:

type (str, optional) – Output type. Can be “lazy” for LazyTensor or “dense” for Tensor. Defaults to “lazy”.

Returns:

The \((i,j)\) component of the allocation matrix is 1 if the source point \(j\) belongs to the particle \(i\) and 0 otherwise.

Return type:

(N,M) Tensor or LazyTensor

barycenters(weight=None, bsr=False)

Compute the (weighted) barycenter of each particle.

Parameters:

  • weight (float or Tensor, optional) – Defaults to 1.

  • bsr (bool, optional) – Use Block-Sparse-Reduction (faster). Defaults to False.

Returns:

barycenters

Return type:

(N,d) Tensor

junctions(r=None, K=None)

Return a matrix of size MxK containing the cell labels of K neighbours of each pixel, padded with -1

Parameters:

  • r (float, optional) – The ‘vision radius’ around each pixel point. By defaults, only the +/-1 neighbouring pixels are considered.

  • K (int, optional) – Must be larger than the number of pixels inside the ‘vision radius’. By default, it is equal to 3**d + 1.

Returns:

A matrix of size MxK containing the cell labels of K neighbours of each pixel, padded with -1

Return type:

(Tensor)

extract_boundary(r=None, K=None)

Return the indices of the grid-cells corresponding to a boundary pixel.

lazy_XY()

Return the XY matrix as a LazyTensor.

The XY matrix is the matrix \((y_j - x_i)_{ij}\) where \(y\) and \(x\) are respectively the source and seed points.

Returns:

(N,M) LazyTensor

sort_y()

Sort the source points according to their labels.

Returns:

Positions before sorting and ranges_ij argument to be passed to the Block-Sparse-Reduction method.

Return type:

(Tensor, tuple)