sisl.Grid

class sisl.Grid

Bases: LatticeChild, _Dispatchs

Real-space grid information with associated geometry.

This grid object handles cell vectors and divisions of said grid.

Parameters:

shape (float or (3,) of int) – the shape of the grid. A float specifies the grid spacing in Angstrom, while a list of integers specifies the exact grid size.
bc (list of int (3, 2) or (3, ), optional) – the boundary conditions for each of the cell’s planes. Default to periodic BC.
lattice – the lattice that this grid represents. lattice has precedence if both geometry and lattice has been specified. Defaults to [1, 1, 1].
dtype (numpy.dtype, optional) – the data-type of the grid, default to numpy.float64.
geometry – associated geometry with the grid. If lattice has not been passed the lattice will be taken from this geometry.

Examples

>>> grid1 = Grid(0.1, lattice=10)
>>> grid2 = Grid(0.1, lattice=Lattice(10))
>>> grid3 = Grid(0.1, lattice=Lattice([10] * 3))
>>> grid1 == grid2
True
>>> grid1 == grid3
True
>>> grid = Grid(0.1, lattice=10, dtype=np.complex128)
>>> grid == grid1
False

It is possible to provide a geometry and a different lattice to make a smaller (or bigger) lattice based on a geometry. This might be useful when creating wavefunctions or expanding densities to grids. Here we create a square grid based on a hexagonal graphene lattice. Expanding wavefunctions from this geometry will automatically convert to the lattice size. >>> lattice = Lattice(10) # square lattice 10x10x10 Ang >>> geometry = geom.graphene() >>> grid = Grid(0.1, lattice=lattice, geometry=geometry)

Conversion

`to`	A dispatcher for classes, using __get__ it converts into ObjectDispatcher upon invocation from an object, or a TypeDispatcher when invoked from a class
`to.Path`(args, *kwargs)
`to.pyamg`([dtype])
`to.str`(args, *kwargs)

Plotting

`plot`	Plotting functions for the `Grid` class.
`plot.grid`([axes, represent, ...])	Builds a `GridPlot` by setting the value of "grid" to the current object.

Methods

`append`(other, axis)	Appends other `Grid` to this grid along axis
`area`(ax0, ax1)	Calculate the area spanned by the two axis ax0 and ax1
`average`(axis[, weights])	Average grid values along direction axis.
`copy`([dtype])	Copy the object, possibly changing the data-type
`cross_section`(idx, axis)	Takes a cross-section of the grid along axis axis
`fill`(val)	Fill the grid with this value
`index`(coord[, axis])	Find the grid index for a given coordinate (possibly only along a given lattice vector axis)
`index2xyz`(index)	Real-space coordinates of indices related to the grid
`index_fold`(index[, unique])	Converts indices from any placement to only exist in the "primary" grid
`index_truncate`(index)	Remove indices from outside the grid to only retain indices in the "primary" grid
`interp`(shape[, order, mode])	Interpolate grid values to a new resolution (retaining lattice vectors)
`isosurface`(level[, step_size])	Calculates the isosurface for a given value
`mean`(axis[, weights])	Average grid values along direction axis.
`mgrid`(*slices)	Return a list of indices corresponding to the slices
`pyamg_boundary_condition`(A, b)	Attach boundary conditions to the pyamg grid-matrix A with default boundary conditions as specified for this `Grid`
`pyamg_fix`(A, b, pyamg_indices, value)	Fix values for the stencil to value.
`pyamg_index`(index)	Calculate pyamg matrix indices from a list of grid indices
`pyamg_source`(b, pyamg_indices, value)	Fix the source term to value.
`read`(sile, args, *kwargs)	Reads grid from the `Sile` using read_grid
`remove`(idx, axis)	Removes certain indices from a specified axis.
`remove_part`(idx, axis, above)	Removes parts of the grid via above/below designations.
`sc_index`(args, *kwargs)	Call local `Lattice.sc_index` function
`set_bc`(bc)
`set_boundary`(bc)
`set_boundary_condition`(bc)
`set_geometry`(geometry[, also_lattice])	Sets the `Geometry` for the grid.
`set_grid`(shape[, dtype])	Create the internal grid of certain size.
`set_lattice`(lattice)	Overwrites the local lattice.
`set_nsc`(args, *kwargs)	Set the number of super-cells in the `Lattice` object
`set_supercell`(lattice)	Overwrites the local lattice.
`smooth`([r, method, mode])	Make a smoother grid by applying a filter
`sub`(idx, axis)	Retains certain indices from a specified axis.
`sub_part`(idx, axis, above)	Retains parts of the grid via above/below designations.
`sum`(axis)	Sum grid values along axis axis.
`swapaxes`(axis1, axis2)	Swap two axes in the grid (also swaps axes in the lattice)
`tile`(reps, axis)	Tile grid to create a bigger one
`topyamg`([dtype])	Create a pyamg stencil matrix to be used in pyamg
`write`(sile, args, *kwargs)	Writes grid to the sile using sile.write_grid

Attributes

`DIRICHLET`
`NEUMANN`
`OPEN`
`PERIODIC`
`boundary_condition`
`cell`	Returns the inherent `Lattice.cell`
`dcell`	Voxel cell size
`dkind`	The data-type of the grid (in str)
`dtype`	Data-type used in grid
`dvolume`	Volume of the grid voxel elements
`icell`	Returns the inherent `Lattice.icell`
`isc_off`	Returns the inherent `Lattice.isc_off`
`length`	Returns the inherent `Lattice.length`
`n_s`	Returns the inherent `Lattice.n_s`
`nsc`	Returns the inherent `Lattice.nsc`
`origin`	Returns the inherent `Lattice.origin`
`pbc`
`rcell`	Returns the inherent `Lattice.rcell`
`sc`	[deprecated] Return the lattice object associated with the `Lattice`.
`sc_off`	Returns the inherent `Lattice.sc_off`
`shape`	Grid shape along the lattice vectors
`size`	Total number of elements in the grid
`volume`	Returns the inherent `Lattice.volume`

append(other, axis)

Appends other Grid to this grid along axis

Parameters:

grid (Grid)
other (GridLike)
axis (CellAxis)

Return type:

Grid

apply(function_, *args, **kwargs)

Applies a function to the grid and returns a new grid

You can also apply a function that does not return a grid (maybe you want to do some measurement). In that case, you will get the result instead of a Grid.

Parameters:

function (str or function) – for a string the full module path to the function should be given. The function that will be called should have the grid as the first argument in its interface.
kwargs (args and) – arguments that go directly to the function call
grid (Grid)

Notes

The function argument name function_ is named so that function can be an eligible keyword argument for the function.

area(ax0, ax1)

Calculate the area spanned by the two axis ax0 and ax1

Return type:: float

average(axis, weights=None)[source]

Average grid values along direction axis.

Parameters:

axis (int) – unit-cell direction to average across
weights (ndarray, optional) – the weights for the individual axis elements, if boolean it corresponds to 0 and 1 for false/true.

See also

numpy.average: for details regarding the weights argument

copy(dtype=None)

Copy the object, possibly changing the data-type

Parameters:: grid (Grid)
Return type:: Grid

cross_section(idx, axis)[source]

Takes a cross-section of the grid along axis axis

Remark: This API entry might change to handle arbitrary cuts via rotation of the axis

fill(val)[source]

Fill the grid with this value

Parameters:: val (numpy.dtype) – all grid-points will have this value after execution

index(coord, axis=None)[source]

Find the grid index for a given coordinate (possibly only along a given lattice vector axis)

Parameters:

coord ((:, 3) or float or Shape) – the coordinate of the axis. If a float is passed axis is also required in which case it corresponds to the length along the lattice vector corresponding to axis. If a Shape a list of coordinates that fits the voxel positions are returned (all internal points also).
axis (int, optional) – the axis direction of the index, or for all axes if none.

index2xyz(index)[source]

Real-space coordinates of indices related to the grid

Parameters:: index (ndarray) – indices for grid-positions
Returns:: coordinates of the indices with respect to this grid spacing
Return type:: numpy.ndarray

index_fold(index, unique=True)[source]

Converts indices from any placement to only exist in the “primary” grid

Examples

>>> grid = Grid([10, 10, 10])
>>> assert np.all(grid.index_fold([-1, -1, -1]) == 9)

Parameters:

index (ndarray) – indices for grid-positions
unique (bool, optional) – if true the returned indices are made unique after having folded the index points

Returns:

all indices are then within the shape of the grid

Return type:

numpy.ndarray

See also

index_truncate: truncate indices by removing indices outside the primary cell

index_truncate(index)[source]

Remove indices from outside the grid to only retain indices in the “primary” grid

Examples

>>> grid = Grid([10, 10, 10])
>>> assert len(grid.index_truncate([-1, -1, -1])) == 0

Parameters:: index (ndarray) – indices for grid-positions
Returns:: all indices are then within the shape of the grid (others have been removed
Return type:: numpy.ndarray

See also

index_fold: fold indices into the primary cell

interp(shape, order=1, mode='wrap', **kwargs)[source]

Interpolate grid values to a new resolution (retaining lattice vectors)

It uses the scipy.ndimage.zoom, which creates a finer or more spaced grid using spline interpolation. The lattice vectors remains unchanged.

Parameters:

shape (int, ndarray of len 3) – the new shape of the grid.
order (int 0-5, optional) – the order of the spline interpolation. 1 means linear, 2 quadratic, etc…
mode ({'wrap', 'mirror', 'constant', 'reflect', 'nearest'}) – determines how to compute the borders of the grid. The default is 'wrap', which accounts for periodic conditions.
**kwargs – optional arguments passed to the interpolation algorithm The interpolation routine is scipy.ndimage.zoom

See also

scipy.ndimage.zoom: method used for interpolation

isosurface(level, step_size=1, **kwargs)[source]

Calculates the isosurface for a given value

It uses skimage.measure.marching_cubes, so you need to have scikit-image installed.

Parameters:

level (float) – contour value to search for isosurfaces in the grid. If not given or None, the average of the min and max of the grid is used.
step_size (int) – step size in voxels. Larger steps yield faster but coarser results. The result will always be topologically correct though.
**kwargs – optional arguments passed directly to skimage.measure.marching_cubes for the calculation of isosurfaces.

Returns:

numpy array of shape (V, 3) – Verts. Spatial coordinates for V unique mesh vertices.
numpy array of shape (n_faces, 3) – Faces. Define triangular faces via referencing vertex indices from verts. This algorithm specifically outputs triangles, so each face has exactly three indices.
numpy array of shape (V, 3) – Normals. The normal direction at each vertex, as calculated from the data.
numpy array of shape (V, 3) – Values. Gives a measure for the maximum value of the data in the local region near each vertex. This can be used by visualization tools to apply a colormap to the mesh.

See also

skimage.measure.marching_cubes: method used to calculate the isosurface.

mean(axis, weights=None)

Average grid values along direction axis.

Parameters:

axis (int) – unit-cell direction to average across
weights (ndarray, optional) – the weights for the individual axis elements, if boolean it corresponds to 0 and 1 for false/true.

See also

numpy.average: for details regarding the weights argument

classmethod mgrid(*slices)[source]

Return a list of indices corresponding to the slices

The returned values are equivalent to numpy.mgrid but they are returned in a (:, 3) array.

Parameters:: *slices (slice or list of int or int) – return a linear list of indices that points to the collective slice made by the passed arguments
Returns:: linear indices for each of the sliced values, shape (*, 3)
Return type:: numpy.ndarray

plot.grid(axes=['z'], represent='real', transforms=(), reduce_method='average', boundary_mode='grid-wrap', nsc=(1, 1, 1), interp=(1, 1, 1), isos=[], smooth=False, colorscale=None, crange=None, cmid=None, show_cell='box', cell_style={}, x_range=None, y_range=None, z_range=None, plot_geom=False, geom_kwargs={}, backend='plotly')

Builds a GridPlot by setting the value of “grid” to the current object.

Plots a grid, with plentiful of customization options.

Parameters:

axes (Axes) – The axes to project the grid to.
represent (Literal['real', 'imag', 'mod', 'phase', 'deg_phase', 'rad_phase']) – The representation of the grid to plot.
transforms (Sequence[Union[str, Callable]]) – List of transforms to apply to the grid before plotting.
reduce_method (Literal['average', 'sum']) – The method used to reduce the grid axes that are not displayed.
boundary_mode (str) – The method used to deal with the boundary conditions. Only used if the grid is to be orthogonalized. See scipy docs for more info on the possible values.
nsc (tuple[int, int, int]) – The number of unit cells to display in each direction.
interp (tuple[int, int, int]) – The interpolation factor to use for each axis to make the grid smoother.
isos (Sequence[dict]) – List of isosurfaces or isocontours to plot. See the showcase notebooks for examples.
smooth (bool) – Whether to ask the plotting backend to make an attempt at smoothing the grid display.
colorscale (Optional[Colorscale]) – Colorscale to use for the grid display in the 2D representation. If None, the default colorscale is used for each backend.
crange (Optional[tuple[float, float]]) – Min and max values for the colorscale.
cmid (Optional[float]) – The value at which the colorscale is centered.
show_cell (Literal['box', 'axes', False]) – Method used to display the unit cell. If False, the cell is not displayed.
cell_style (dict) – Style specification for the cell. See the showcase notebooks for examples.
x_range (Optional[Sequence[float]]) – The range of the x axis to take into account. Even if the X axis is not displayed! This is important because the reducing operation will only be applied on this range.
y_range (Optional[Sequence[float]]) – The range of the y axis to take into account. Even if the Y axis is not displayed! This is important because the reducing operation will only be applied on this range.
z_range (Optional[Sequence[float]]) – The range of the z axis to take into account. Even if the Z axis is not displayed! This is important because the reducing operation will only be applied on this range.
plot_geom (bool) – Whether to plot the associated geometry (if any).
geom_kwargs (dict) – Keyword arguments to pass to the geometry plot of the associated geometry.
backend (str) – The backend to use to generate the figure.

Return type:

GridPlot

See also

scipy.ndimage.affine_transform: method used to orthogonalize the grid if needed.

pyamg_boundary_condition(A, b)[source]

Attach boundary conditions to the pyamg grid-matrix A with default boundary conditions as specified for this Grid

Parameters:

A (scipy.sparse.csr_matrix) – sparse matrix describing the grid
b (numpy.ndarray) – a vector containing RHS of \(\mathbf A \mathbf x = \mathbf b\) for the solution of the grid stencil

pyamg_fix(A, b, pyamg_indices, value)[source]

Fix values for the stencil to value.

Parameters:

A (csr_matrix/csc_matrix) – sparse matrix describing the LHS for the linear system of equations
b (numpy.ndarray) – a vector containing RHS of \(\mathbf A \mathbf x = \mathbf b\) for the solution of the grid stencil
pyamg_indices (list of int) – the linear pyamg matrix indices where the value of the grid is fixed. I.e. the indices should correspond to returned quantities from pyamg_indices.
value (float) – the value of the grid to fix the value at

pyamg_index(index)[source]

Calculate pyamg matrix indices from a list of grid indices

Parameters:: index ((:, 3) of int) – a list of indices of the grid along each grid axis
Returns:: linear indices for the matrix
Return type:: numpy.ndarray

See also

index: query indices from coordinates (directly passable to this method)
mgrid: Grid equivalent to numpy.mgrid. Grid.mgrid returns indices in shapes (:, 3), contrary to numpy’s numpy.mgrid

Raises:: ValueError – if any of the passed indices are below 0 or above the number of elements per axis

classmethod pyamg_source(b, pyamg_indices, value)[source]

Fix the source term to value.

Parameters:

b (numpy.ndarray) – a vector containing RHS of \(\mathbf A \mathbf x = \mathbf b\) for the solution of the grid stencil
pyamg_indices (list of int) – the linear pyamg matrix indices where the value of the grid is fixed. I.e. the indices should correspond to returned quantities from pyamg_indices.

static read(sile, *args, **kwargs)[source]

Reads grid from the Sile using read_grid

Parameters:

sile (Sile, str or pathlib.Path) – a Sile object which will be used to read the grid if it is a string it will create a new sile using get_sile.
* (args passed directly to read_grid(,**))

remove(idx, axis)

Removes certain indices from a specified axis.

Works exactly opposite to sub.

Parameters:

idx (int | Sequence[int]) – the indices of the grid axis axis to be removed
axis (Literal[0, 1, 2, 'a', 'b', 'c']) – the axis segment from which we remove all indices idx
grid (Grid)

Return type:

Grid

remove_part(idx, axis, above)[source]

Removes parts of the grid via above/below designations.

Works exactly opposite to sub_part

Parameters:

idx (int) – the index of the grid axis axis to be removed for above=True grid[:idx,…] for above=False grid[idx:,…]
axis (int) – the axis segment from which we retain the indices idx
above (bool) –

if True will retain the grid:
grid[:idx,...]

else it will retain the grid:
grid[idx:,...]

sc_index(*args, **kwargs)

Call local Lattice.sc_index function

Return type:: int | Sequence[int]

set_bc(bc)[source]

set_boundary(bc)[source]

set_boundary_condition(bc)[source]

set_geometry(geometry, also_lattice=True)[source]

Sets the Geometry for the grid.

Setting the Geometry for the grid is a possibility to attach atoms to the grid.

It is not a necessary entity, so passing None is a viable option.

Parameters:

geometry (Geometry or None) – specify the new geometry in the Grid. If None will remove the geometry (but not the lattice)
also_lattice (bool, optional) – whether to also set the lattice for the grid according to the lattice of the geometry, if False it will keep the lattice as it was.

set_grid(shape, dtype=None)[source]: Create the internal grid of certain size.

set_lattice(lattice)

Overwrites the local lattice.

Parameters:: lattice (LatticeLike)

set_nsc(*args, **kwargs)

Set the number of super-cells in the Lattice object

See set_nsc for allowed parameters.

See also

Lattice.set_nsc: the underlying called method

set_supercell(lattice)

Overwrites the local lattice.

Parameters:: lattice (LatticeLike)

smooth(r=0.7, method='gaussian', mode='wrap', **kwargs)[source]

Make a smoother grid by applying a filter

Parameters:

r (float or ndarray of len 3, optional) –
the radius of the filter in Angstrom for each axis. If the method is "gaussian", this is the standard deviation!

If a single float is provided, then the same distance will be used for all axes.
method ({'gaussian', 'uniform'}) – the type of filter to apply to smoothen the grid.
mode ({'wrap', 'mirror', 'constant', 'reflect', 'nearest'}) – determines how to compute the borders of the grid. The default is wrap, which accounts for periodic conditions.

See also

scipy.ndimage.gaussian_filter

sub(idx, axis)

Retains certain indices from a specified axis.

Works exactly opposite to remove.

Parameters:

idx (int | Sequence[int]) – the indices of the grid axis axis to be retained
axis (Literal[0, 1, 2, 'a', 'b', 'c']) – the axis segment from which we retain the indices idx
grid (Grid)

Return type:

Grid

sub_part(idx, axis, above)[source]

Retains parts of the grid via above/below designations.

Works exactly opposite to remove_part

Parameters:

idx (int) – the index of the grid axis axis to be retained for above=True grid[idx:,…] for above=False grid[:idx,…]
axis (int) – the axis segment from which we retain the indices idx
above (bool) –

if True will retain the grid:
grid[idx:,...]

else it will retain the grid:
grid[:idx,...]

sum(axis)[source]

Sum grid values along axis axis.

Parameters:: axis (int) – unit-cell direction to sum across

swapaxes(axis1, axis2)

Swap two axes in the grid (also swaps axes in the lattice)

If swapaxes(0, 1) it returns the 0 in the 1 values.

Parameters:

axis1 (Literal[0, 1, 2, 'a', 'b', 'c']) – axes indices to be swapped
axis2 (Literal[0, 1, 2, 'a', 'b', 'c']) – axes indices to be swapped
grid (Grid)

Return type:

Grid

tile(reps, axis)

Tile grid to create a bigger one

The atomic indices for the base Geometry will be retained.

Parameters:

reps (int) – number of tiles (repetitions)
axis (Literal[0, 1, 2, 'a', 'b', 'c']) – direction of tiling, 0, 1, 2 according to the cell-direction
grid (Grid)

Return type:

Grid

:raises SislError : when the lattice is not commensurate with the geometry:

See also

Geometry.tile: equivalent method for Geometry class

to.Path(*args, **kwargs)

to.pyamg(dtype=None)

to.str(*args, **kwargs)

topyamg(dtype=None)[source]

Create a pyamg stencil matrix to be used in pyamg

This allows retrieving the grid matrix equivalent of the real-space grid. Subsequently the returned matrix may be used in pyamg for solutions etc.

The pyamg suite is it-self a rather complicated code with many options. For details we refer to pyamg.

Parameters:

dtype (numpy.dtype, optional) – data-type used for the sparse matrix, default to use the grid data-type

Returns:

scipy.sparse.csr_matrix – the stencil for the pyamg solver
numpy.ndarray – RHS of the linear system of equations

Examples

This example proves the best method for a variety of cases in regards of the 3D Poisson problem:

>>> grid = Grid(0.01)
>>> A, b = grid.topyamg() # automatically setups the current boundary conditions
>>> # add terms etc. to A and/or b
>>> import pyamg
>>> from scipy.sparse.linalg import cg
>>> ml = pyamg.aggregation.smoothed_aggregation_solver(A, max_levels=1000)
>>> M = ml.aspreconditioner(cycle='W') # pre-conditioner
>>> x, info = cg(A, b, tol=1e-12, M=M)

See also

pyamg_index: convert grid indices into the sparse matrix indices for A
pyamg_fix: fixes stencil for indices and fixes the source for the RHS matrix (uses pyamg_source)
pyamg_source: fix the RHS matrix b to a constant value
pyamg_boundary_condition: setup the sparse matrix A to given boundary conditions (called in this routine)

write(sile, *args, **kwargs)

Writes grid to the sile using sile.write_grid

Parameters:

sile (SileLike) – a Sile object which will be used to write the grid if it is a string it will create a new sile using get_sile
*args – Any other args will be passed directly to the underlying routine
**kwargs – Any other args will be passed directly to the underlying routine
grid (Grid)

Return type:

None

See also

Grid.read: reads a Grid from a given Sile/file

DIRICHLET = 3

NEUMANN = 4

OPEN = 5

PERIODIC = 2

property boundary_condition: ndarray

property cell: ndarray: Returns the inherent Lattice.cell

property dcell: Voxel cell size

property dkind: The data-type of the grid (in str)

property dtype: Data-type used in grid

property dvolume: Volume of the grid voxel elements

property icell: ndarray: Returns the inherent Lattice.icell

property isc_off: ndarray: Returns the inherent Lattice.isc_off

property length: float: Returns the inherent Lattice.length

property n_s: int: Returns the inherent Lattice.n_s

new = <TypeDispatcher{obj=<class 'sisl.Grid'>}>

Parameters:: obj (Any)
Return type:: Any

property nsc: ndarray: Returns the inherent Lattice.nsc

property origin: ndarray: Returns the inherent Lattice.origin

property pbc: ndarray

plot: Plotting functions for the Grid class.

property rcell: ndarray: Returns the inherent Lattice.rcell

property sc: [deprecated] Return the lattice object associated with the Lattice.

property sc_off: ndarray: Returns the inherent Lattice.sc_off

property shape: Grid shape along the lattice vectors

property size: Total number of elements in the grid

to

A dispatcher for classes, using __get__ it converts into ObjectDispatcher upon invocation from an object, or a TypeDispatcher when invoked from a class

This is a class-placeholder allowing a dispatcher to be a class attribute and converted into an ObjectDispatcher when invoked from an object.

If it is called on the class, it will return a TypeDispatcher.

This class should be an attribute of a class. It heavily relies on the __get__ special method.

Parameters:

name (str) – name of the attribute in the class
dispatchs (dict, optional) – dictionary of dispatch methods
obj_getattr (callable, optional) – method with 2 arguments, an obj and the attr which may be used to control how the attribute is called.
instance_dispatcher (AbstractDispatcher, optional) – control how instance dispatchers are handled through __get__ method. This controls the dispatcher used if called from an instance.
type_dispatcher (AbstractDispatcher, optional) – control how class dispatchers are handled through __get__ method. This controls the dispatcher used if called from a class.

Examples

>>> class A:
...   new = ClassDispatcher("new", obj_getattr=lambda obj, attr: getattr(obj.sub, attr))

The above defers any attributes to the contained A.sub attribute.

property volume: float: Returns the inherent Lattice.volume