PotentialArray

class abtem.potentials.iam.PotentialArray(array, slice_thickness=None, extent=None, sampling=None, exit_planes=None, ensemble_axes_metadata=None, metadata=None)

Bases: BasePotential, FieldArray

The potential array represents slices of the electrostatic potential as an array. All other potentials build potential arrays.

Parameters:

• array (3D np.ndarray) – The array representing the potential slices. The first dimension is the slice index and the last two are the spatial dimensions.

• slice_thickness (float) – The thicknesses of potential slices [Å]. If a float, the thickness is the same for all slices. If a sequence, the length must equal the length of the potential array.

• extent (one or two float, optional) – Lateral extent of the potential [Å].

• sampling (one or two float, optional) – Lateral sampling of the potential [1 / Å].

• exit_planes (int or tuple of int, optional) – The exit_planes argument can be used to calculate thickness series. Providing exit_planes as a tuple of int indicates that the tuple contains the slice indices after which an exit plane is desired, and hence during a multislice simulation a measurement is created. If exit_planes is an integer a measurement will be collected every exit_planes number of slices.

• ensemble_axes_metadata (list of AxesMetadata) – Axis metadata for each ensemble axis. The axis metadata must be compatible with the shape of the array.

• metadata (dict) – A dictionary defining wave function metadata. All items will be added to the metadata of measurements derived from the waves.

__init__(array, slice_thickness=None, extent=None, sampling=None, exit_planes=None, ensemble_axes_metadata=None, metadata=None)

Methods

__init__(array[, slice_thickness, extent, ...])
apply_func(func, **kwargs)	rtype: TypeVar(T, bound= ArrayObject)
apply_transform(transform[, max_batch])	Transform the wave functions by a given transformation.
build([first_slice, last_slice, chunks, lazy])
compute([progress_bar, profiler, ...])	Turn a lazy abTEM object into its in-memory equivalent.
copy()	Make a copy.
copy_to_device(device)	Copy array to specified device.
ensemble_blocks([chunks])	Split the ensemble into an array of smaller ensembles.
ensure_lazy([chunks])	Creates an equivalent lazy version of the array object.
expand_dims([axis, axis_metadata])	Expand the shape of the array object.
from_array_and_metadata(array, ...)	Creates array object from a given array and metadata.
from_zarr(url[, chunks])	Read wave functions from a hdf5 file.
generate_blocks([chunks])	Generate chunks of the ensemble.
generate_ensemble([keepdims])	Generate every member of the ensemble.
generate_slices([first_slice, last_slice])	Generate the slices for the potential.
get_from_metadata(name[, broadcastable])
get_items(items[, keepdims])	Index the array and the corresponding axes metadata.
lazy([chunks])	rtype: TypeVar(T, bound= ArrayObject)
match_grid(other[, check_match])	Match the grid to another object with a Grid.
max([axis, keepdims, split_every])	Maximum of array object over one or more axes.
mean([axis, keepdims, split_every])	Mean of array object over one or more axes.
min([axis, keepdims, split_every])	Minmimum of array object over one or more axes.
no_base_chunks()	Rechunk to remove chunks across the base dimensions.
project()	Create a 2D array representing a projected image of the potential(s).
rechunk(chunks, **kwargs)	Rechunk dask array.
select_block(index, chunks)	Select a block from the ensemble.
set_ensemble_axes_metadata(axes_metadata, axis)	Sets the axes metadata of an ensemble axis.
show([project])	Show the potential projection.
squeeze([axis])	Remove axes of length one from array object.
std([axis, keepdims, split_every])	Standard deviation of array object over one or more axes.
sum([axis, keepdims, split_every])	Sum of array object over one or more axes.
tile(repetitions)	Tile the potential.
to_cpu()	Move the array to the host memory from an arbitrary source array.
to_data_array()	Convert ArrayObject to a xarray DataArray.
to_gpu([device])	Move the array from the host memory to a gpu.
to_hyperspy()	Convert ArrayObject to a Hyperspy signal.
to_images()	Convert slices of the potential to a stack of images.
to_tiff(filename, **kwargs)	Write data to a tiff file.
to_zarr(url[, compute, overwrite])	Write data to a zarr file.
transmission_function(energy)	Calculate the transmission functions for each slice for a specific energy.
transmit(waves[, conjugate])	Transmit a wave function through a potential slice.

Attributes

array	Underlying array describing the array object.
axes_metadata	List of AxisMetadata.
base_axes_metadata	List of AxisMetadata for the base axes.
base_dims	Number of base dimensions.
base_shape	Shape of the base axes of the potential.
device	The device where the array is stored.
dtype	Datatype of array.
ensemble_axes_metadata	List of AxisMetadata of the ensemble axes.
ensemble_dims	Number of ensemble dimensions.
ensemble_shape	Shape of the ensemble axes of the underlying array.
exit_planes	The "exit planes" of the potential.
exit_thicknesses	The "exit thicknesses" of the potential.
extent	Extent of grid for each dimension in Ångstrom.
gpts	Number of grid points for each dimension.
grid	Simulation grid.
is_complex	True if array is complex.
is_lazy	True if array is lazy.
metadata	Metadata stored as a dictionary.
num_configurations	Number of frozen phonons in the ensemble of potentials.
num_exit_planes	Number of exit planes.
num_slices	Number of projected potential slices.
reciprocal_space_sampling	Reciprocal-space sampling in reciprocal Ångstrom.
sampling	Grid sampling for each dimension in Ångstrom per grid point.
shape	Shape of the underlying array.
slice_limits	The entrance and exit thicknesses of each slice [Å].
slice_thickness	Slice thicknesses for each slice.
thickness	Thickness of the potential [Å].

apply_transform(transform, max_batch='auto')

Transform the wave functions by a given transformation.

Parameters:

• transform (ArrayObjectTransform) – The array object transformation to apply.

• max_batch (int, optional) – The number of wave functions in each chunk of the Dask array. If ‘auto’ (default), the batch size is automatically chosen based on the abtem user configuration settings “dask.chunk-size” and “dask.chunk-size-gpu”.

Returns:

transformed_array_object – The transformed array object.

Return type:

ArrayObjectTransform

property array: np.ndarray | da.core.Array

Underlying array describing the array object.

property axes_metadata: AxesMetadataList

List of AxisMetadata.

property base_axes_metadata

List of AxisMetadata for the base axes.

property base_dims

Number of base dimensions.

property base_shape

Shape of the base axes of the potential.

compute(progress_bar=None, profiler=False, resource_profiler=False, **kwargs)

Turn a lazy abTEM object into its in-memory equivalent.

Parameters:

• progress_bar (bool) – Display a progress bar in the terminal or notebook during computation. The progress bar is only displayed with a local scheduler.

• profiler (bool) – Return Profiler class used to profile Dask’s execution at the task level. Only execution with a local is profiled.

• resource_profiler (bool) – Return ResourceProfiler class is used to profile Dask’s execution at the resource level.

• kwargs – Additional keyword arguments passes to dask.compute.

copy()

Make a copy.

copy_to_device(device)

Copy array to specified device.

Parameters:

device (str)

Returns:

object_on_device

Return type:

T

property device: str

The device where the array is stored.

property dtype

Datatype of array.

property ensemble_axes_metadata

List of AxisMetadata of the ensemble axes.

ensemble_blocks(chunks=None)

Split the ensemble into an array of smaller ensembles.

Parameters:

chunks (iterable of tuples) – Block sizes along each dimension.

Return type:

Array

property ensemble_dims

Number of ensemble dimensions.

property ensemble_shape: tuple[int, ...]

Shape of the ensemble axes of the underlying array.

ensure_lazy(chunks='auto')

Creates an equivalent lazy version of the array object.

Parameters:

chunks (int or tuple or str) – How to chunk the array. See dask.array.from_array.

Returns:

lazy_array_object – Lazy version of the array object.

Return type:

ArrayObject or subclass of ArrayObject

property exit_planes: tuple[int, ...]

The “exit planes” of the potential. The indices of slices where a measurement is returned.

property exit_thicknesses: tuple[float]

The “exit thicknesses” of the potential. The thicknesses in the potential where a measurement is returned.

expand_dims(axis=None, axis_metadata=None)

Expand the shape of the array object.

Parameters:

• axis (int or tuple of ints) – Position in the expanded axes where the new axis (or axes) is placed.

• axis_metadata (AxisMetadata or List of AxisMetadata, optional) – The axis metadata describing the expanded axes. Default is UnknownAxis.

Returns:

expanded – View of array object with the number of dimensions increased.

Return type:

ArrayObject or subclass of ArrayObject

property extent: tuple[float] | tuple[float, float] | tuple[float, ...]

Extent of grid for each dimension in Ångstrom.

classmethod from_array_and_metadata(array, axes_metadata, metadata)

Creates array object from a given array and metadata.

Parameters:

• array (array) – Complex array defining one or more 2D wave functions. The second-to-last and last dimensions are the wave function y- and x-axis, respectively.

• axes_metadata (list of AxesMetadata) – Axis metadata for each axis. The axis metadata must be compatible with the shape of the array. The last two axes must be RealSpaceAxis.

• metadata (dict) – A dictionary defining wave function metadata. All items will be added to the metadata of measurements derived from the waves. The metadata must contain the electron energy [eV].

Returns:

wave_functions – The created wave functions.

Return type:

Waves

classmethod from_zarr(url, chunks='auto')

Read wave functions from a hdf5 file.

Return type:

TypeVar(T, bound= ArrayObject)

urlstr

Location of the data, typically a path to a local file. A URL can also include a protocol specifier like s3:// for remote data.

chunkstuple of ints or tuples of ints

Passed to dask.array.from_array(), allows setting the chunks on initialisation, if the chunking scheme in the on-disc dataset is not optimal for the calculations to follow.

generate_blocks(chunks=1)

Generate chunks of the ensemble.

Parameters:

chunks (iterable of tuples) – Block sizes along each dimension.

generate_ensemble(keepdims=False)

Generate every member of the ensemble.

Parameters:

keepdims (bool, opptional) – If True, all ensemble axes are left in the result as dimensions with size one. Default is False.

Yields:

ArrayObject or subclass of ArrayObject – Member of the ensemble.

generate_slices(first_slice=0, last_slice=None)

Generate the slices for the potential.

Parameters:

• first_slice (int, optional) – Index of the first slice of the generated potential.

• last_slice (int, optional) – Index of the last slice of the generated potential.

Yields:

slices (generator of np.ndarray) – Generator for the array of slices.

get_items(items, keepdims=False)

Index the array and the corresponding axes metadata. Only ensemble axes can be indexed.

Parameters:

• items (int or tuple of int or slice) – The array is indexed according to this.

• keepdims (bool, optional) – If True, all ensemble axes are left in the result as dimensions with size one. Default is False.

Returns:

indexed_array – The indexed array object.

Return type:

ArrayObject or subclass of ArrayObject

property gpts: tuple[int] | tuple[int, int] | tuple[int, ...]

Number of grid points for each dimension.

property grid: Grid

Simulation grid.

property is_complex: bool

True if array is complex.

property is_lazy: bool

True if array is lazy.

match_grid(other, check_match=False)

Match the grid to another object with a Grid.

max(axis=None, keepdims=False, split_every=2)

Maximum of array object over one or more axes. Only ensemble axes can be reduced.

Parameters:

• axis (int or tuple of ints, optional) – Axis or axes along which a maxima are calculated. The default is to compute the mean of the flattened array. If this is a tuple of ints, the maxima are calculated over multiple axes. The indicated axes must be ensemble axes.

• keepdims (bool, optional) – If True, the reduced axes are left in the result as dimensions with size one. Default is False.

• split_every (int) – Only used for lazy arrays. See dask.array.reductions.

Returns:

reduced_array – The reduced array object.

Return type:

ArrayObject or subclass of ArrayObject

mean(axis=None, keepdims=False, split_every=2)

Mean of array object over one or more axes. Only ensemble axes can be reduced.

Parameters:

• axis (int or tuple of ints, optional) – Axis or axes along which a means are calculated. The default is to compute the mean of the flattened array. If this is a tuple of ints, the mean is calculated over multiple axes. The indicated axes must be ensemble axes.

• keepdims (bool, optional) – If True, the reduced axes are left in the result as dimensions with size one. Default is False.

• split_every (int) – Only used for lazy arrays. See dask.array.reductions.

Returns:

reduced_array – The reduced array object.

Return type:

ArrayObject or subclass of ArrayObject

property metadata

Metadata stored as a dictionary.

min(axis=None, keepdims=False, split_every=2)

Minmimum of array object over one or more axes. Only ensemble axes can be reduced.

Parameters:

• axis (int or tuple of ints, optional) – Axis or axes along which a minima are calculated. The default is to compute the mean of the flattened array. If this is a tuple of ints, the minima are calculated over multiple axes. The indicated axes must be ensemble axes.

• keepdims (bool, optional) – If True, the reduced axes are left in the result as dimensions with size one. Default is False.

• split_every (int) – Only used for lazy arrays. See dask.array.reductions.

Returns:

reduced_array – The reduced array object.

Return type:

ArrayObject or subclass of ArrayObject

no_base_chunks()

Rechunk to remove chunks across the base dimensions.

property num_configurations

Number of frozen phonons in the ensemble of potentials.

property num_exit_planes: int

Number of exit planes.

property num_slices: int

Number of projected potential slices.

project()

Create a 2D array representing a projected image of the potential(s).

Returns:

images – One or more images of the projected potential(s).

Return type:

Images

rechunk(chunks, **kwargs)

Rechunk dask array.

chunksint or tuple or str

How to rechunk the array. See dask.array.rechunk.

kwargs :

Additional keyword arguments passes to dask.array.rechunk.

property reciprocal_space_sampling: tuple[float] | tuple[float, float] | tuple[float, ...]

Reciprocal-space sampling in reciprocal Ångstrom.

property sampling: tuple[float] | tuple[float, float] | tuple[float, ...]

Grid sampling for each dimension in Ångstrom per grid point.

select_block(index, chunks)

Select a block from the ensemble.

Parameters:

• index (tuple of ints) – Index of selected block.

• chunks (iterable of tuples) – Block sizes along each dimension.

set_ensemble_axes_metadata(axes_metadata, axis)

Sets the axes metadata of an ensemble axis.

Parameters:

• axes_metadata (AxisMetadata) – The new axis metadata.

• axis (int) – The axis to set.

property shape: tuple[int, ...]

Shape of the underlying array.

show(project=True, **kwargs)

Show the potential projection. This requires building all potential slices.

Parameters:

• project (bool, optional) – Show the projected potential (True, default) or show all potential slices. It is recommended to index a subset of the potential slices when this keyword set to False.

• kwargs – Additional keyword arguments for the show method of Images.

property slice_limits: list[tuple[float, float]]

The entrance and exit thicknesses of each slice [Å].

property slice_thickness: tuple[float, ...]

Slice thicknesses for each slice.

squeeze(axis=None)

Remove axes of length one from array object.

Parameters:

axis (int or tuple of ints, optional) – Selects a subset of the entries of length one in the shape.

Returns:

squeezed – The input array object, but with all or a subset of the dimensions of length 1 removed.

Return type:

ArrayObject or subclass of ArrayObject

std(axis=None, keepdims=False, split_every=2)

Standard deviation of array object over one or more axes. Only ensemble axes can be reduced.

Parameters:

• axis (int or tuple of ints, optional) – Axis or axes along which a standard deviations are calculated. The default is to compute the mean of the flattened array. If this is a tuple of ints, the standard deviations are calculated over multiple axes. The indicated axes must be ensemble axes.

• keepdims (bool, optional) – If True, the reduced axes are left in the result as dimensions with size one. Default is False.

• split_every (int) – Only used for lazy arrays. See dask.array.reductions.

Returns:

reduced_array – The reduced array object.

Return type:

ArrayObject or subclass of ArrayObject

sum(axis=None, keepdims=False, split_every=2)

Sum of array object over one or more axes. Only ensemble axes can be reduced.

Parameters:

• axis (int or tuple of ints, optional) – Axis or axes along which a sums are performed. The default is to compute the mean of the flattened array. If this is a tuple of ints, the sum is performed over multiple axes. The indicated axes must be ensemble axes.

• keepdims (bool, optional) – If True, the reduced axes are left in the result as dimensions with size one. Default is False.

• split_every (int) – Only used for lazy arrays. See dask.array.reductions.

Returns:

reduced_array – The reduced array object.

Return type:

ArrayObject or subclass of ArrayObject

property thickness: float

Thickness of the potential [Å].

tile(repetitions)

Tile the potential.

Parameters:

repetitions (two or three int) – The number of repetitions of the potential along each axis. NOTE: if three integers are given, the first represents the number of repetitions along the z-axis.

Returns:

The tiled potential.

Return type:

PotentialArray object

to_cpu()

Move the array to the host memory from an arbitrary source array.

Return type:

TypeVar(T, bound= ArrayObject)

to_data_array()

Convert ArrayObject to a xarray DataArray.

to_gpu(device='gpu')

Move the array from the host memory to a gpu.

Return type:

TypeVar(T, bound= ArrayObject)

to_hyperspy()

Convert ArrayObject to a Hyperspy signal.

to_images()

Convert slices of the potential to a stack of images.

to_tiff(filename, **kwargs)

Write data to a tiff file.

Parameters:

• filename (str) – The filename of the file to write.

• kwargs – Keyword arguments passed to tifffile.imwrite.

to_zarr(url, compute=True, overwrite=False, **kwargs)

Write data to a zarr file.

Parameters:

• url (str) – Location of the data, typically a path to a local file. A URL can also include a protocol specifier like s3:// for remote data.

• compute (bool) – If true compute immediately; return dask.delayed.Delayed otherwise.

• overwrite (bool) – If given array already exists, overwrite=False will cause an error, where overwrite=True will replace the existing data.

• kwargs – Keyword arguments passed to dask.array.to_zarr.

transmission_function(energy)

Calculate the transmission functions for each slice for a specific energy.

Parameters:

energy (float) – Electron energy [eV].

Returns:

transmissionfunction – Transmission functions for each slice.

Return type:

TransmissionFunction

transmit(waves, conjugate=False)

Transmit a wave function through a potential slice.

Parameters:

• waves (Waves) – Waves object to transmit.

• conjugate (bool, optional) – If True, use the conjugate of the transmission function. Default is False.

Returns:

transmission_function – Transmission function for the wave function through the potential slice.

Return type:

TransmissionFunction