IndexedDiffractionPatterns

class abtem.measurements.IndexedDiffractionPatterns(array, miller_indices, reciprocal_lattice_vectors, ensemble_axes_metadata=None, metadata=None)

Bases: BaseMeasurements

Diffraction patterns indexed by their Miller indices.

Parameters:

• array (np.ndarray) – 1D or greater array of type float or complex. The last axis represents the diffraction spots and should have the same length as the number of miller indices, any preceding axis represents an ensemble axis.

• miller_indices (np.ndarray) – The miller indices of the diffraction spots as an N x 3 array where N is the number of miller indices. The order of the miller indices must correspond to the array of intensities. The second axis represents each hkl miller index.

• reciprocal_lattice_vectors (np.ndarray) – The reciprocal lattice vectors of the crystal as a 3 x 3 array. The first axis represents miller indices and the order of the items must correspond to the array of intensities. The second axis represents the reciprocal space positions in x, y and z [1/Å].

• ensemble_axes_metadata (list of AxisMetadata, optional) – List of metadata associated with the ensemble axes. The length and item order must match the ensemble axes.

• metadata (dict, optional) – A dictionary defining measurement metadata.

__init__(array, miller_indices, reciprocal_lattice_vectors, ensemble_axes_metadata=None, metadata=None)

Methods

__init__(array, miller_indices, ...[, ...])
abs()	Calculates the absolute value of a complex-valued measurement.
apply_func(func, **kwargs)	rtype: TypeVar(T, bound= ArrayObject)
apply_transform(transform[, max_batch])	Transform the wave functions by a given transformation.
block_direct()	Remove the zero-order spot.
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.
crop([max_angle, k_max])	Crop the indexed diffraction patterns such that they only include spots with spatial frequencies (scattering angles) up to a given limit.
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.
get_from_metadata(name[, broadcastable])
get_items(items[, keepdims])	Index the array and the corresponding axes metadata.
imag()	Returns the imaginary part of a complex-valued measurement.
intensity()	Calculates the squared norm of a complex-valued measurement.
lazy([chunks])	rtype: TypeVar(T, bound= ArrayObject)
max([axis, keepdims, split_every])	Maximum of array object over one or more axes.
max_reciprocal_space_vector_length()
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.
normalize_ensemble([scale, shift])	Normalize the ensemble by shifting ad scaling each member.
normalize_to_spot([spot])	Normalize the intensity of the diffraction spots.
phase()	Calculates the phase of a complex-valued measurement.
poisson_noise([dose_per_area, total_dose, ...])	Add Poisson noise (i.e. shot noise) to a measurement corresponding to the provided 'total_dose' (per measurement if applied to an ensemble) or 'dose_per_area' (not applicable for single measurements).
real()	Returns the real part of a complex-valued measurement.
rechunk(chunks, **kwargs)	Rechunk dask array.
reduce_ensemble()	Calculates the mean of an ensemble measurement (e.g. of frozen phonon configurations).
relative_difference(other[, min_relative_tol])	Calculates the relative difference with respect to another compatible measurement.
remove_low_intensity([threshold])	Remove diffraction spots with intensity below a threshold for all ensemble dimensions.
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([ax, cbar, cmap, vmin, vmax, power, ...])	Show the diffraction spots as an EllipseCollection using matplotlib.
sort([criterion])	Sort the diffraction spots according to a given criterion.
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.
to_cpu()	Move the array to the host memory from an arbitrary source array.
to_data_array()	Convert the indexed diffraction patterns to xarray DataArray.
to_dataframe()	Convert the indexed diffraction patterns to pandas DataFrame.
to_gpu([device])	Move the array from the host memory to a gpu.
to_hyperspy()	Convert ArrayObject to a Hyperspy signal.
to_measurement_ensemble()
to_tiff(filename, **kwargs)	Write data to a tiff file.
to_zarr(url[, compute, overwrite])	Write data to a zarr file.

Attributes

all_positions	Reciprocal space positions of the diffraction spots.
angular_positions	Scattering angles of the diffraction spots.
array	Underlying array describing the array object.
axes_metadata	List of AxisMetadata.
base_axes_metadata	List of AxisMetadata of the base axes.
base_dims	Number of base dimensions.
base_shape	Shape of the base axes of the underlying array.
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.
intensities	Intensities of the diffraction spots.
intensities_dict	A dictionary mapping miller indices to intensities.
is_complex	True if array is complex.
is_lazy	True if array is lazy.
metadata	Metadata describing the measurement.
miller_indices	Miller indices of the diffraction spots.
positions	Reciprocal space positions of the diffraction spots.
positions_dict	A dictionary mapping miller indices to reciprocal space positions [1/Å].
reciprocal_lattice_vectors	Reciprocal lattice vectors of the diffraction spots.
shape	Shape of the underlying array.

abs()

Calculates the absolute value of a complex-valued measurement.

Return type:

TypeVar(T, bound= BaseMeasurements)

property all_positions: ndarray

Reciprocal space positions of the diffraction spots.

property angular_positions

Scattering angles of the diffraction spots.

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

List of AxisMetadata of the base axes.

property base_dims

Number of base dimensions.

property base_shape: tuple[int, ...]

Shape of the base axes of the underlying array.

block_direct()

Remove the zero-order spot.

Returns:

blocked – The indexed diffraction spots without the zero-order spot.

Return type:

IndexedDiffractionPatterns

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

crop(max_angle=None, k_max=None)

Crop the indexed diffraction patterns such that they only include spots with spatial frequencies (scattering angles) up to a given limit.

Parameters:

• max_angle (float, optional) – The maximum included scattering angle in the cropped diffraction patterns.

• k_max (float, optional) – The maximum included reciprocal lattice vector in the cropped diffraction spots.

Returns:

cropped

Return type:

IndexedDiffractionPatterns

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

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

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

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.

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

imag()

Returns the imaginary part of a complex-valued measurement.

Return type:

TypeVar(T, bound= BaseMeasurements)

property intensities: ndarray

Intensities of the diffraction spots.

property intensities_dict: Dict[tuple[int, int, int], ndarray]

A dictionary mapping miller indices to intensities.

intensity()

Calculates the squared norm of a complex-valued measurement.

Return type:

TypeVar(T, bound= BaseMeasurements)

property is_complex: bool

True if array is complex.

property is_lazy: bool

True if array is lazy.

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: dict

Metadata describing the measurement.

property miller_indices: ndarray

Miller indices of the diffraction spots.

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.

normalize_ensemble(scale='max', shift='mean')

Normalize the ensemble by shifting ad scaling each member.

Parameters:

• scale ({'max', 'min', 'sum', 'mean', 'ptp'})

• shift ({'max', 'min', 'sum', 'mean', 'ptp'})

Returns:

normalized_measurements

Return type:

BaseMeasurements or subclass of _BaseMeasurement

normalize_to_spot(spot=None)

Normalize the intensity of the diffraction spots.

Parameters:

spot (tuple of three int) – The intensities will be normalized with respect to the intensity of this spot. Defaults to the most intense spot.

Returns:

normalized_indexed_diffraction_patterns

Return type:

IndexedDiffractionPatterns

phase()

Calculates the phase of a complex-valued measurement.

Return type:

TypeVar(T, bound= BaseMeasurements)

poisson_noise(dose_per_area=None, total_dose=None, samples=1, seed=None)

Add Poisson noise (i.e. shot noise) to a measurement corresponding to the provided ‘total_dose’ (per measurement if applied to an ensemble) or ‘dose_per_area’ (not applicable for single measurements).

Parameters:

• dose_per_area (float, optional) – The irradiation dose [electrons per Å:sup:2].

• total_dose (float, optional) – The irradiation dose per diffraction pattern.

• samples (int, optional) – The number of samples to draw from a Poisson distribution. If this is greater than 1, an additional ensemble axis will be added to the measurement.

• seed (int, optional) – Seed the random number generator.

Returns:

noisy_measurement – The noisy measurement.

Return type:

BaseMeasurements or subclass of _BaseMeasurement

property positions: ndarray

Reciprocal space positions of the diffraction spots.

property positions_dict: Dict[tuple[int, int, int], ndarray]

A dictionary mapping miller indices to reciprocal space positions [1/Å].

real()

Returns the real part of a complex-valued measurement.

Return type:

TypeVar(T, bound= BaseMeasurements)

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_lattice_vectors: ndarray

Reciprocal lattice vectors of the diffraction spots.

reduce_ensemble()

Calculates the mean of an ensemble measurement (e.g. of frozen phonon configurations).

Return type:

TypeVar(T, bound= BaseMeasurements)

relative_difference(other, min_relative_tol=0.0)

Calculates the relative difference with respect to another compatible measurement.

Parameters:

• other (BaseMeasurements) – Measurement to which the difference is calculated.

• min_relative_tol (float) – Avoids division by zero errors by defining a minimum value of the divisor in the relative difference.

Returns:

difference – The relative difference as a measurement of the same type.

Return type:

BaseMeasurements

remove_low_intensity(threshold=0.001)

Remove diffraction spots with intensity below a threshold for all ensemble dimensions.

Parameters:

threshold (float) – Intensity threshold for removing diffraction spots.

Returns:

thresholded_spots – The indexed diffraction spots with an intensity above the given threshold.

Return type:

IndexedDiffractionPatterns

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(ax=None, cbar=False, cmap=None, vmin=None, vmax=None, power=1.0, common_color_scale=False, scale=0.5, explode=(), overlay=(), figsize=None, title=True, units=None, interact=False, display=True, **kwargs)

Show the diffraction spots as an EllipseCollection using matplotlib.

Parameters:

• ax (matplotlib.axes.Axes, optional) – If given the plots are added to the axis. This is not available for exploded plots.

• cbar (bool, optional) – Add colorbar(s) to the image(s). The size and padding of the colorbars may be adjusted using the set_cbar_size and set_cbar_padding methods.

• cmap (str, optional) – Matplotlib colormap name used to map scalar data to colors. If the measurement is complex the colormap must be one of ‘hsv’ or ‘hsluv’.

• vmin (float, optional) – Minimum of the intensity color scale. Default is the minimum of the array values.

• vmax (float, optional) – Maximum of the intensity color scale. Default is the maximum of the array values.

• power (float) – Show diffraction spots intensities on a power scale.

• common_color_scale (bool, optional) – If True all images in an image grid are shown on the same colorscale, and a single colorbar is created (if it is requested). Default is False.

• scale (float, optional) – Scale the radii of the circles representing the diffraction spots.

• explode (bool or sequence of bool, optional) – If True, a grid of plots is created for all the items of the last two ensemble axes. If False, the first ensemble item is shown. May be given as a sequence of axis indices to create a grid of plots from the specified axes. The default is determined by the axis metadata.

• figsize (two int, optional) – The figure size given as width and height in inches, passed to matplotlib.pyplot.figure.

• title (bool or str, optional) – Set the column title of the plots. If True is given instead of a string the title will be given by the value corresponding to the “name” key of the axes metadata dictionary, if this item exists.

• units (str) – The units used for the x and y axes. The given units must be compatible with the axes of the plots.

• interact (bool) – If True, create an interactive visualization. This requires enabling the ipympl Matplotlib backend.

• display (bool, optional) – If True (default) the figure is displayed immediately.

Returns:

visualization

Return type:

Visualization

sort(criterion='distance')

Sort the diffraction spots according to a given criterion.

Parameters:

criterion ({'distance', 'intensity'}) –

The boundary parameter determines how the images are extended beyond their boundaries when the filter overlaps with a border.

distance :

Sort according to the distance in reciprocal space from the zero frequency.

intensity :

Sort according to the intensity of the diffraction spots.

Returns:

sorted_spots

Return type:

IndexedDiffractionPatterns

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

to_cpu()

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

Return type:

TypeVar(T, bound= ArrayObject)

to_data_array()

Convert the indexed diffraction patterns to xarray DataArray.

Returns:

data_array_of_indexed_spots

Return type:

xarray.DataArray

to_dataframe()

Convert the indexed diffraction patterns to pandas DataFrame.

Returns:

data_frame

Return type:

pd.DataFrame

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_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.