ReciprocalSpaceLineProfiles

class abtem.measurements.ReciprocalSpaceLineProfiles(array, sampling=None, ensemble_axes_metadata=None, metadata=None)

Bases: _BaseMeasurement1D

A collection of reciprocal-space line profile(s).

Parameters:

• array (np.ndarray) – 1D or greater array containing data of type float or complex.

• sampling (float) – Sampling of line profiles [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, sampling=None, ensemble_axes_metadata=None, metadata=None)

Methods

__init__(array[, sampling, ...])
abs()	Calculates the absolute value of a complex-valued measurement.
apply_func(func, **kwargs)	Apply a function to the array object.
apply_transform(transform[, max_batch])	Transform the wave functions by a given transformation.
compute([progress_bar, profiler, ...])	Turn a lazy *ab*TEM 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, axes_metadata)	Creates line profile(s) 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.
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.
interpolate([sampling, gpts, order, endpoint])	Interpolate line profile(s) producing equivalent line profile(s) with a different sampling.
lazy([chunks])
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.
normalize_ensemble([scale, shift])	Normalize the ensemble by shifting ad scaling each member.
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.
set_ensemble_axes_metadata(axes_metadata, axis)	Sets the axes metadata of an ensemble axis.
show([ax, common_scale, explode, overlay, ...])	Show the reciprocal-space line profile(s) using matplotlib.
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 ArrayObject to a xarray DataArray.
to_gpu([device])	Move the array from the host memory to a gpu.
to_hyperspy([transpose])	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.
width([height])	Calculate the width of line(s) at a given height, e.g. full width at half maximum (the default).

Attributes

angular_extent	Extent of line profiles given as scattering angels [mrad].
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.
extent	Extent of measurements [Å] or [1/Å].
is_complex	True if array is complex.
is_lazy	True if array is lazy.
metadata	Metadata describing the measurement.
sampling	Extent of measurements [Å] or [1/Å].
shape	Shape of the underlying array.

abs()

Calculates the absolute value of a complex-valued measurement.

Return type:

Self

property angular_extent

Extent of line profiles given as scattering angels [mrad].

apply_func(func, **kwargs)

Apply a function to the array object. The function must take an array as its first argument, only the array is modified, the metadata is not changed. The function is applied lazily if the array object is lazy.

Parameters:

• func (callable) – Function to apply to the array object.

• kwargs – Additional keyword arguments passed to the function.

Returns:

array_object – The array object with the function applied.

Return type:

ArrayObject or subclass of ArrayObject

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:

ArrayObject

property array: ndarray | Array

Underlying array describing the array object.

property axes_metadata: AxesMetadataList

List of AxisMetadata.

property base_axes_metadata: list[AxisMetadata]

List of AxisMetadata of the base axes.

property base_dims: int

Number of base dimensions.

property base_shape: tuple[int, ...]

Shape of the base axes of the underlying array.

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

Turn a lazy *ab*TEM 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 scheduler is profiled.

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

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

Return type:

Union[Self, tuple[Self, tuple]]

copy()

Make a copy.

Return type:

Self

copy_to_device(device)

Copy array to specified device.

Parameters:

device (str)

Returns:

object_on_device

Return type:

ArrayObject

property device: str

The device where the array is stored.

property dtype: dtype

Datatype of array.

property ensemble_axes_metadata: list[AxisMetadata]

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: int

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

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: float

Extent of measurements [Å] or [1/Å].

classmethod from_array_and_metadata(array, axes_metadata, metadata=None)

Creates line profile(s) from a given array and metadata.

Parameters:

• array (array) – Complex array defining one or more 1D line profiles.

• 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, optional) – A dictionary defining the measurement metadata.

Returns:

line_profiles – Line profiles from the array and metadata.

Return type:

RealSpaceLineProfiles

classmethod from_zarr(url, chunks='auto')

Read wave functions from a hdf5 file.

Return type:

Self

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.

Return type:

Generator[tuple[tuple[int, ...], tuple[slice, ...], ndarray], None, None]

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:

Self

intensity()

Calculates the squared norm of a complex-valued measurement.

Return type:

Self

interpolate(sampling=None, gpts=None, order=3, endpoint=False)

Interpolate line profile(s) producing equivalent line profile(s) with a different sampling. Either ‘sampling’ or ‘gpts’ must be provided (but not both).

Parameters:

• sampling (float, optional) – Sampling of line profiles after interpolation [Å].

• gpts (int, optional) – Number of grid points of line profiles after interpolation. Do not use if ‘sampling’ is used.

• order (int, optional) – The order of the spline interpolation (default is 3). The order has to be in the range 0-5.

• endpoint (bool, optional) – If True, end is the last position. Otherwise, it is not included. Default is False.

Returns:

interpolated_profiles – The interpolated line profile(s).

Return type:

RealSpaceLineProfiles

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.

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

phase()

Calculates the phase of a complex-valued measurement.

Return type:

Self

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, sequence of float, optional) – The irradiation dose [electrons per Å:sup:2]. May be given as a single value or as a sequence of values for each ensemble member.

• 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

real()

Returns the real part of a complex-valued measurement.

Return type:

Self

rechunk(chunks, **kwargs)

Rechunk dask array.

Return type:

ArrayObject

chunksint or tuple or str

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

kwargs :

Additional keyword arguments passes to dask.array.rechunk.

reduce_ensemble()

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

Return type:

Self

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

property sampling: float

Extent of measurements [Å] or [1/Å].

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.

Return type:

Self

property shape: tuple[int, ...]

Shape of the underlying array.

show(ax=None, common_scale=True, explode=False, overlay=None, figsize=None, title=True, units=None, legend=False, interact=False, display=True, **kwargs)

Show the reciprocal-space line profile(s) using matplotlib.

Parameters:

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

• common_scale (bool) – If True all plots are shown with a common y-axis. Default is False.

• 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, only the one plot is created. 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.

• overlay (bool or sequence of int, optional) – If True, all line profiles in the ensemble are shown in a single plot. If False, only the first ensemble item is shown. May be given as a sequence of axis indices to specify which line profiles in the ensemble to show together. 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.

• legend (bool) – Add a legend to the plot. The labels will be derived from

• units (str, optional) – The units used for the x-axis. The given units must be compatible.

• 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

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:

Self

to_data_array()

Convert ArrayObject to a xarray DataArray. Requires xarray to be installed.

Returns:

The converted xarray DataArray.

Return type:

xarray.DataArray

Raises:

ImportError – If xarray is not installed.

to_gpu(device='gpu')

Move the array from the host memory to a gpu.

Return type:

Self

to_hyperspy(transpose=True)

Convert ArrayObject to a Hyperspy signal.

Parameters:

transpose (bool, optional) – If True, transpose the base axes of the array before converting to a Hyperspy signal. Default is True.

Returns:

signal – The converted Hyperspy signal.

Return type:

Hyperspy signal

Raises:

• ImportError – If Hyperspy is not installed.

• RuntimeError – If the number of base dimensions is not 1 or 2.

Notes

This method requires Hyperspy to be installed. You can find more information about Hyperspy at https://hyperspy.org.

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.

width(height=0.5)

Calculate the width of line(s) at a given height, e.g. full width at half maximum (the default).

Parameters:

height (float) – Fractional height at which the width is calculated.

Returns:

width – The calculated width.

Return type:

float