.gitignore

+!.gitignore
+!.gitlab-ci.yml
+.*
+desktop.ini
+*.pyc
+*.egg-info
+*.DS_Store
+*.DS
+*.ipynb_checkpoints*
+build/*
+docs/_build/*
+dist/*
+src/empyre/version.py
+htmlcov/
+coverage.xml

.gitlab-ci.yml

+workflow:
+  rules:
+    - if: $CI_PIPELINE_SOURCE == "merge_request_event"
+    - if: $CI_COMMIT_BRANCH && $CI_OPEN_MERGE_REQUESTS
+      when: never
+    - if: $CI_COMMIT_BRANCH
+    - if: $CI_COMMIT_TAG
+
+before_script:
+    # Install requirements for empyre:
+    - source ${CONDA_DIR}/etc/profile.d/conda.sh
+    - conda create -q --name empyre # -q: quiet/ no progressbar, because it spams the log!
+    - conda activate empyre
+    - conda install -y python numpy sphinx pip setuptools jupyter pandoc uv
+    - uv pip install .[tests,docs]
+    - conda info --envs
+    # Install jutil via deploy token access:  # TODO: still needed?
+    #- pip install git+https://empyre:"$JUTIL_DEPLOY_TOKEN"@jugit.fz-juelich.de/j.ungermann/jutil.git
+
+stages:
+    - test
+    - deploy
+
+test_style:
+    stage: test
+    image: condaforge/miniforge3:latest
+    script:
+        - pip install pre-commit
+        - pre-commit install
+        - pre-commit run --all-files
+
+test_function:
+    stage: test
+    image: condaforge/miniforge3:latest
+    script:
+        # Execute all tests and also check coverage with --cov:
+        - pip install "numpy>=2"
+        - pytest --cov
+    artifacts:
+        paths:
+            - .coverage
+        expire_in: 1 week
+
+test_docs:
+    stage: test
+    image: condaforge/miniforge3:latest
+    script:
+        # -f: Force overwriting of any existing generated files.
+        # -e: Put documentation for each module on its own page.
+        # -o: Directory to place the output files. If it does not exist, it is created.
+        # last parameter: module path
+        # - python setup.py  clean  # TODO: Simplest way to generate version.py without doing anything else?
+        #- sphinx-apidoc -f -e -o docs/api src/empyre
+        # Build the documentation from 'docs' and put into 'build/sphinx':
+        - sphinx-build docs build/sphinx -W  # -w fails the build if warnings appear!
+    artifacts:
+        paths:
+            - build/sphinx
+        expire_in: 1 week
+
+test_install:
+    stage: test
+    image: condaforge/miniforge3:latest
+    before_script: []  # before_script not needed here!
+    script:
+        - conda install -y "python<3.12"
+        - pip install .[all]
+
+pages:
+    stage: deploy
+    image: busybox
+    before_script: []  # before_script not needed here!
+    script:
+        - mkdir public
+        - cp -r build/sphinx/* public/
+        # -r: recursive, also copies subfolders!
+    artifacts:
+        paths:
+            - public
+    rules:
+        - if:  '$CI_COMMIT_BRANCH == "master" || $CI_COMMIT_TAG =~ /^\d+\.\d+(\.\d+)?$/'
+
+pypi:
+    stage: deploy
+    image: condaforge/miniforge3:latest
+    before_script: []  # before_script not needed here!
+    script:
+        - pip install hatch twine
+        - hatch build
+        - twine upload -u __token__ -p $PYPI_ACCESS_TOKEN dist/*  # -u user -p password upload_source
+    rules:  # similar to only/except, but newer!
+        # Job is executed if branch is master AND if a tag is building which matches the regular expression!
+        # ONLY executes if commit to master has a tag, ^:start, $:end, valid example: "1.2.3", no "-dev" at the end!
+        - if: '$CI_COMMIT_TAG =~ /^\d+\.\d+(\.\d+)?$/'

.gitlab/issue_templates/bug.md

+<!--
+Please read this!
+
+Before opening a new issue, make sure to search for keywords in the issues
+filtered by the "bug" label:
+- https://iffgit.fz-juelich.de/empyre/empyre/issues?label_name%5B%5D=bug
+
+and verify the issue you're about to submit isn't a duplicate.
+-->
+
+### Summary
+
+<!-- Summarize the bug encountered concisely. -->
+
+### Steps to reproduce
+
+<!-- How one can reproduce the issue - this is very important. -->
+
+### What is the current *bug* behavior?
+
+<!-- What actually happens. -->
+
+### What is the expected *correct* behavior?
+
+<!-- What you should see instead. -->
+
+### Relevant logs and/or screenshots
+
+<!-- Paste any relevant logs - please use code blocks (```) to format console output,
+logs, and code as it's tough to read otherwise.. -->
+
+### Possible fixes
+
+<!-- If you can, link to the line of code that might be responsible for the problem. -->
+
+~bug

.gitlab/issue_templates/feature request.md

+### Problem to solve
+
+<!-- What problem do we solve? -->
+
+### Intended users
+
+<!-- Who will use this feature? . It's okay to write "Unknown" and fill this field in later. -->
+
+### Further details
+
+<!-- Include use cases, benefits, and/or goals -->
+
+### Proposal
+
+<!-- How are we going to solve the problem? -->
+
+### Documentation
+
+<!-- Add all known Documentation Requirements here. -->
+
+~feature
\ No newline at end of file

.hgignore

-syntax: glob
-*~
-.spyderworkspace
-.spyderproject
-.cproject
-*.pyc
-*.pyd
-*.so
-*.os
-output*
-build*
\ No newline at end of file

.pre-commit-config.yaml

+# See https://pre-commit.com for more information
+# See https://pre-commit.com/hooks.html for more hooks
+repos:
+- repo: https://github.com/pre-commit/pre-commit-hooks
+  rev: v4.6.0
+  hooks:
+  - id: trailing-whitespace
+    files: ^src/
+  - id: end-of-file-fixer
+    files: ^src/
+  - id: check-yaml
+  - id: check-added-large-files
+- repo: https://github.com/pycqa/flake8
+  rev: 7.0.0
+  hooks:
+  - id: flake8
+    exclude: ^prototypes/
+- repo: https://github.com/regebro/pyroma
+  rev: "4.2"
+  hooks:
+  - id: pyroma
\ No newline at end of file

MANIFEST.in

+include src/empyre/vis/mplstyles/*.mplstyle
+graft tests

README.rst

+|pipeline|_ |coverage|_ |pypi|_
+
+.. |pipeline| image:: https://iffgit.fz-juelich.de/empyre/empyre/badges/master/pipeline.svg
+.. _pipeline: https://iffgit.fz-juelich.de/empyre/empyre/commits/master
+
+.. |coverage| image:: https://iffgit.fz-juelich.de/empyre/empyre/badges/master/coverage.svg
+.. _coverage: https://iffgit.fz-juelich.de/empyre/empyre
+
+.. |pypi| image:: https://badge.fury.io/py/empyre.svg
+.. _pypi: https://pypi.org/project/empyre/
+
+
+EMPyRe is an open source framework for constructing and solving hyperdimensional inverse problems and visualizing the corresponding input and output data. it has
+its roots in the reconstruction of three-dimensional magnetization distributions from magnetic phase images generated by electron holography but is meant to be
+extendable for many other problems that are based on forward models that are expressable as a combination of linear subproblems. EMPyRe is purely Python
+package, so all platforms should be supported.
+
+
+Installation
+------------
+
+EMPyRe is available on the `Python Package Index <http://pypi.python.org/pypi>`_ and can be simply be installed via `pip <http://pypi.python.org/pypi/pip>`_:
+
+.. code-block:: bash
+
+    $ pip install empyre
+
+Per default, only the strictly required libraries are installed, but there are a few additional dependencies that will unlock additional capabilites of EMPYRE.
+
+* ``io`` will install the `tvtk <http://docs.enthought.com/mayavi/tvtk/README.html>`_  & `HyperSpy <https://hyperspy.org/>`_ packages that are used for loading and saving additional file formats.
+
+    .. warning::
+        Due to this `issue <https://github.com/hyperspy/hyperspy/issues/2315>`_, a pip install of hyperspy is currently not possible. Please use
+        `conda <https://docs.conda.io/en/latest/>`_ to install HyperSpy, instead.
+
+
+* ``fftw`` will install `PyFFTW <https://github.com/pyFFTW/pyFFTW>`_ to speed up Fourier transforms used in some forward models.
+
+* ``colors`` will install the `cmocean <https://matplotlib.org/cmocean/>`_, whose ``balance`` color map is used as a default for the ``imshow`` commmand, if available.
+
+* ``3d`` will install the `mayavi <https://docs.enthought.com/mayavi/mayavi/>`_ package for 3D plotting capabilities.
+
+* ``tests`` will install all dependencies that are needed to test the package (usually not necessary for the average user).
+
+* ``all`` will install all of the dependencies listed above.
+
+
+You can choose these settings by using, *e.g.*:
+
+.. code-block:: bash
+
+    $ pip install empyre[all]
+
+
+Structure
+---------
+
+EMPyRe has several dedicated modules which are fully documented `here <https://empyre.iffgit.fz-juelich.de/empyre/>`_!
+
+* The ``fields`` module provides the ``Field`` container class for multidimensional scalar or vector fields and is the fundamental data structure used in EMPyRe.
+
+* The ``vis`` module enables the plotting of ``Field`` objects, based on and similar in syntax to the commonly known `matplotlib <https://matplotlib.org/>`_ framework.
+
+* The ``models`` module provides tools for constructing forward models that describe processes in Electron Microscopy.
+
+* The ``reconstruct`` module is a collection of tools for solving the inverse problems corresponding to the constructed forward models and diagnostic tools for their assessment.
+
+* The ``io`` module is used to load and save ``Field`` objects and the models generated by the ``models`` subpackage.
+
+* The ``utils`` module, which houses utility functionality used throughout EMPyRe.
+
+
+
+License
+-------
+EMPyRe is licensed under `GPLv3 <https://iffgit.fz-juelich.de/empyre/empyre/-/blob/master/LICENSE>`_.

authors.json

+[
+    {
+        "displayname": "Jan Caron",
+        "authorname": "Caron, Jan",
+        "affiliation": "Jülich Research Centre, Ernst Ruska Centre (ER-C)",
+        "gitlab": "jan-car",
+        "contribution": "Design, implementation, documentation, testing, management, majority of the code",
+        "orcid": "0000-0002-0873-889X"
+    },
+    {
+        "displayname": "Jörn Ungermann",
+        "authorname": "Ungermann, Jörn",
+        "affiliation": "Jülich Research Centre, Institute of Energy and Climate Research - Stratosphere (IEK-7)",
+        "gitlab": "unger",
+        "contribution": "Discussions, structure, reconstruction code from jutil",
+        "orcid": "0000-0001-9095-8332"
+    },
+    {
+        "displayname": "Alexander Clausen",
+        "authorname": "Clausen, Alexander",
+        "affiliation": "Jülich Research Centre, Ernst Ruska Centre (ER-C)",
+        "gitlab": "clausen",
+        "contribution": "Discussions, structure, testing",
+        "orcid": "0000-0002-9555-7455"
+    },
+    {
+        "displayname": "Dieter Weber",
+        "authorname": "Weber, Dieter",
+        "affiliation": "Jülich Research Centre, Ernst Ruska Centre (ER-C)",
+        "gitlab": "weber",
+        "contribution": "Discussions, structure, testing",
+        "orcid": "0000-0001-6635-9567"
+    },
+    {
+        "displayname": "Teresa Weßels",
+        "authorname": "Weßels, Teresa",
+        "affiliation": "Jülich Research Centre, Ernst Ruska Centre (ER-C)",
+        "gitlab": "wessels",
+        "contribution": "Discussions, testing",
+        "orcid": "0000-0001-5526-639X"
+    },
+    {
+        "displayname": "Matthew Bryan",
+        "authorname": "Bryan, Matthew",
+        "affiliation": "CEA-Leti",
+        "gitlab": "bryan",
+        "orcid": "0000-0001-9134-384X",
+        "contribution": "Small bugfixes, CI and conda packaging"
+    }
+]

demos/demo1_first_steps.py

+# -*- coding: utf-8 -*-
+# flake8:noqa
+
+# %% [markdown]
+## Demo 1): First steps and the Field class
+# In this first demo notebook, you'll learn how to import the `empyre` package and how to utilize the `Field` class,
+# which can contain multidimensional vector and scalar fields and is core to many functions of `empyre`. If you haven't
+# already, please visit the [documentation](https://empyre.iffgit.fz-juelich.de/empyre/) to see how to install `empyre`.
+
+
+# %% [markdown]
+### Import:
+# First import `empyre`, we recommend to use the abbreviation `emp`. We'll numpy as well.
+# %%
+import empyre as emp
+import numpy as np
+
+
+# %% [markdown]
+### Represent your data with the 'Field' class
+# A `Field` object is a container for multi-dimensional vector or scalar fields, each Field has three parameters:
+#
+# * **data**: Your underlying data, *e.g.* as a numpy array.
+#
+# * **scale**: The axis scaling along each axis, given as a tuple. `scale` can be a given as a single number during
+# construction of the `Field` object, which assumes that the scale is the same for all axes.
+#
+# * **vector**: Determines if the field is a scalar field (`vector=False`, which is the default) or a vector field
+# (`vector=True`). Please note that, if `vector=True`, the last axis of `data` is interpreted as the dimension of the
+# vector components. The component dimension is the last one, so that the `Field` class can be indexed similarily to
+# numpy arrays. This way, indexing a field with just spatial indices (by dropping the trailing component dimension)
+# will work on scalar and vector fields at the same time. Most functions of `Field` are designed to work on both
+# vector and scalar fields, as well.
+#
+#
+# We'll start with a 2D scalar and a 2D vector field. You'll find the base `Field` class in the `fields` submodule.
+# Note that you can print fields to get a short summary about their parameters.
+# %%
+scalar_data = np.zeros((16, 16))
+scalar_field = emp.fields.Field(data=scalar_data, scale=1, vector=False)
+print(scalar_field)
+
+vector_data = np.zeros((16, 16, 3))
+vector_field = emp.fields.Field(data=vector_data, scale=1, vector=True)
+print(vector_field)
+
+
+# %% [markdown]
+### Create more interesting fields with `create_...` functions
+# The two fields created before are empty and not very interesting. The `fields` submodule has a few alternate
+# constructor functions to generate shapes and vector fields in particular.
+# Let's look at the `shapes` submodule first, whose documentation can be found
+# [here](https://empyre.iffgit.fz-juelich.de/empyre/fields.html#module-empyre.fields.shapes) (Note that all functions
+# can be directly accessed via `emp.fields.create_...`, no need to access `shapes` directly).
+# A simple example is the disc shape:
+# %%
+field_disc = emp.fields.create_shape_disc(dim=(32, 32), radius=10)
+print(field_disc)
+
+
+# %% [markdown]
+### Visualize fields with the 'vis' subpackage
+# The `vis` subpackage is used to visualize field objects. Its interface mirrors that of matplotlib and should be easy
+# to learn if you are familiar with the latter. You can find the documentation
+# [here](https://empyre.iffgit.fz-juelich.de/empyre/vis.html).
+# Usually, scalar fields can be visualised with the `imshow` function (additional *kwargs* will be forwarded to the
+# underlying matplotlib function, a behaviour shared by almost all 2D plot functions in `vis`):
+#
+# %%
+emp.vis.imshow(field_disc)
+
+
+
+# %% [markdown]
+### Some `vis` basics
+# The `vis` package has a lot of decorators that you can use to enhance your plots, you can find the documentation
+# [here](https://empyre.iffgit.fz-juelich.de/empyre/vis.html#module-empyre.vis.decorators).
+# To apply them to a plot, just use the commands in the lines following a plot command. To generate a new plot, use the
+# `vis.new()` function. If you are in a Jupyter notebook, like here, you don't need `new` at the beginning of each cell,
+# but `new` has some other neat features (like returning a grid of subplots) that could be useful for your specific
+# case. Furthermore, `empyre` uses custom matplotlib stylesheets for 'images' and 'plots', respectively, which you can
+# explicitely set in the `new` function with the `mode` parameter. For publications, `new` can specify the exact size
+# of your plots according to your LaTeX document and save them afterwards with the `savefig` function.
+# See [here](https://empyre.iffgit.fz-juelich.de/empyre/vis.html#empyre.vis.tools.new) for more info on all of those
+# features. `empyre` provides mainly plotting routines for images, but you can mix and match with matplotlib routines,
+# for plots.
+# %%
+emp.vis.new(mode='image')  # Not necessary here, just for clarity, 'image' is the default!
+emp.vis.imshow(field_disc)
+emp.vis.scalebar()
+# Create a new figure with two plots
+fig, axes = emp.vis.new(nrows=1, ncols=2, aspect=0.3, mode='plot')
+x = np.arange(10)
+axes[0].plot(x, np.random.rand(10))
+axes[1].plot(x, np.random.rand(10))
+
+# %% [markdown]
+### Creation of vector fields
+# The `fields` module can not only create shapes but also some special vector fields like homogeneous distributions
+# (all vectors point in the same direction) or vortices / skyrmions, all of which you can find
+# [here](https://empyre.iffgit.fz-juelich.de/empyre/fields.html#module-empyre.fields.vectors).
+# The according functions all start with `emp.vis.create_vector_...`.
+# `vis` also has special plotting functions for vector fields, often with directional color encoding, where the vectors
+# are colored according to:
+# * **hue**: encodes the in-plane direction of the vector.
+#
+# * **brightness**: encodes the out-of-plane component of the vector (light: up, dark: down)
+#
+# * **saturation**: encodes the amplitude of the vector with central gray corresponding to an amplitude of zero.
+#
+# One example for such a plot is the `colorvec` funtion. You can always add the colorwheel to your plots with the
+# `colorwheel` function, as well. Let's try all of this out with a vortex vector distribution with an out-of-plain core
+# with a radius of 3 pixels, pointing upwards.
+# %%
+field_vortex = emp.fields.create_vector_vortex(dim=(32, 32), core_r=3, oop_r=5)
+print(field_vortex)
+# And plot (colorwheel shows directional color encoding):
+emp.vis.colorvec(field_vortex)
+emp.vis.scalebar()
+emp.vis.colorwheel()
+
+
+# %% [markdown]
+### Quiver plot
+# Another way of plotting vector fields is provided by the `quiver` plot function (using the matplotlib function of the
+# same name under the hood). `quiver` automatically reduces the number of drawn arrows for clarities sake. Have a look
+# into the function documentation to learn more.
+# %%
+emp.vis.quiver(field_vortex)
+emp.vis.scalebar()
+emp.vis.colorwheel()
+
+
+# %% [markdown]
+### Combining vector and shapes
+# The `Field` class implements many basic math operators like `+`, `-` or `*`. The latter can be used to combine a
+# constructed vector field and a shape (that acts like a mask in this case). Furthermore, you can combine `colorvec` and
+# `quiver` plots to create appealing images.
+# %%
+field_comb = field_disc * field_vortex
+emp.vis.colorvec(field_comb)
+emp.vis.quiver(field_comb)
+emp.vis.scalebar()
+emp.vis.colorwheel()
+
+
+# %% [markdown]
+### Congratulations
+# You managed to create and plot your first 2D vector fields! Look at the functions docstrings or the documentation of
+# `empyre` to learn more or have a look at the next demos to find out how to handle 3D fields and more functionality of
+# the `Field` class.
\ No newline at end of file

demos/demo2_handling_3d_fields.py

+# -*- coding: utf-8 -*-
+# flake8:noqa
+
+# %% [markdown]
+## Demo 2): Handling 3-dimensional fields
+# In this demo, you'll learn the intricacies of how to handle and especially how to plot 3-dimensional fields, the
+# specific pitfalls during plotting and how to avoid them.
+
+
+# %% [markdown]
+### Import:
+# %%
+import empyre as emp
+import logging
+logger = logging.getLogger()
+logger.setLevel(logging.WARNING)
+
+
+# %% [markdown]
+### Create a 3D vortex
+# Similar to the first demo, we create a vortex distribution and the shape of a disc, which we'll combine to generate a
+# `Field` object (note that you can also use compound assignment operators like `*=`). This time, however, we generate
+# a 3D distribution by using a shape of `(32, 32, 32)` for the dimension.
+# %%
+field = emp.fields.create_vector_vortex(dim=(32, 32, 32), core_r=3, oop_r=5)
+field *= emp.fields.create_shape_disc(dim=(32, 32, 32), radius=10)
+
+
+# %% [markdown]
+### How to plot 3D distributions
+# If you try to use:
+#
+# `emp.vis.colorvec(field)`
+#
+# for plotting, you'll get an error, telling you that you can only plot 2 dimensions (which makes sense for all 2D
+# matplotlib plots). Instead of plotting the whole 3D volume, we can instead plot slices of it by using indices with
+# the usual numpy bracket notation on our `Field` objects. Let's try to plot a central slice along the z-direction.
+# Note that the `field_slice_z` object is only two-dimensional with shape `(32, 32)`!
+# %%
+field_slice_z = field[15, ...]
+emp.vis.colorvec(field_slice_z)
+print(field)
+print(field_slice_z)
+
+# %% [markdown]
+### Slices along other directions
+# Next, let's slice along the y-direction of the 3D volume (let's again take a central slice through the volume) and
+# compare the two slices. The dashed line in the left image shows, where the slice in the right image lies. You'll
+# notice that the color encoding in both images corresponds to the 3D directions of the vectors in our original 3D
+# volume. This is due to the fact that our 2D slice still has information about the 3 components of the vector field.
+# Furthermore, we'll use some more decoration functions of `vis`, which should be self explanatory.
+# %%
+fig, axes = emp.vis.new(1, 2)
+field_slice_y = field[:, 15, :]
+emp.vis.colorvec(field_slice_z, axis=axes[0])
+emp.vis.colorwheel(axis=axes[0])
+emp.vis.annotate('z-slice', axis=axes[0])
+emp.vis.coords(coords=('x', 'y'), axis=axes[0])
+axes[0].axhline(y=16, linestyle='--')
+emp.vis.colorvec(field_slice_y, axis=axes[1])
+emp.vis.annotate('y-slice', axis=axes[1])
+emp.vis.coords(coords=('x', 'z'), axis=axes[1])
+print(field)
+print(field_slice_y)
+
+# %% [markdown]
+### Quiver and its ambiguity in 3D
+# Let's try the exact same plot with `quiver` instead of `colorvec` now. Note that we use the `color_angles=True` mode,
+# which let's us color the insides of the arrows the same way colorvec would. While the z-slice works finde, the y-slice
+# may show the right colors, but the direction of the arrows are wrong. This is due to the fact that `colorvec` takes
+# the information about all three vector components into account for coloring the pixels. This 3D color information is
+# the same, however you slice the 3D volume (the vortex core will always point in positive z-direction, corresponding to
+# white coloration). The arrows plotted by `quiver`, however have to be adapted to the current slicing plane and therefore
+# need information about what this plane is! Note that `field_slice_y` has the shape `(32, 32)` and therefore is only
+# 2-dimensional. `quiver` does not know how to assign the 3 vector components correctly to only 2 dimensions. To solve
+# this ambiguity, `quiver` will only take the first two components, which erroneously interprets the slice as an
+# x-y-plane. `quiver` will, however, warn the user about ambiguous assignments like this, if the number of vector
+# components is larger than the number of dimensions.
+# %%
+fig, axes = emp.vis.new(1, 2)
+field_slice_y = field[:, 15, :]
+emp.vis.quiver(field_slice_z, color_angles=True, axis=axes[0])
+emp.vis.colorwheel(axis=axes[0])
+emp.vis.annotate('z-slice', axis=axes[0])
+emp.vis.coords(coords=('x', 'y'), axis=axes[0])
+axes[0].axhline(y=16, linestyle='--')
+emp.vis.quiver(field_slice_y, color_angles=True, axis=axes[1])
+emp.vis.annotate('y-slice', axis=axes[1])
+emp.vis.coords(coords=('x', 'z'), axis=axes[1])
+print(field)
+print(field_slice_y)
+
+# %% [markdown]
+### How to correctly use quiver in 3D
+# We can solve the ambiguity, by providing `quiver` with the information about which slice we really want to show. This
+# can be done by slicing differently. Instead of using a single number to specify the slice in the y-direction, we use
+# a slicing object (notation `15:16` in the example, or `to:from` in general). This way, the resulting field object will
+# retain its 3-dimensional shape, but with a length of 1 along the slicing axis (here: `(32, 1, 32)`). In general, all
+# 2D plotting routines can handle higher dimensional slices, as long as you can "squeeze" the fields to 2D by discarding
+# dimensions of size 1. This is exaclty what is done in `quiver`, as well, but by providing the info about which axes
+# are squeezed at the start of the function, `quiver` can now which vector components it should take to correctly plot
+# the slice that the user wanted to plot. Note how in this example, the arrows in the vortex core are correctly pointing
+# in positive z-direction (and are colored correctly, as well).#
+# %%
+fig, axes = emp.vis.new(1, 2)
+field_slice_z_correct = field[15:16, ...]
+field_slice_y_correct = field[:, 15:16, :]
+emp.vis.quiver(field_slice_z_correct, color_angles=True, axis=axes[0])
+emp.vis.colorwheel(axis=axes[0])
+emp.vis.annotate('z-slice', axis=axes[0])
+emp.vis.coords(coords=('x', 'y'), axis=axes[0])
+axes[0].axhline(y=16, linestyle='--')
+emp.vis.quiver(field_slice_y_correct, color_angles=True, axis=axes[1])
+emp.vis.annotate('y-slice', axis=axes[1])
+emp.vis.coords(coords=('x', 'z'), axis=axes[1])
+print(field)
+print(field_slice_y)
+print(field_slice_y_correct)
+
+# %% [markdown]
+### Combined plot
+# Let's show `colorvec` and `quiver` in combination to generate a nice plot. Note that the points in the y-slice image
+# (purple and green background) correspond to arrows in positive and negative y-direction (compare with the z-slice
+# image) and are therefore out-of-plane for this specific slice.
+# %%
+fig, axes = emp.vis.new(1, 2)
+emp.vis.colorvec(field_slice_z_correct, axis=axes[0])
+emp.vis.quiver(field_slice_z_correct, axis=axes[0])
+emp.vis.colorwheel(axis=axes[0])
+emp.vis.annotate('z-slice', axis=axes[0])
+emp.vis.coords(coords=('x', 'y'), axis=axes[0])
+axes[0].axhline(y=16, linestyle='--')
+emp.vis.colorvec(field_slice_y_correct, axis=axes[1])
+emp.vis.quiver(field_slice_y_correct, axis=axes[1])
+emp.vis.annotate('y-slice', axis=axes[1])
+emp.vis.coords(coords=('x', 'z'), axis=axes[1])
+
+# %% [markdown]
+### Conclusion
+# This demo showed you how to correctly slice higher dimensional `Field` objects to utilize the 2D plot functions.
+# In the next demo, we'll see how we can load experimental data and how to use the many manipulation and transformation
+# tools, that come with the `Field` class.

demos/demo3_io_and_field_manipulation.py

+# -*- coding: utf-8 -*-
+# flake8:noqa
+
+# %% [markdown]
+## Demo 3): File IO and basic field manipulation
+# In this demo, you'll learn how to import your own data, more plotting routines and how to postprocess data
+# with the inherent functionality of the `Field` class.
+
+
+# %% [markdown]
+### Import:
+# %%
+import empyre as emp
+import os
+import logging
+logger = logging.getLogger()
+logger.setLevel(logging.WARNING)
+
+
+# %% [markdown]
+### Loading data
+# You can use the `io` module (documentation will follow soon) to load a variety of different data formats. It uses
+# the HyperSpy package (see [here](https://hyperspy.org/) for more info) for a lot of the underlying work, but also has
+# some routines for other formats as well. In general, all image files should work, as well as numpy data and others.
+# The example here is the magnetic structure of a litographic Cobalt pattern. Note how we have to specify, that we want
+# to load a vector field by setting `vector=True`. For vector fields, we can also set, which axis should be interpreted
+# as the component axis (default is `comp_pos=-1` for the last axis).
+# %%
+field_io = emp.io.load_field(os.path.join('files', 'magdata.hdf5'), vector=True, comp_pos=0)
+print(field_io)
+
+# %% [markdown]
+### Scaling data
+# Note how the loaded field is quite large (512 x 512 pixels). You can manipulate the size of your fields with the `bin`
+# function, to bin over a certain number of pixels, or use `zoom` to interpolate to higher numbers of pixels. Here,
+# we'll do the former. Note how the scale automatically changes after binning.
+# %%
+field = field_io.bin(3)
+print(field)
+
+
+# %% [markdown]
+### Plot the loaded field
+# We now want to plot our loaded data. Note how the scalebar always tries to show "nice" numbers, even though the scale
+# itself had long floating points. We are not content with the quiver plot though.
+# %%
+emp.vis.colorvec(field)
+emp.vis.quiver(field)
+emp.vis.colorwheel()
+emp.vis.scalebar()
+
+
+# %% [markdown]
+### Nicer plot
+# The default binning size of `quiver` is determined in a way that tries to show 16 arrows across the whole field of
+# view. In this case, we want to tweak this number to show more, but smaller arrows, which can be done with the `n_bin`
+# parameter.
+# %%
+emp.vis.colorvec(field)
+emp.vis.quiver(field, n_bin=4)
+emp.vis.colorwheel()
+emp.vis.scalebar()
+
+
+# %% [markdown]
+### Split vector fields into its components as scalar fields
+# Furthermore, we can split our vector fields into its scalar components (also returned as fields), by accessing the
+# `comp` attribute. We'll also plot the in-plane components here.
+# %%
+x_field, y_field, z_field = field.comp
+print(x_field)
+fig, axes = emp.vis.new(1, 2)
+emp.vis.imshow(x_field, axis=axes[0])
+emp.vis.scalebar(axis=axes[0])
+emp.vis.imshow(y_field, axis=axes[1])
+
+# %% [markdown]
+### Merge scalars into vector fields
+# The opposite can be done as well, by using the class method `from_scalar_fields` of the `Field` class as an alternate
+# constructor.
+# %%
+field_recombined = emp.fields.Field.from_scalar_fields([x_field, y_field, z_field])
+print(field_recombined)
+
+# %% [markdown]
+### Load more data and combine them
+# Let's load more data from different formats, in this case the magnetic phase map that results from the magnetisation
+# distribution from above, as well as a mask that determines the position of the litographic pattern and a "confidence"
+# array that shows which regions of the (experimentally acquired) phase image we want to trust. Note that some loading
+# routines need to be provided with the `scale`, otherwise they would be defaulting to 1, as not all formats are capable
+# of saving the scale correctly. All fiels are scalar fields and thus don't need the `vector` parameter.
+# %%
+field_phase = emp.io.load_field(os.path.join('files', 'phase.unf'))
+field_mask = emp.io.load_field(os.path.join('files', 'mask.png'), scale=field_phase.scale)
+field_conf = emp.io.load_field(os.path.join('files', 'confidence.npy'), scale=field_phase.scale)
+# Plots
+fig, axes = emp.vis.new(1, 3)
+emp.vis.imshow(field_phase, axis=axes[0])
+emp.vis.annotate('phase', axis=axes[0])
+emp.vis.imshow(field_mask, axis=axes[1])
+emp.vis.annotate('mask', axis=axes[1])
+emp.vis.imshow(field_conf, axis=axes[2])
+emp.vis.annotate('confidence', axis=axes[2])
+
+# %% [markdown]
+### Combined plot
+# We now want to plot all the loaded information into the same image.
+# * We plot the phase with `imshow`, just like before.
+# * We plot the mask as a `contour` plot.
+# * We plot the confidence as another `imshow`, but with a special colormap.
+# * We add a colorbar that needs the phase image as an input to work.
+# * We add a scalebar.
+# %%
+im = emp.vis.imshow(field_phase)
+emp.vis.contour(field_mask)
+emp.vis.imshow(field_conf, cmap=emp.vis.colors.cmaps.transparent_confidence)
+emp.vis.colorbar(im, label='phase [rad]')
+emp.vis.scalebar()
+
+# %% [markdown]
+### Holographic contour plots
+# Magnetic phase images are often shown as holographic contour maps, which you get by calculating the curl (or rotation)
+# of the magnetic phase and overlay it with cosine contours (the cosine of the phase, amplified by a gain factor). Due
+# to `empyre` being rooted in the analysis of magnetic phase images, the according functionality is here as well. First,
+# let's create the rotation of the phase image by using the `curl` function. Visualizing it with `colorvec` shows a
+# problem, though. The strongest saturation is fixed to obviously erroneous pixels and the interesting parts of the
+# image seem faded out and unsaturated.
+# %%
+emp.vis.colorvec(field_phase.curl())
+
+# %% [markdown]
+### The curl and clipping
+# We can use the `clip` function to clip the values to all lie in a Gaussian distribution with a certain `sigma`
+# (the usual numpy functionality with specifying `vmin` and `vmax` is available as well). This clips noisy regions where
+# the rotation is very strong due to sharp boundaries or noise.
+# %%
+emp.vis.colorvec(field_phase.curl().clip(sigma=2))
+
+
+# %% [markdown]
+### Cosine contours
+# Next we look at the cosine contours of the phase, which we can plot via the `cosine_contours` plot function in `vis`.
+# Not that normally, a `gain` factor is determined automatically (default: `gain='auto'`), but we'll look at the pure,
+# unaltered cosine here first.
+# %%
+emp.vis.cosine_contours(field_phase, gain=1)
+
+# %% [markdown]
+### The full contour map
+# Now let's combine both plots, add confidence and mask plots again, as well as a colorwheel and a scalebar.
+# The cosine contour now searches for an adequate gain automatically. Also try out other colormaps (e.g. the
+# `cyclic_classic` one that corresponds to many holographic contour plots in older publications)
+# %%
+cmap = emp.vis.colors.cmaps.cyclic_cubehelix
+emp.vis.colorvec(field_phase.curl().clip(sigma=2), cmap=cmap)
+emp.vis.cosine_contours(field_phase)
+emp.vis.contour(field_mask, colors='w')
+emp.vis.imshow(field_conf, cmap=emp.vis.colors.cmaps.transparent_confidence)
+emp.vis.colorwheel(cmap=cmap)
+emp.vis.scalebar()