Generic tools
-------------

Below we briefly introduce some of the most commonly used tools (methods). For
more details about a particular method click on its name. For a detailed list
of all the methods available see the :class:`~.api.signals.BaseSignal` documentation.

The methods of this section are available to all the signals. In other chapters
methods that are only available in specialized subclasses are listed.

.. _math.operations:

Mathematical operations
^^^^^^^^^^^^^^^^^^^^^^^

A number of mathematical operations are available
in :class:`~.api.signals.BaseSignal`. Most of them are just wrapped numpy
functions.

The methods that perform mathematical operation over one or more axis at a
time are:

* :meth:`~.api.signals.BaseSignal.sum`
* :meth:`~.api.signals.BaseSignal.max`
* :meth:`~.api.signals.BaseSignal.min`
* :meth:`~.api.signals.BaseSignal.mean`
* :meth:`~.api.signals.BaseSignal.std`
* :meth:`~.api.signals.BaseSignal.var`
* :meth:`~.api.signals.BaseSignal.nansum`
* :meth:`~.api.signals.BaseSignal.nanmax`
* :meth:`~.api.signals.BaseSignal.nanmin`
* :meth:`~.api.signals.BaseSignal.nanmean`
* :meth:`~.api.signals.BaseSignal.nanstd`
* :meth:`~.api.signals.BaseSignal.nanvar`

Note that by default all this methods perform the operation over *all*
navigation axes.

Example:

.. code-block:: python

    >>> s = hs.signals.BaseSignal(np.random.random((2,4,6)))
    >>> s.axes_manager[0].name = 'E'
    >>> s
    <BaseSignal, title: , dimensions: (|6, 4, 2)>
    >>> # by default perform operation over all navigation axes
    >>> s.sum()
    <BaseSignal, title: , dimensions: (|6, 4, 2)>
    >>> # can also pass axes individually
    >>> s.sum('E')
    <Signal2D, title: , dimensions: (|4, 2)>
    >>> # or a tuple of axes to operate on, with duplicates, by index or directly
    >>> ans = s.sum((-1, s.axes_manager[1], 'E', 0))
    >>> ans
    <BaseSignal, title: , dimensions: (|1)>
    >>> ans.axes_manager[0]
    <Scalar axis, size: 1>

The following methods operate only on one axis at a time:

* :meth:`~.api.signals.BaseSignal.diff`
* :meth:`~.api.signals.BaseSignal.derivative`
* :meth:`~.api.signals.BaseSignal.integrate_simpson`
* :meth:`~.api.signals.BaseSignal.integrate1D`
* :meth:`~.api.signals.BaseSignal.indexmin`
* :meth:`~.api.signals.BaseSignal.indexmax`
* :meth:`~.api.signals.BaseSignal.valuemin`
* :meth:`~.api.signals.BaseSignal.valuemax`

.. _ufunc-label:

All numpy ufunc can operate on :class:`~.api.signals.BaseSignal`
instances, for example:

.. code-block:: python

    >>> s = hs.signals.Signal1D([0, 1])
    >>> s.metadata.General.title = "A"
    >>> s
    <Signal1D, title: A, dimensions: (|2)>
    >>> np.exp(s)
    <Signal1D, title: exp(A), dimensions: (|2)>
    >>> np.exp(s).data
    array([1. , 2.71828183])
    >>> np.power(s, 2)
    <Signal1D, title: power(A, 2), dimensions: (|2)>
    >>> np.add(s, s)
    <Signal1D, title: add(A, A), dimensions: (|2)>
    >>> np.add(hs.signals.Signal1D([0, 1]), hs.signals.Signal1D([0, 1]))
    <Signal1D, title: add(Untitled Signal 1, Untitled Signal 2), dimensions: (|2)>


Notice that the title is automatically updated. When the signal has no title
a new title is automatically generated:

.. code-block:: python

    >>> np.add(hs.signals.Signal1D([0, 1]), hs.signals.Signal1D([0, 1]))
    <Signal1D, title: add(Untitled Signal 1, Untitled Signal 2), dimensions: (|2)>


Functions (other than unfucs) that operate on numpy arrays can also operate
on :class:`~.api.signals.BaseSignal` instances, however they return a numpy
array instead of a :class:`~.api.signals.BaseSignal` instance e.g.:

.. code-block:: python

    >>> np.angle(s)
    array([0., 0.])

.. note::
    For numerical **differentiation** and **integration**, use the proper
    methods :meth:`~.api.signals.BaseSignal.derivative` and
    :meth:`~.api.signals.BaseSignal.integrate1D`. In certain cases, particularly
    when operating on a non-uniform axis, the approximations using the
    :meth:`~.api.signals.BaseSignal.diff` and :meth:`~.api.signals.BaseSignal.sum`
    methods will lead to erroneous results.


.. _signal.operations:

Signal operations
^^^^^^^^^^^^^^^^^

:class:`~.api.signals.BaseSignal` supports all the Python binary arithmetic
operations (+, -, \*, //, %, divmod(), pow(), \*\*, <<, >>, &, ^, \|),
augmented binary assignments (+=, -=, \*=, /=, //=, %=, \*\*=, <<=, >>=, &=,
^=, \|=), unary operations (-, +, abs() and ~) and rich comparisons operations
(<, <=, ==, x!=y, <>, >, >=).

These operations are performed element-wise. When the dimensions of the signals
are not equal `numpy broadcasting rules apply
<https://numpy.org/doc/stable/user/basics.broadcasting.html>`_ independently
for the navigation and signal axes.

.. WARNING::

    Hyperspy does not check if the calibration of the signals matches.

In the following example `s2` has only one navigation axis while `s` has two.
However, because the size of their first navigation axis is the same, their
dimensions are compatible and `s2` is
broadcasted to match `s`'s dimensions.

.. code-block:: python

    >>> s = hs.signals.Signal2D(np.ones((3,2,5,4)))
    >>> s2 = hs.signals.Signal2D(np.ones((2,5,4)))
    >>> s
    <Signal2D, title: , dimensions: (2, 3|4, 5)>
    >>> s2
    <Signal2D, title: , dimensions: (2|4, 5)>
    >>> s + s2
    <Signal2D, title: , dimensions: (2, 3|4, 5)>

In the following example the dimensions are not compatible and an exception
is raised.

.. code-block:: python

    >>> s = hs.signals.Signal2D(np.ones((3,2,5,4)))
    >>> s2 = hs.signals.Signal2D(np.ones((3,5,4)))
    >>> s
    <Signal2D, title: , dimensions: (2, 3|4, 5)>
    >>> s2
    <Signal2D, title: , dimensions: (3|4, 5)>
    >>> s + s2 # doctest: +SKIP
    Traceback (most recent call last):
      File "<ipython-input-55-044bb11a0bd9>", line 1, in <module>
        s + s2
      File "<string>", line 2, in __add__
      File "/home/fjd29/Python/hyperspy/hyperspy/signal.py", line 2686, in _binary_operator_ruler
        raise ValueError(exception_message)
    ValueError: Invalid dimensions for this operation


Broadcasting operates exactly in the same way for the signal axes:

.. code-block:: python

    >>> s = hs.signals.Signal2D(np.ones((3,2,5,4)))
    >>> s2 = hs.signals.Signal1D(np.ones((3, 2, 4)))
    >>> s
    <Signal2D, title: , dimensions: (2, 3|4, 5)>
    >>> s2
    <Signal1D, title: , dimensions: (2, 3|4)>
    >>> s + s2
    <Signal2D, title: , dimensions: (2, 3|4, 5)>

In-place operators also support broadcasting, but only when broadcasting would
not change the left most signal dimensions:

.. code-block:: python

    >>> s += s2
    >>> s
    <Signal2D, title: , dimensions: (2, 3|4, 5)>
    >>> s2 += s # doctest: +SKIP
    Traceback (most recent call last):
      File "<ipython-input-64-fdb9d3a69771>", line 1, in <module>
        s2 += s
      File "<string>", line 2, in __iadd__
      File "/home/fjd29/Python/hyperspy/hyperspy/signal.py", line 2737, in _binary_operator_ruler
        self.data = getattr(sdata, op_name)(odata)
    ValueError: non-broadcastable output operand with shape (3,2,1,4) doesn\'t match the broadcast shape (3,2,5,4)


.. _signal.iterator:

Iterating over the navigation axes
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

BaseSignal instances are iterables over the navigation axes. For example, the
following code creates a stack of 10 images and saves them in separate "png"
files by iterating over the signal instance:

.. code-block:: python

    >>> image_stack = hs.signals.Signal2D(np.random.randint(10, size=(2, 5, 64,64)))
    >>> for single_image in image_stack:
    ...    single_image.save("image %s.png" % str(image_stack.axes_manager.indices)) # doctest: +SKIP
    The "image (0, 0).png" file was created.
    The "image (1, 0).png" file was created.
    The "image (2, 0).png" file was created.
    The "image (3, 0).png" file was created.
    The "image (4, 0).png" file was created.
    The "image (0, 1).png" file was created.
    The "image (1, 1).png" file was created.
    The "image (2, 1).png" file was created.
    The "image (3, 1).png" file was created.
    The "image (4, 1).png" file was created.

The data of the signal instance that is returned at each iteration is a view of
the original data, a property that we can use to perform operations on the
data.  For example, the following code rotates the image at each coordinate  by
a given angle and uses the :func:`~.api.stack` function in combination
with `list comprehensions
<https://docs.python.org/3/tutorial/datastructures.html#list-comprehensions>`_
to make a horizontal "collage" of the image stack:

.. code-block:: python

    >>> import scipy.ndimage
    >>> image_stack = hs.signals.Signal2D(np.array([scipy.datasets.ascent()]*5))
    >>> image_stack.axes_manager[1].name = "x"
    >>> image_stack.axes_manager[2].name = "y"
    >>> for image, angle in zip(image_stack, (0, 45, 90, 135, 180)):
    ...    image.data[:] = scipy.ndimage.rotate(image.data, angle=angle,
    ...    reshape=False)
    >>> # clip data to integer range:
    >>> image_stack.data = np.clip(image_stack.data, 0, 255)
    >>> collage = hs.stack([image for image in image_stack], axis=0)
    >>> collage.plot(scalebar=False)

.. figure::  ../images/rotate_ascent.png
  :align:   center
  :width:   500

  Rotation of images by iteration.

.. _map-label:

Iterating external functions with the map method
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Performing an operation on the data at each coordinate, as in the previous example,
using an external function can be more easily accomplished using the
:meth:`~.api.signals.BaseSignal.map` method:

.. code-block:: python

    >>> import scipy.ndimage
    >>> image_stack = hs.signals.Signal2D(np.array([scipy.datasets.ascent()]*4))
    >>> image_stack.axes_manager[1].name = "x"
    >>> image_stack.axes_manager[2].name = "y"
    >>> image_stack.map(scipy.ndimage.rotate, angle=45, reshape=False)
    >>> # clip data to integer range
    >>> image_stack.data = np.clip(image_stack.data, 0, 255)
    >>> collage = hs.stack([image for image in image_stack], axis=0)
    >>> collage.plot()

.. figure::  ../images/rotate_ascent_apply_simple.png
  :align:   center
  :width:   500

  Rotation of images by the same amount using :meth:`~.api.signals.BaseSignal.map`.

The :meth:`~.api.signals.BaseSignal.map` method can also take variable
arguments as in the following example.

.. code-block:: python

    >>> import scipy.ndimage
    >>> image_stack = hs.signals.Signal2D(np.array([scipy.datasets.ascent()]*4))
    >>> image_stack.axes_manager[1].name = "x"
    >>> image_stack.axes_manager[2].name = "y"
    >>> angles = hs.signals.BaseSignal(np.array([0, 45, 90, 135]))
    >>> image_stack.map(scipy.ndimage.rotate, angle=angles.T, reshape=False)

.. figure::  ../images/rotate_ascent_apply_ndkwargs.png
  :align:   center
  :width:   500

  Rotation of images using :meth:`~.api.signals.BaseSignal.map` with different
  arguments for each image in the stack.

.. versionadded:: 1.2.0
    ``inplace`` keyword and non-preserved output shapes

If all function calls do not return identically-shaped results, only navigation
information is preserved, and the final result is an array where
each element corresponds to the result of the function (or arbitrary object
type). These are :ref:`ragged arrays <signal.ragged>` and has the dtype `object`.
As such, most HyperSpy functions cannot operate on such signals, and the
data should be accessed directly.

The ``inplace`` keyword (by default ``True``) of the
:meth:`~.api.signals.BaseSignal.map` method allows either overwriting the current
data (default, ``True``) or storing it to a new signal (``False``).

.. code-block:: python

    >>> import scipy.ndimage
    >>> image_stack = hs.signals.Signal2D(np.array([scipy.datasets.ascent()]*4))
    >>> angles = hs.signals.BaseSignal(np.array([0, 45, 90, 135]))
    >>> result = image_stack.map(scipy.ndimage.rotate,
    ...                            angle=angles.T,
    ...                            inplace=False,
    ...                            ragged=True,
    ...                            reshape=True)

    >>> result
    <BaseSignal, title: , dimensions: (4|ragged)>
    >>> result.data.dtype
    dtype('O')
    >>> for d in result.data.flat:
    ...     print(d.shape)
    (512, 512)
    (724, 724)
    (512, 512)
    (724, 724)

.. versionadded:: 1.4
    Iterating over signal using a parameter with no navigation dimension.

In this case, the parameter is cyclically iterated over the navigation
dimension of the input signal. In the example below, signal s is
multiplied by a cosine parameter d, which is repeated over the
navigation dimension of s.

.. code-block:: python

    >>> s = hs.signals.Signal1D(np.random.rand(10, 512))
    >>> d = hs.signals.Signal1D(np.cos(np.linspace(0., 2*np.pi, 512)))
    >>> s.map(lambda A, B: A * B, B=d)


.. _lazy_output-map-label:

.. versionadded:: 1.7
    Get result as lazy signal

Especially when working with very large datasets, it can be useful to
not do the computation immediately. For example if it would make you run
out of memory. In that case, the `lazy_output` parameter can be used.

.. code-block:: python

    >>> from scipy.ndimage import gaussian_filter
    >>> s = hs.signals.Signal2D(np.random.random((4, 4, 128, 128)))
    >>> s_out = s.map(gaussian_filter, sigma=5, inplace=False, lazy_output=True)
    >>> s_out
    <LazySignal2D, title: , dimensions: (4, 4|128, 128)>

`s_out` can then be saved to a hard drive, to avoid it being loaded into memory.
Alternatively, it can be computed and loaded into memory using `s_out.compute()`

.. code-block:: python

    >>> s_out.save("gaussian_filter_file.hspy") # doctest: +SKIP

Another advantage of using `lazy_output=True` is the ability to "chain" operations,
by running :meth:`~.api.signals.BaseSignal.map` on the output from a previous
:meth:`~.api.signals.BaseSignal.map` operation.
For example, first running a Gaussian filter, followed by peak finding. This can
improve the computation time, and reduce the memory need.

.. code-block:: python

    >>> s_out = s.map(scipy.ndimage.gaussian_filter, sigma=5, inplace=False, lazy_output=True)
    >>> from skimage.feature import blob_dog
    >>> s_out1 = s_out.map(blob_dog, threshold=0.05, inplace=False, ragged=True, lazy_output=False)
    >>> s_out1
    <BaseSignal, title: , dimensions: (4, 4|ragged)>

This is especially relevant for very large datasets, where memory use can be a
limiting factor.


Cropping
^^^^^^^^

Cropping can be performed in a very compact and powerful way using
:ref:`signal.indexing` . In addition it can be performed using the following
method or GUIs if cropping :ref:`signal1D <signal1D.crop>` or :ref:`signal2D
<signal2D.crop>`. There is also a general :meth:`~.api.signals.BaseSignal.crop`
method that operates *in place*.


.. _rebin-label:

Rebinning
^^^^^^^^^
.. versionadded:: 1.3
    :meth:`~.api.signals.BaseSignal.rebin` generalized to remove the constrain
    of the ``new_shape`` needing to be a divisor of ``data.shape``.


The :meth:`~.api.signals.BaseSignal.rebin` methods supports rebinning the data to
arbitrary new shapes as long as the number of dimensions stays the same.
However, internally, it uses two different algorithms to perform the task. Only
when the new shape dimensions are divisors of the old shape's, the operation
supports :ref:`lazy-evaluation <big-data-label>` and is usually faster.
Otherwise, the operation requires linear interpolation.

For example, the following two equivalent rebinning operations can be  performed
lazily:

.. code-block:: python

    >>> s = hs.data.two_gaussians().as_lazy()
    >>> print(s)
    <LazySignal1D, title: Two Gaussians, dimensions: (32, 32|1024)>
    >>> print(s.rebin(scale=[1, 1, 2]))
    <LazySignal1D, title: Two Gaussians, dimensions: (32, 32|512)>


.. code-block:: python

    >>> s = hs.data.two_gaussians().as_lazy()
    >>> print(s.rebin(new_shape=[32, 32, 512]))
    <LazySignal1D, title: Two Gaussians, dimensions: (32, 32|512)>


On the other hand, the following rebinning operation requires interpolation and
cannot be performed lazily:

.. code-block:: python

    >>> s = hs.signals.Signal1D(np.ones([4, 4, 10]))
    >>> s.data[1, 2, 9] = 5
    >>> print(s)
    <Signal1D, title: , dimensions: (4, 4|10)>
    >>> print ('Sum = ', s.data.sum())
    Sum =  164.0
    >>> scale = [0.5, 0.5, 5]
    >>> test = s.rebin(scale=scale)
    >>> test2 = s.rebin(new_shape=(8, 8, 2)) # Equivalent to the above
    >>> print(test)
    <Signal1D, title: , dimensions: (8, 8|2)>
    >>> print(test2)
    <Signal1D, title: , dimensions: (8, 8|2)>
    >>> print('Sum =', test.data.sum())
    Sum = 164.0
    >>> print('Sum =', test2.data.sum())
    Sum = 164.0
    >>> s.as_lazy().rebin(scale=scale) # doctest: +SKIP
    Traceback (most recent call last):
      File "<ipython-input-26-49bca19ebf34>", line 1, in <module>
        spectrum.as_lazy().rebin(scale=scale)
      File "/home/fjd29/Python/hyperspy3/hyperspy/_signals/eds.py", line 184, in rebin
        m = super().rebin(new_shape=new_shape, scale=scale, crop=crop, out=out)
      File "/home/fjd29/Python/hyperspy3/hyperspy/_signals/lazy.py", line 246, in rebin
        "Lazy rebin requires scale to be integer and divisor of the "
    NotImplementedError: Lazy rebin requires scale to be integer and divisor of the original signal shape


The ``dtype``  argument can be used to specify the ``dtype`` of the returned
signal::

    >>> s = hs.signals.Signal1D(np.ones((2, 5, 10), dtype=np.uint8))
    >>> print(s)
    <Signal1D, title: , dimensions: (5, 2|10)>
    >>> print(s.data.dtype)
    uint8

Use ``dtype=np.unit16`` to specify a dtype::

    >>> s2 = s.rebin(scale=(5, 2, 1), dtype=np.uint16)
    >>> print(s2.data.dtype)
    uint16

Use ``dtype="same"`` to keep the same dtype::

    >>> s3 = s.rebin(scale=(5, 2, 1), dtype="same")
    >>> print(s3.data.dtype)
    uint8

By default ``dtype=None``, the dtype is determined by the behaviour of
numpy.sum, in this case, unsigned integer of the same precision as the
platform interger::

    >>> s4 = s.rebin(scale=(5, 2, 1))
    >>> print(s4.data.dtype)
    uint32


Interpolate to a different axis
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

The :meth:`~.api.signals.BaseSignal.interpolate_on_axis` method makes it possible to
exchange any existing axis of a signal with a new axis,
regardless of the signals dimension or the axes types.
This is achieved by interpolating the data using :func:`scipy.interpolate.make_interp_spline`
from the old axis to the new axis. Replacing multiple axes can be done iteratively.

.. code-block:: python

    >>> from hyperspy.axes import UniformDataAxis, DataAxis
    >>> x = {"offset": 0, "scale": 1, "size": 10, "name": "X", "navigate": True}
    >>> e = {"offset": 0, "scale": 1, "size": 50, "name": "E", "navigate": False}
    >>> s = hs.signals.Signal1D(np.random.random((10, 50)), axes=[x, e])
    >>> s
    <Signal1D, title: , dimensions: (10|50)>
    >>> x_new = UniformDataAxis(offset=1.5, scale=0.8, size=7, name="X_NEW", navigate=True)
    >>> e_new = DataAxis(axis=np.arange(8)**2, name="E_NEW", navigate=False)
    >>> s2 = s.interpolate_on_axis(x_new, 0, inplace=False)
    >>> s2
    <Signal1D, title: , dimensions: (7|50)>
    >>> s2.interpolate_on_axis(e_new, "E", inplace=True)
    >>> s2
    <Signal1D, title: , dimensions: (7|8)>


.. _squeeze-label:

Squeezing
^^^^^^^^^

The :meth:`~.api.signals.BaseSignal.squeeze` method removes any zero-dimensional
axes, i.e. axes of ``size=1``, and the attributed data dimensions from a signal.
The method returns a reduced copy of the signal and does not operate in place.

.. code-block:: python

    >>> s = hs.signals.Signal2D(np.random.random((2, 1, 1, 6, 8, 8)))
    >>> s
    <Signal2D, title: , dimensions: (6, 1, 1, 2|8, 8)>
    >>> s = s.squeeze()
    >>> s
    <Signal2D, title: , dimensions: (6, 2|8, 8)>

Squeezing can be particularly useful after a rebinning operation that leaves
one dimension with ``shape=1``:

    >>> s = hs.signals.Signal2D(np.random.random((5,5,5,10,10)))
    >>> s.rebin(new_shape=(5,1,5,5,5))
    <Signal2D, title: , dimensions: (5, 1, 5|5, 5)>
    >>> s.rebin(new_shape=(5,1,5,5,5)).squeeze()
    <Signal2D, title: , dimensions: (5, 5|5, 5)>


Folding and unfolding
^^^^^^^^^^^^^^^^^^^^^

When dealing with multidimensional datasets it is sometimes useful to transform
the data into a two dimensional dataset. This can be accomplished using the
following two methods:

* :meth:`~.api.signals.BaseSignal.fold`
* :meth:`~.api.signals.BaseSignal.unfold`

It is also possible to unfold only the navigation or only the signal space:

* :meth:`~.api.signals.BaseSignal.unfold_navigation_space`
* :meth:`~.api.signals.BaseSignal.unfold_signal_space`


.. _signal.stack_split:

Splitting and stacking
^^^^^^^^^^^^^^^^^^^^^^

Several objects can be stacked together over an existing axis or over a
new axis using the :func:`~.api.stack` function, if they share axis
with same dimension.

.. code-block:: python

    >>> image = hs.signals.Signal2D(scipy.datasets.ascent())
    >>> image = hs.stack([hs.stack([image]*3,axis=0)]*3,axis=1)
    >>> image.plot()

.. figure::  ../images/stack_ascent_3_3.png
  :align:   center
  :width:   500

  Stacking example.

.. note::

    When stacking signals with large amount of
    :attr:`~.api.signals.BaseSignal.original_metadata`, these metadata will be
    stacked and this can lead to very large amount of metadata which can in
    turn slow down processing. The ``stack_original_metadata`` argument can be
    used to disable stacking :attr:`~.api.signals.BaseSignal.original_metadata`.

An object can be split into several objects
with the :meth:`~.api.signals.BaseSignal.split` method. This function can be used
to reverse the :func:`~.api.stack` function:

.. code-block:: python

    >>> image = image.split()[0].split()[0]
    >>> image.plot()

.. figure::  ../images/split_ascent_3_3.png
  :align:   center
  :width:   400

  Splitting example.


.. _signal.fft:

Fast Fourier Transform (FFT)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^

The `fast Fourier transform <https://en.wikipedia.org/wiki/Fast_Fourier_transform>`_
of a signal can be computed using the :meth:`~.api.signals.BaseSignal.fft` method. By default,
the FFT is calculated with the origin at (0, 0), which will be displayed at the
bottom left and not in the centre of the FFT. Conveniently, the ``shift`` argument of the
the :meth:`~.api.signals.BaseSignal.fft` method can be used to center the output of the FFT.
In the following example, the FFT of a hologram is computed using ``shift=True`` and its
output signal is displayed, which shows that the FFT results in a complex signal with a
real and an imaginary parts:

.. code-block:: python

    >>> im = hs.data.wave_image()
    >>> fft_shifted = im.fft(shift=True)
    >>> fft_shifted.plot()

.. figure::  ../images/FFT_vacuum_reference_hologram.png
  :align:   center
  :width:   800

The strong features in the real and imaginary parts correspond to the lattice fringes of the
hologram.

For visual inspection of the FFT it is convenient to display its power spectrum
(i.e. the square of the absolute value of the FFT) rather than FFT itself as it is done
in the example above by using the ``power_spectum`` argument:

.. code-block:: python

    >>> im = hs.data.wave_image()
    >>> fft = im.fft(True)
    >>> fft.plot(True)

Where ``power_spectum`` is set to ``True`` since it is the first argument of the
:meth:`~.api.signals.ComplexSignal.plot` method for complex signal.
When ``power_spectrum=True``, the plot will be displayed on a log scale by default.


.. figure::  ../images/FFT_vacuum_reference_hologram_power_spectrum.png
  :align:   center
  :width:   400

The visualisation can be further improved by setting the minimum value to display to the 30-th
percentile; this can be done by using ``vmin="30th"`` in the plot function:

.. code-block:: python

    >>> im = hs.data.wave_image()
    >>> fft = im.fft(True)
    >>> fft.plot(True, vmin="30th")

.. figure::  ../images/FFT_vacuum_reference_hologram_power_spectrum_vmin30th.png
  :align:   center
  :width:   400

The streaks visible in the FFT come from the edge of the image and can be removed by
applying an `apodization <https://en.wikipedia.org/wiki/Apodization>`_ function to the original
signal before the computation of the FFT. This can be done using the ``apodization`` argument of
the :meth:`~.api.signals.BaseSignal.fft` method and it is usually used for visualising FFT patterns
rather than for quantitative analyses. By default, the so-called ``hann`` windows is
used but different type of windows such as the ``hamming`` and ``tukey`` windows.

.. code-block:: python

    >>> im = hs.data.wave_image()
    >>> fft = im.fft(shift=True)
    >>> fft_apodized = im.fft(shift=True, apodization=True)
    >>> fft_apodized.plot(True, vmin="30th")

.. figure::  ../images/FFT_vacuum_reference_hologram_power_spectrum_vmin30th-apodization.png
  :align:   center
  :width:   400



Inverse Fast Fourier Transform (iFFT)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Inverse fast Fourier transform can be calculated from a complex signal by using the
:meth:`~.api.signals.BaseSignal.ifft` method. Similarly to the :meth:`~.api.signals.BaseSignal.fft` method,
the ``shift`` argument can be provided to shift the origin of the iFFT when necessary:

.. code-block:: python

    >>> im_ifft = im.fft(shift=True).ifft(shift=True)


.. _signal.change_dtype:

Changing the data type
^^^^^^^^^^^^^^^^^^^^^^

Even if the original data is recorded with a limited dynamic range, it is often
desirable to perform the analysis operations with a higher precision.
Conversely, if space is limited, storing in a shorter data type can decrease
the file size. The :meth:`~.api.signals.BaseSignal.change_dtype` changes the data
type in place, e.g.:

.. code-block:: python

    >>> s = hs.load('EELS Signal1D Signal2D (high-loss).dm3') # doctest: +SKIP
        Title: EELS Signal1D Signal2D (high-loss).dm3
        Signal type: EELS
        Data dimensions: (21, 42, 2048)
        Data representation: spectrum
        Data type: float32
    >>> s.change_dtype('float64') # doctest: +SKIP
    >>> print(s) # doctest: +SKIP
        Title: EELS Signal1D Signal2D (high-loss).dm3
        Signal type: EELS
        Data dimensions: (21, 42, 2048)
        Data representation: spectrum
        Data type: float64


In addition to all standard numpy dtypes, HyperSpy supports four extra dtypes
for RGB images **for visualization purposes only**: ``rgb8``, ``rgba8``,
``rgb16`` and ``rgba16``. This includes of course multi-dimensional RGB images.

The requirements for changing from and to any ``rgbx`` dtype are more strict
than for most other dtype conversions. To change to a ``rgbx`` dtype the
``signal_dimension`` must be 1 and its size 3 (4) 3(4) for ``rgb`` (or
``rgba``) dtypes and the dtype must be ``uint8`` (``uint16``) for
``rgbx8`` (``rgbx16``). After conversion the ``signal_dimension`` becomes 2.

Most operations on signals with RGB dtypes will fail. For processing simply
change their dtype to ``uint8`` (``uint16``).The dtype of images of
dtype ``rgbx8`` (``rgbx16``) can only be changed to ``uint8`` (``uint16``) and
the ``signal_dimension`` becomes 1.

In the following example we create a 1D signal with signal size 3 and with
dtype ``uint16`` and change its dtype to ``rgb16`` for plotting.

.. code-block:: python

    >>> rgb_test = np.zeros((1024, 1024, 3))
    >>> ly, lx = rgb_test.shape[:2]
    >>> offset_factor = 0.16
    >>> size_factor = 3
    >>> Y, X = np.ogrid[0:lx, 0:ly]
    >>> rgb_test[:,:,0] = (X - lx / 2 - lx*offset_factor) ** 2 + \
    ...                   (Y - ly / 2 - ly*offset_factor) ** 2 < \
    ...                   lx * ly / size_factor **2
    >>> rgb_test[:,:,1] = (X - lx / 2 + lx*offset_factor) ** 2 + \
    ...                   (Y - ly / 2 - ly*offset_factor) ** 2 < \
    ...                   lx * ly / size_factor **2
    >>> rgb_test[:,:,2] = (X - lx / 2) ** 2 + \
    ...                   (Y - ly / 2 + ly*offset_factor) ** 2 \
    ...                   < lx * ly / size_factor **2
    >>> rgb_test *= 2**16 - 1
    >>> s = hs.signals.Signal1D(rgb_test)
    >>> s.change_dtype("uint16")
    >>> s
    <Signal1D, title: , dimensions: (1024, 1024|3)>
    >>> s.change_dtype("rgb16")
    >>> s
    <Signal2D, title: , dimensions: (|1024, 1024)>
    >>> s.plot()


.. figure::  ../images/rgb_example.png
  :align:   center
  :width:   500

  RGB data type example.


.. _signal.transpose:

Transposing (changing signal spaces)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.. versionadded:: 1.1

:meth:`~.api.signals.BaseSignal.transpose` method changes how the dataset
dimensions are interpreted (as signal or navigation axes). By default is
swaps the signal and navigation axes. For example:


.. code-block:: python

   >>> s = hs.signals.Signal1D(np.zeros((4,5,6)))
   >>> s
   <Signal1D, title: , dimensions: (5, 4|6)>
   >>> s.transpose()
   <Signal2D, title: , dimensions: (6|5, 4)>

For :meth:`~.api.signals.BaseSignal.T` is a shortcut for the default behaviour:

.. code-block:: python

   >>> s = hs.signals.Signal1D(np.zeros((4,5,6))).T
   >>> s
   <Signal2D, title: , dimensions: (6|5, 4)>


The method accepts both explicit axes to keep in either space, or just a number
of axes required in one space (just one number can be specified, as the other
is defined as "all other axes"). When axes order is not explicitly defined,
they are "rolled" from one space to the other as if the ``<navigation axes |
signal axes >`` wrap a circle. The example below should help clarifying this.


.. code-block:: python

    >>> # just create a signal with many distinct dimensions
    >>> s = hs.signals.BaseSignal(np.random.rand(1, 2, 3, 4, 5, 6, 7, 8, 9))
    >>> s
    <BaseSignal, title: , dimensions: (|9, 8, 7, 6, 5, 4, 3, 2, 1)>
    >>> s.transpose(signal_axes=5) # roll to leave 5 axes in signal space
    <BaseSignal, title: , dimensions: (4, 3, 2, 1|9, 8, 7, 6, 5)>
    >>> s.transpose(navigation_axes=3) # roll leave 3 axes in navigation space
    <BaseSignal, title: , dimensions: (3, 2, 1|9, 8, 7, 6, 5, 4)>
    >>> # 3 explicitly defined axes in signal space
    >>> s.transpose(signal_axes=[0, 2, 6])
    <BaseSignal, title: , dimensions: (8, 6, 5, 4, 2, 1|9, 7, 3)>
    >>> # A mix of two lists, but specifying all axes explicitly
    >>> # The order of axes is preserved in both lists
    >>> s.transpose(navigation_axes=[1, 2, 3, 4, 5, 8], signal_axes=[0, 6, 7])
    <BaseSignal, title: , dimensions: (8, 7, 6, 5, 4, 1|9, 3, 2)>

A convenience functions :func:`~.api.transpose` is available to operate on
many signals at once, for example enabling plotting any-dimension signals
trivially:

.. code-block:: python

    >>> s2 = hs.signals.BaseSignal(np.random.rand(2, 2)) # 2D signal
    >>> s3 = hs.signals.BaseSignal(np.random.rand(3, 3, 3)) # 3D signal
    >>> s4 = hs.signals.BaseSignal(np.random.rand(4, 4, 4, 4)) # 4D signal
    >>> hs.plot.plot_images(hs.transpose(s2, s3, s4, signal_axes=2)) # doctest: +SKIP

.. _signal.transpose_optimize:

The :meth:`~.api.signals.BaseSignal.transpose` method accepts keyword argument
``optimize``, which is ``False`` by default, meaning modifying the output
signal data **always modifies the original data** i.e. the data is just a view
of the original data. If ``True``, the method ensures the data in memory is
stored in the most efficient manner for iterating by making a copy of the data
if required, hence modifying the output signal data **not always modifies the
original data**.

The convenience methods :meth:`~.api.signals.BaseSignal.as_signal1D` and
:meth:`~.api.signals.BaseSignal.as_signal2D` internally use
:meth:`~.api.signals.BaseSignal.transpose`, but always optimize the data
for iteration over the navigation axes if required. Hence, these methods do not
always return a view of the original data. If a copy of the data is required
use
:meth:`~.api.signals.BaseSignal.deepcopy` on the output of any of these
methods e.g.:

.. code-block:: python

   >>> hs.signals.Signal1D(np.zeros((4,5,6))).T.deepcopy()
   <Signal2D, title: , dimensions: (6|5, 4)>


Applying apodization window
^^^^^^^^^^^^^^^^^^^^^^^^^^^

Apodization window (also known as apodization function) can be applied to a signal
using :meth:`~.api.signals.BaseSignal.apply_apodization` method. By default standard
Hann window is used:

.. code-block:: python

    >>> s = hs.signals.Signal1D(np.ones(1000))
    >>> sa = s.apply_apodization()
    >>> sa.metadata.General.title = 'Hann window'
    >>> sa.plot()


.. figure::  ../images/hann_window.png
  :align:   center
  :width:   400

Higher order Hann window can be used in order to keep larger fraction of intensity of original signal.
This can be done providing an integer number for the order of the window through
keyword argument ``hann_order``. (The last one works only together with default value of ``window`` argument
or with ``window='hann'``.)

.. code-block:: python

    >>> im = hs.data.wave_image().isig[:200, :200]
    >>> ima = im.apply_apodization(window='hann', hann_order=3)
    >>> hs.plot.plot_images([im, ima], vmax=3000, tight_layout=True)
    [<Axes: >, <Axes: >]


.. figure::  ../images/hann_3d_order_ref_holo.png
  :align:   center
  :width:   800

In addition to Hann window also Hamming or Tukey windows can be applied using ``window`` attribute
selecting ``'hamming'`` or ``'tukey'`` respectively.

The shape of Tukey window can be adjusted using parameter alpha
provided through ``tukey_alpha`` keyword argument (only used when ``window='tukey'``).
The parameter represents the fraction of the window inside the cosine tapered region,
i.e. smaller is alpha larger is the middle flat region where the original signal
is preserved. If alpha is one, the Tukey window is equivalent to a Hann window.
(Default value is 0.5)

Apodization can be applied in place by setting keyword argument ``inplace`` to ``True``.
In this case method will not return anything.