Tools: the Signal class *********************** The Signal class and its subclasses ----------------------------------- .. WARNING:: This subsection can be a bit confusing for beginners. Do not worry if you do not understand it all. HyperSpy stores the data in the :py:class:`~.signal.BaseSignal` class, that is the object that you get when e.g. you load a single file using :py:func:`~.io.load`. Most of the data analysis functions are also contained in this class or its specialized subclasses. The :py:class:`~.signal.BaseSignal` class contains general functionality that is available to all the subclasses. The subclasses provide functionality that is normally specific to a particular type of data, e.g. the :py:class:`~._signals.signal1d.Signal1D` class provides common functionality to deal with one-dimensional (e.g. spectral) data and :py:class:`~._signals.eels.EELSSpectrum` (which is a subclass of :py:class:`~._signals.signal1d.Signal1D`) adds extra functionality to the :py:class:`~._signals.signal1d.Signal1D` class for electron energy-loss spectroscopy data analysis. .. versionchanged:: 0.8.5 Currently the following signal subclasses are available: * :py:class:`~._signals.signal1d.Signal1D` * :py:class:`~._signals.signal2d.Signal2D` * :py:class:`~._signals.eels.EELSSpectrum` * :py:class:`~._signals.eds_tem.EDSTEMSpectrum` * :py:class:`~._signals.eds_sem.EDSSEMSpectrum` * :py:class:`~._signals.spectrum_simulation.SpectrumSimulation` * :py:class:`~._signals.image_simulation.ImageSimulation` .. versionchanged:: 0.8.5 Note that in 0.8.5 the :py:class:`~._signals.signal1d.Signal1D` and :py:class:`~._signals.signal2d.Signal2D` classes were created to deprecate the old :py:class:`~._signals.spectrum.Spectrum` and :py:class:`~._signals.image.Image` classes. The :py:mod:`~.signals` module, which contains all available signal subclasses, is imported in the user namespace when loading hyperspy. In the following example we create a Signal2D instance from a 2D numpy array: .. code-block:: python >>> im = hs.signals.Signal2D(np.random.random((64,64))) The different signals store other objects in what are called attributes. For examples, the data is stored in a numpy array in the :py:attr:`~.signal.BaseSignal.data` attribute, the original parameters in the :py:attr:`~.signal.BaseSignal.original_metadata` attribute, the mapped parameters in the :py:attr:`~.signal.BaseSignal.metadata` attribute and the axes information (including calibration) can be accessed (and modified) in the :py:attr:`~.signal.BaseSignal.axes_manager` attribute. .. _transforming.signal: Transforming between signal subclasses ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The different subclasses are characterized by three :py:attr:`~.signal.BaseSignal.metadata` attributes (see the table below): `record_by` Can be "spectrum", "image" or "", the latter meaning undefined and describes the way the data is arranged in memory. It is possible to transform any :py:class:`~.signal.BaseSignal` subclass to a :py:class:`~._signals.signal1d.Signal1D` or :py:class:`~._signals.signal2d.Signal2D` subclass using the following :py:class:`~.signal.BaseSignal` methods: :py:meth:`~.signal.BaseSignal.as_signal2D` and :py:meth:`~.signal.BaseSignal.as_signal1D`. In addition :py:class:`~._signals.signal1d.Signal1D` instances can be transformed into two-dimensional signals using :py:meth:`~._signals.signal1d.Signal1D.to_signal2D` and two-dimensional instances transformed into one dimensional instances using :py:meth:`~._signals.signal2d.Signal2D.to_signal1D`. When transforming between one and two dimensinoal signal classes the order in which the data array is stored in memory is modified to improve performance. Also, some functions, e.g. plotting or decomposing, will behave differently. `signal_type` Describes the nature of the signal. It can be any string, normally the acronym associated with a particular signal. In certain cases HyperSpy provides features that are only available for a particular signal type through :py:class:`~.signal.BaseSignal` subclasses. The :py:class:`~.signal.BaseSignal` method :py:meth:`~.signal.BaseSignal.set_signal_type` changes the signal_type in place, which may result in a :py:class:`~.signal.BaseSignal` subclass transformation. `signal_origin` Describes the origin of the signal and can be "simulation" or "experiment" or "", the latter meaning undefined. In certain cases HyperSpy provides features that are only available for a particular signal origin. The :py:class:`~.signal.BaseSignal` method :py:meth:`~.signal.BaseSignal.set_signal_origin` changes the signal_origin in place, which may result in a :py:class:`~.signal.BaseSignal` subclass transformation. .. table:: BaseSignal subclass :py:attr:`~.signal.BaseSignal.metadata` attributes. +---------------------------------------------------------------+-----------+-------------+---------------+ | BaseSignal subclass | record_by | signal_type | signal_origin | +===============================================================+===========+=============+===============+ | :py:class:`~.signal.BaseSignal` | - | - | - | +---------------------------------------------------------------+-----------+-------------+---------------+ | :py:class:`~._signals.signal1d.Signal1D` | spectrum | - | - | +---------------------------------------------------------------+-----------+-------------+---------------+ | :py:class:`~._signals.spectrum_simulation.SpectrumSimulation` | spectrum | - | simulation | +---------------------------------------------------------------+-----------+-------------+---------------+ | :py:class:`~._signals.eels.EELSSpectrum` | spectrum | EELS | - | +---------------------------------------------------------------+-----------+-------------+---------------+ | :py:class:`~._signals.eds_sem.EDSSEMSpectrum` | spectrum | EDS_SEM | - | +---------------------------------------------------------------+-----------+-------------+---------------+ | :py:class:`~._signals.eds_tem.EDSTEMSpectrum` | spectrum | EDS_TEM | - | +---------------------------------------------------------------+-----------+-------------+---------------+ | :py:class:`~._signals.signal2d.Signal2D` | image | - | - | +---------------------------------------------------------------+-----------+-------------+---------------+ | :py:class:`~._signals.image_simulation.ImageSimulation` | image | - | simulation | +---------------------------------------------------------------+-----------+-------------+---------------+ The following example shows how to transform between different subclasses. .. code-block:: python >>> s = hs.signals.Signal1D(np.random.random((10,20,100))) >>> s >>> s.metadata ├── record_by = spectrum ├── signal_origin = ├── signal_type = └── title = >>> im = s.to_signal2D() >>> im >>> im.metadata ├── record_by = image ├── signal_origin = ├── signal_type = └── title = >>> s.set_signal_type("EELS") >>> s >>> s.set_signal_origin("simulation") >>> s The navigation and signal dimensions ------------------------------------ HyperSpy can deal with data of arbitrary dimensions. Each dimension is internally classified as either "navigation" or "signal" and the way this classification is done determines the behaviour of the signal. The concept is probably best understood with an example: let's imagine a three dimensional dataset. This dataset could be an spectrum image acquired by scanning over a sample in two dimensions. In HyperSpy's terminology the spectrum dimension would be the signal dimension and the two other dimensions would be the navigation dimensions. We could see the same dataset as an image stack instead. Actually it could has been acquired by capturing two dimensional images at different wavelengths. Then it would be natural to identify the two spatial dimensions as the signal dimensions and the wavelength dimension as the navigation dimension. However, for data analysis purposes, one may like to operate with an image stack as if it was a set of spectra or viceversa. One can easily switch between these two alternative ways of classifiying the dimensions of a three-dimensional dataset by :ref:`transforming between BaseSignal subclasses `. .. NOTE:: Although each dimension can be arbitrarily classified as "navigation dimension" or "signal dimension", for most common tasks there is no need to modify HyperSpy's default choice. .. _signal.binned: Binned and unbinned signals --------------------------- .. versionadded:: 0.7 Signals that are a histogram of a probability density function (pdf) should have the ``signal.metadata.Signal.binned`` attribute set to ``True``. This is because some methods operate differently in signals that are *binned*. The default value of the ``binned`` attribute is shown in the following table: .. table:: Binned default values for the different subclasses. +---------------------------------------------------------------+--------+ | BaseSignal subclass | binned | +===============================================================+========+ | :py:class:`~.signal.BaseSignal` | False | +---------------------------------------------------------------+--------+ | :py:class:`~._signals.signal1d.Signal1D` | False | +---------------------------------------------------------------+--------+ | :py:class:`~._signals.spectrum_simulation.SpectrumSimulation` | False | +---------------------------------------------------------------+--------+ | :py:class:`~._signals.eels.EELSSpectrum` | True | +---------------------------------------------------------------+--------+ | :py:class:`~._signals.eds_sem.EDSSEMSpectrum` | True | +---------------------------------------------------------------+--------+ | :py:class:`~._signals.eds_tem.EDSTEMSpectrum` | True | +---------------------------------------------------------------+--------+ | :py:class:`~._signals.signal2d.Signal2D` | False | +---------------------------------------------------------------+--------+ | :py:class:`~._signals.image_simulation.ImageSimulation` | False | +---------------------------------------------------------------+--------+ To change the default value: .. code-block:: python >>> s.metadata.Signal.binned = True 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 :py:class:`~.signal.BaseSignal` documentation. The methods of this section are available to all the signals. In other chapters methods that are only available in specialized subclasses. .. _signal.indexing: Indexing ^^^^^^^^ .. versionadded:: 0.6 .. versionchanged:: 0.8.1 Indexing a :py:class:`~.signal.BaseSignal` provides a powerful, convenient and Pythonic way to access and modify its data. In HyperSpy indexing is achieved using ``isig`` and ``inav``, which allow the navigation and signal dimensions to be indexed independently. The idea is essentially to specify a subset of the data based on its position in the array and it is therefore essential to know the convention adopted for specifying that position, which is described here. Those new to Python may find indexing a somewhat esoteric concept but once mastered it is one of the most powerful features of Python based code and greatly simplifies many common tasks. HyperSpy's Signal indexing is similar to numpy array indexing and those new to Python are encouraged to read the associated `numpy documentation on the subject `_. Key features of indexing in HyperSpy are as follows (note that some of these features differ from numpy): * HyperSpy indexing does: + Allow independent indexing of signal and navigation dimensions + Support indexing with decimal numbers. + Use the image order for indexing i.e. [x, y, z,...] (hyperspy) vs [...,z,y,x] (numpy) * HyperSpy indexing does not: + Support indexing using arrays. + Allow the addition of new axes using the newaxis object. The examples below illustrate a range of common indexing tasks. First consider indexing a single spectrum, which has only one signal dimension (and no navigation dimensions) so we use ``isig``: .. code-block:: python >>> s = hs.signals.Signal1D(np.arange(10)) >>> s >>> s.data array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) >>> s.isig[0] >>> s.isig[0].data array([0]) >>> s.isig[9].data array([9]) >>> s.isig[-1].data array([9]) >>> s.isig[:5] >>> s.isig[:5].data array([0, 1, 2, 3, 4]) >>> s.isig[5::-1] >>> s.isig[5::-1] >>> s.isig[5::2] >>> s.isig[5::2].data array([5, 7, 9]) Unlike numpy, HyperSpy supports indexing using decimal numbers, in which case HyperSpy indexes using the axis scales instead of the indices. .. code-block:: python >>> s = hs.signals.Signal1D(np.arange(10)) >>> s >>> s.data array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) >>> s.axes_manager[0].scale = 0.5 >>> s.axes_manager[0].axis array([ 0. , 0.5, 1. , 1.5, 2. , 2.5, 3. , 3.5, 4. , 4.5]) >>> s.isig[0.5:4.].data array([1, 2, 3, 4, 5, 6, 7]) >>> s.isig[0.5:4].data array([1, 2, 3]) >>> s.isig[0.5:4:2].data array([1, 3]) Importantly the original :py:class:`~.signal.BaseSignal` and its "indexed self" share their data and, therefore, modifying the value of the data in one modifies the same value in the other. Note also that in the example below s.data is used to access the data as a numpy array directly and this array is then indexed using numpy indexing. .. code-block:: python >>> s = hs.signals.Spectrum(np.arange(10)) >>> s >>> s.data array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) >>> si = s.isig[::2] >>> si.data array([0, 2, 4, 6, 8]) >>> si.data[:] = 10 >>> si.data array([10, 10, 10, 10, 10]) >>> s.data array([10, 1, 10, 3, 10, 5, 10, 7, 10, 9]) >>> s.data[:] = 0 >>> si.data array([0, 0, 0, 0, 0]) Of course it is also possible to use the same syntax to index multidimensional data treating navigation axes using ``inav`` and signal axes using ``isig``. .. code-block:: python >>> s = hs.signals.Signal1D(np.arange(2*3*4).reshape((2,3,4))) >>> s >>> s.data array([[[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]], [[12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23]]]) >>> s.axes_manager[0].name = 'x' >>> s.axes_manager[1].name = 'y' >>> s.axes_manager[2].name = 't' >>> s.axes_manager.signal_axes (,) >>> s.axes_manager.navigation_axes (, ) >>> s.inav[0,0].data array([0, 1, 2, 3]) >>> s.inav[0,0].axes_manager ,)> >>> s.inav[0,0].isig[::-1].data array([3, 2, 1, 0]) >>> s.isig[0] >>> s.isig[0].axes_manager , )> >>> s.isig[0].data array([[ 0, 4, 8], [12, 16, 20]]) Independent indexation of the signal and navigation dimensions is demonstrated further in the following: .. code-block:: python >>> s = hs.signals.Signal1D(np.arange(2*3*4).reshape((2,3,4))) >>> s >>> s.data array([[[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]], [[12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23]]]) >>> s.axes_manager[0].name = 'x' >>> s.axes_manager[1].name = 'y' >>> s.axes_manager[2].name = 't' >>> s.axes_manager.signal_axes (,) >>> s.axes_manager.navigation_axes (, ) >>> s.inav[0,0].data array([0, 1, 2, 3]) >>> s.inav[0,0].axes_manager ,)> >>> s.isig[0] >>> s.isig[0].axes_manager , )> >>> s.isig[0].data array([[ 0, 4, 8], [12, 16, 20]]) The same syntax can be used to set the data values in signal and navigation dimensions respectively: .. code-block:: python >>> s = hs.signals.Signal1D(np.arange(2*3*4).reshape((2,3,4))) >>> s >>> s.data array([[[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]], [[12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23]]]) >>> s.inav[0,0].data array([0, 1, 2, 3]) >>> s.inav[0,0] = 1 >>> s.inav[0,0].data array([1, 1, 1, 1]) >>> s.inav[0,0] = s[1,1] >>> s.inav[0,0].data array([16, 17, 18, 19]) .. _signal.operations: Signal operations ^^^^^^^^^^^^^^^^^ .. versionadded:: 0.6 .. versionadded:: 0.8.3 :py:class:`~.signal.BaseSignal` supports all the Python binary arithmetic opearations (+, -, \*, //, %, 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 `_ independently for the navigation and signal axes. 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 broacasted 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 >>> s2 >>> s + s2 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 >>> s2 >>> s + s2 Traceback (most recent call last): File "", line 1, in s + s2 File "", 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 Broacasting 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 >>> s2 >>> s + s2 In-place operators also support broadcasting, but only when broadcasting would not change the left most signal dimensions: .. code-block:: python >>> s += s2 >>> s >>> s2 += s Traceback (most recent call last): File "", line 1, in s2 += s File "", 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 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Signal 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.random((2, 5, 64,64))) >>> for single_image in image_stack: ... single_image.save("image %s.png" % str(image_stack.axes_manager.indices)) 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 :py:func:`~.utils.stack` function in combination with `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.misc.lena()]*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) >>> collage = hs.stack([image for image in image_stack], axis=0) >>> collage.plot() .. figure:: images/rotate_lena.png :align: center :width: 500 Rotation of images by iteration. .. versionadded:: 0.7 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 :py:meth:`~.signal.BaseSignal.map` method: .. code-block:: python >>> import scipy.ndimage >>> image_stack = hs.signals.Signal2D(np.array([scipy.misc.lena()]*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) >>> collage = hs.stack([image for image in image_stack], axis=0) >>> collage.plot() .. figure:: images/rotate_lena_apply_simple.png :align: center :width: 500 Rotation of images by the same amount using :py:meth:`~.signal.BaseSignal.map`. The :py:meth:`~.signal.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.misc.lena()]*4)) >>> image_stack.axes_manager[1].name = "x" >>> image_stack.axes_manager[2].name = "y" >>> angles = hs.signals.Signal(np.array([0, 45, 90, 135])) >>> angles.axes_manager.set_signal_dimension(0) >>> modes = hs.signals.Signal(np.array(['constant', 'nearest', 'reflect', 'wrap'])) >>> modes.axes_manager.set_signal_dimension(0) >>> image_stack.map(scipy.ndimage.rotate, ... angle=angles, ... reshape=False, ... mode=modes) calculating 100% |#############################################| ETA: 00:00:00Cropping .. figure:: images/rotate_lena_apply_ndkwargs.png :align: center :width: 500 Rotation of images using :py:meth:`~.signal.BaseSignal.map` with different arguments for each image in the stack. 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 ` or :ref:`signal2D `. There is also a general :py:meth:`~.signal.BaseSignal.crop` method that operates *in place*. Rebinning ^^^^^^^^^ The :py:meth:`~.signal.BaseSignal.rebin` method rebins data in place down to a size determined by the user. 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: * :py:meth:`~.signal.BaseSignal.fold` * :py:meth:`~.signal.BaseSignal.unfold` It is also possible to unfold only the navigation or only the signal space: * :py:meth:`~.signal.BaseSignal.unfold_navigation_space` * :py:meth:`~.signal.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 :py:func:`~.utils.stack` function, if they share axis with same dimension. .. code-block:: python >>> image = hs.signals.Signal2D(scipy.misc.lena()) >>> image = hs.stack([hs.stack([image]*3,axis=0)]*3,axis=1) >>> image.plot() .. figure:: images/stack_lena_3_3.png :align: center :width: 500 Stacking example. An object can be splitted into several objects with the :py:meth:`~.signal.BaseSignal.split` method. This function can be used to reverse the :py:func:`~.utils.stack` function: .. code-block:: python >>> image = image.split()[0].split()[0] >>> image.plot() .. figure:: images/split_lena_3_3.png :align: center :width: 400 Splitting example. Simple operations over one axis ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ * :py:meth:`~.signal.BaseSignal.sum` * :py:meth:`~.signal.BaseSignal.mean` * :py:meth:`~.signal.BaseSignal.max` * :py:meth:`~.signal.BaseSignal.min` * :py:meth:`~.signal.BaseSignal.std` * :py:meth:`~.signal.BaseSignal.var` * :py:meth:`~.signal.BaseSignal.diff` * :py:meth:`~.signal.BaseSignal.derivative` * :py:meth:`~.signal.BaseSignal.integrate_simpson` .. _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 :py:meth:`~.signal.BaseSignal.change_dtype` changes the data type in place, e.g.: .. code-block:: python >>> s = hs.load('EELS Spectrum Image (high-loss).dm3') Title: EELS Spectrum Image (high-loss).dm3 Signal type: EELS Data dimensions: (21, 42, 2048) Data representation: spectrum Data type: float32 >>> s.change_dtype('float64') >>> print(s) Title: EELS Spectrum Image (high-loss).dm3 Signal type: EELS Data dimensions: (21, 42, 2048) Data representation: spectrum Data type: float64 .. versionadded:: 0.7 In addition to all standard numpy dtypes HyperSpy supports four extra dtypes for RGB images: rgb8, rgba8, rgb16 and rgba16. Changing from and to any rgbx dtype is more constrained than most other dtype conversions. To change to a rgbx dtype the signal `record_by` must be "spectrum", `signal_dimension` must be 3(4) for rgb(rgba) dtypes and the dtype must be uint8(uint16) for rgbx8(rgbx16). After conversion `record_by` becomes `image` and the spectra dimension is removed. The dtype of images of dtype rgbx8(rgbx16) can only be changed to uint8(uint16) and the `record_by` becomes "spectrum". In the following example we create .. 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 >>> s.change_dtype("rgb16") >>> s >>> s.plot() .. figure:: images/rgb_example.png :align: center :width: 500 RGB data type example. Basic statistical analysis -------------------------- .. versionadded:: 0.7 :py:meth:`~.signal.BaseSignal.get_histogram` computes the histogram and conveniently returns it as signal instance. It provides methods to calculate the bins. :py:meth:`~.signal.BaseSignal.print_summary_statistics` prints the five-number summary statistics of the data. These two methods can be combined with :py:meth:`~.signal.BaseSignal.get_current_signal` to compute the histogram or print the summary stastics of the signal at the current coordinates, e.g: .. code-block:: python >>> s = hs.signals.EELSSpectrum(np.random.normal(size=(10,100))) >>> s.print_summary_statistics() Summary statistics ------------------ mean: 0.021 std: 0.957 min: -3.991 Q1: -0.608 median: 0.013 Q3: 0.652 max: 2.751 >>> s.get_current_signal().print_summary_statistics() Summary statistics ------------------ mean: -0.019 std: 0.855 min: -2.803 Q1: -0.451 median: -0.038 Q3: 0.484 max: 1.992 Histogram of different objects can be compared with the functions :py:func:`~.drawing.utils.plot_histograms` (see :ref:`visualisation ` for the plotting options). For example, with histograms of several random chi-square distributions: .. code-block:: python >>> img = hs.signals.Signal2D([np.random.chisquare(i+1,[100,100]) for i in range(5)]) >>> hs.plot.plot_histograms(img,legend='auto') .. figure:: images/plot_histograms_chisquare.png :align: center :width: 500 Comparing histograms. .. _signal.noise_properties: Setting the noise properties ---------------------------- Some data operations require the data variance. Those methods use the ``metadata.Signal.Noise_properties.variance`` attribute if it exists. You can set this attribute as in the following example where we set the variance to be 10: .. code-block:: python s.metadata.Signal.set_item("Noise_properties.variance", 10) For heterocedastic noise the ``variance`` attribute must be a :class:`~.signal_base.BaseSignal`. Poissonian noise is a common case of heterocedastic noise where the variance is equal to the expected value. The :meth:`~.signal_base.BaseSignal.estimate_poissonian_noise_variance` :class:`~.signal_base.BaseSignal` method can help setting the variance of data with semi-poissonian noise. With the default arguments, this method simply sets the variance attribute to the given ``expected_value``. However, more generally (although then noise is not strictly poissonian), the variance may be proportional to the expected value. Moreover, when the noise is a mixture of white (gaussian) and poissonian noise, the variance is described by the following linear model: .. math:: \mathrm{Var}[X] = (a * \mathrm{E}[X] + b) * c Where `a` is the ``gain_factor``, `b` is the ``gain_offset`` (the gaussian noise variance) and `c` the ``correlation_factor``. The correlation factor accounts for correlation of adjacent signal elements that can be modeled as a convolution with a gaussian point spread function. :meth:`~.signal.BaseSignal.estimate_poissonian_noise_variance` can be used to set the noise properties when the variance can be described by this linear model, for example: .. code-block:: python >>> s = hs.signals.SpectrumSimulation(np.ones(100)) >>> s.add_poissonian_noise() >>> s.metadata ├── General │ └── title = └── Signal ├── binned = False ├── record_by = spectrum ├── signal_origin = simulation └── signal_type = >>> s.estimate_poissonian_noise_variance() >>> s.metadata ├── General │ └── title = └── Signal ├── Noise_properties │ ├── Variance_linear_model │ │ ├── correlation_factor = 1 │ │ ├── gain_factor = 1 │ │ └── gain_offset = 0 │ └── variance = ├── binned = False ├── record_by = spectrum ├── signal_origin = simulation └── signal_type =