# 2. Basic Concepts¶

## 2.1. Data¶

The data is stored in a tree-like structure. The root element is the *project*.
The next lower level is that of the *plots*, each of which can hold an arbitrary
number of *sets*. A *set* is a 2d array containing the x-y data, where the
x-data is ordered (typical for spectroscopic data). This data structure is
represented by the tree view on the right side of the main window. In addition
to the plain x-y data, a set can have various objects attached, such as
transformations (*trafo*), a fit *model* and *weights*.

Unlike many other data analysis programs, peak-o-mat allows for data
manipulation/transformation on a higher level than operating on the raw data
through a spreadsheet like interface. As peak-o-mat is especially designed to
work with spectroscopic data, arithmetics on *sets* will do what you would
expect intuitively, e.g. adding two *sets* will only add the y-data, while
interpolating the x-axes in case they differ. Those kind of manipulations can be
done using the ‘Set operations’ module. If you need to do more complicate
operations, you can still copy the data to a *data grid* and manipulate the data
there by means of a python shell.

## 2.2. Models¶

A *model* is a function ofone ore more parameters which is fitted to
the data. It may be described by

- a valid python expression, where
*x*stands for the set’s x-values. You can use arbitrary variable names containing alphanumeric characters, e.g. “a*x-b0*x**2”. Also, all mathematical functions, which are defined in the toplevel namespace of the python*numpy*package are avilable. In the model expression the function name has to be prefixed by*np.*, e.g. “amp*np.exp(-x/beta)”. In case the model is too complicated to be entered in a single line, or you just need more flexibility, you can use your own python functions as model. Physical constants are available through prefixing their common name by ‘c_’, e.g. ‘c_e’ referes to the elementary charge. See the ‘customisation’ section for how to define custom functions and add constants. - a space separated list of pre-defined symbols, here called
*tokens*, which represent common background and peak shapes. The function values represented by the tokens are finally added, e.g. “CB LO GA LO” represents a model with a constant background, one gaussian peak and two lorenzian peak shapes. You can append a number to any token to be able to distinguish them later, e.g. “CB LO1 GA LO2”. Instead of the whitespace between the tokens, the ‘+’ operator can be used. In some rare cases you might want to multiply the function represented by the tokens. This can be achieved by using the ‘*’ operator. The model is evaluated from left to right and the usual sign rules do not apply. You may define customs tokens similar to the definition of custom functions. See the ‘customisation’ section for details.

Once a model has been fitted to a data set, the model including the fitted parameters is attached to the set and whenever the set is selected, the model is evaluated and displayed together with the data.

## 2.3. Transformations and masks¶

A *trafo* denotes any transformation of the x- or y-data of a set. Instead of
changing the original data, all trafos are attached to a data set and evaluated
on demand whenever the set data is accessed. Like this, the original data can
be restored by simply removing all trafos. Furthermore, if you remove bad data
points from a set, a *mask* is applied to the data so that all points can be
restored at any time. Use the popup menu in the tree view to unset a mask or
remove the transformations attached to the currently selected sets. The ‘Set
Info’ model allows for manipulation of every single transformation of a set. The
transformation expresseion can be changed, transformations can be deactivated
and both masks and tranformations can be made permanent, i.e. they are applied
once and the original data is overwritten with the result from the evaluation.

## 2.4. Weights¶

The residuals of a fit may be weighted in order to improve the fit but this is not in particular meant to reduce the effect of outliers on the fit, as those can be erased before fitting. In spectrosopy it is quite common that only a part of the measured data, i.e. in a certain region of the independent variable can be sufficiently well described by a model and that the data is overlayed by the results of unknown physical and/or measurement effects. In that sense you may want to assign low weights to regions which you are not interested in and high weights in regions where the model should work well. Though talking of weights, you actually specify the standard deviation of the data rather than the weight of the residual which is just the inverse of the standard deviation.