Writing a custom model

Writing a model is quite easy in GenX. There is a couple of things one need to keep in mind in order to successful which will be covered in this tutorial. The only mandatory thing the model file has to contain is a function called Sim taking a member of the class Data as input parameter. However, to make the model useful, functions for setting the values have to be incorporated. Note that GenX uses function to set the parameters during fitting, this is why we need to have them.

Programming Python

Since writing a model actually involves writing a script in Python it is good to have some basic knowledge of the syntax. However, if you have some basic knowledge about programming it should be fairly easy to just look at the examples and write your own models without having to learn to program in Python. On the other hand, there exists a number of free introductory books as well as tutorials on the internet for the interested reader, see below.

In addition there are a number of tutorials on SciPy’s homepage which deal w ith numerical computations. There is also a migration guide for those who are familiar with MatLab.

The Data class

In order to write the Sim class it is necessary to know the structure of the class Data which is taken as a parameter. The variables which could be useful in the Sim function are:

  • x A list of 1-D arrays (vectors) containing the x-values of the processed data
  • y A list of 1-D arrays (vectors) containing the y-values of the processed data
  • xraw A list of 1-D arrays (vectors) containing the raw x-values (the data loaded from the data file)
  • yraw A list of 1-D arrays (vectors) containing the raw y-values (the data loaded from the data file)
  • use A list of booleans (True or False) denoting if the data should be fitted

Simple example

Knowing what the Data class contains we will start with a simple example, making a model that fits one Gaussian to the first data set. The free parameters of the Gaussian are; the center of the peak, Xc, the peak width, W, and the amplitude of the peak, A. Writing a model for it would produce a code as shown below. Note that a # produce a comment.

# Create a class for user variables
MyVar=UserVars()
# Create your variables + set the initial values
MyVar.newVar(’A’,1.0)
MyVar.newVar(’W’,2.0)
MyVar.newVar(’Xc’,0.0)

# Define the function for a Gaussian
# i.e. definition of the model
def Gaussian(x):
   return MyVar.A*exp((x-MyVar.Xc)**2/MyVar.W**2)

# Define the function Sim
def Sim(data):
   # Calculate the Gaussian
   I=Gauss(data[0].x)
   # The returned value has to be a list
   return [I]

The following is a brief description of the code above. First an object of the class UserVars? is created. This object is used to store user defined variables. Then the variables are initialized (created) with their names given as strings. After that a function for calculating a Gaussian variable is created. The function takes an array of x values as input parameters and returns the calculated y-values. At last the Sim function is defined. The function Gauss is called to calculate the y-values with the x-data as the input argument. The x-values of the first data set are extracted as data.x[0], and those of the second data set would be extracted by data.x[1]. Note that a list is returned by taking the array (vector) I and making a list with one element. Note that this requires that only one data set has been loaded. In order to fit the parameters created in by MyVar the user only has to right click on a cell in the grid of the Parameter Window and choose the MyVar.set[Name] function, i.e. MyVar.setA.

Making a class

The code above is usually sufficient for prototyping and simple problems. For more complex models it is recommended to write a library. This is what has been done for the simulation of x-ray reflectivity data. Also, instead of writing a lot of functions for each model, a class, or several, can be written to make the model simple to use. As a more elaborate example the previous simple example can be transformed into a class:

# Definition of the class
class Gauss:
    # A class for a Gaussian
    # The creator of the class
    def __init__(self,w=1.0,xc=0.0,A=1.0):
        self.w=w
        self.xc=xc
        self.A=A

    # The set functions used in the parameters column
    def setW(w):
    self.w=w

    def setXc(xc):
        self.xc=xc

    def setA(A):
        self.A=A

    # The function to calculate the model (A Gaussian)
    def Simulate(x):
        return A*exp((x-self.xc)**2/self.w**2)

# Make a Gaussian:
Peak1=Gauss(w=2.0,xc=1.5,A=2.0)

def Sim(data):
    # Calculate the Gaussian
    I=Peak1.Simulate(data[0].x)
    # The returned value has to be a list
    return [I]

This code is quite similar to the first version with only functions. It starts with the definition of the class Gauss. This class has a constructor, init, to initialize the parameters of the object and functions to set the member variables, denoted as self.*. It also contains a member function to calculate a Gaussian with the member variables. After the class definition an object, Peak1, of the Gauss class is created. Then the Sim function is defined as in the previous example but with the function call exchanged to Peak1.Simulate(data.x[0]) in order to simulate the object Peak1. The function names that should go into the parameter column in the parameter window will be: Peak1.setW, Peak1.setXc and Peak1.setA.

Multiple Gaussians

Making the model based on a class makes it easier to extend. For example if two peaks should be fitted the class does not have to be changed. Instead an additional object of the class Gauss, for example called Peak2, can be created and the two contributions are then added in the Sim function. The code would then be modified to (omitting the class definition):

# Insert the class definition from above
# Make Gaussians:
Peak1=Gauss(w=2.0,xc=1.5,A=2.0)
Peak2=Gauss(w=2.0,xc=1.5,A=2.0)

def Sim(data):
    # Calculate the Gaussian
    I=Peak1.Simulate(data[0].x)+Peak2.Simulate(data[0].x)
    # The returned value has to be a list
    return [I]

Thus, for fitting the parameters for the second Gaussian the functions used should be Peak2.setW, Peak2.setXc and Peak2.setA.

Parameter coupling

When the base class is created it can be extended with more problem oriented constraints by using functions as in the first example. For example, in some cases it might be known that the width of the two Gaussians should be the same. This can be solved by defining a new variable:

#Insert the class definition from above
# Make Gaussians:
Peak1=Gauss(w=2.0,xc=1.5,A=2.0)
Peak2=Gauss(w=2.0,xc=1.5,A=2.0)
# Create a class for user variables
MyVar=UserVars()
# Create your variables + set the initial values
MyVar.newVar(’BothW’,1.0)

def Sim(data):
    Peak1.setW(MyVar.BothW)
    Peak2.setW(MyVar.BothW)
    # Calculate the Gaussian
    I=Peak1.Simulate(data[0].x)+Peak2.Simulate(data[0].x)
    # The returned value has to be a list
    return [I]

Instead of using the *.setW methods the MyVar.setBothW can be used, which is automatically created by the MyVar class. In summary it is recommended that the models implemented in libraries are defined as classes and that these are as general as possible with respect to the parameters. The specific parameter couplings can be included as functions in the model file. The methods shown with the examples in this section also apply to the libraries included for x-ray reflectivity. The classes are different but the general use is the same.