Modeling Van der Waal’s Equation With Chaco and Traits

Overview

This tutorial walks through the creation of an example program that plots a scientific equation. In particular, we will model Van Der Waal’s Equation, which is a modification to the ideal gas law that takes into account the nonzero size of molecules and the attraction to each other that they experience.

Development Setup

In review, Traits is a manifest typing and reactive programming package for Python. It also provides UI features that will be used to create a simple GUI. The Traits and Traits UI user manuals are good resources for learning about the packages and can be found on the Traits Wiki. The wiki includes features, technical notes, cookbooks, FAQ and more.

You must have Chaco and its dependencies installed:

  • Traits
  • TraitsGUI
  • Enable

Writing the Program

First, define a Traits class and the elements necessary need to model the task. The following Traits class is made for the Van Der Waal equation, whose variables can be viewed on this wiki page. The volume and pressure attributes hold lists of our X- and Y-coordinates, respectively, and are defined as arrays. The attributes attraction and totVolume are input parameters specified by the user. The type of the variables dictates their appearance in the GUI. For example, attraction and totVolume are defined as Ranges, so they show up as slider bars. Likewise, plot_type is shown as a drop-down list, since it is defined as an Enum.

# We'll also import a few things to be used later.
from enthought.traits.api \
    import HasTraits, Array, Range, Float, Enum, on_trait_change, Property
from enthought.traits.ui.api import View, Item
from enthought.chaco.chaco_plot_editor import ChacoPlotItem
from numpy import arange

class Data(HasTraits):
    volume = Array
    pressure = Array
    attraction = Range(low=-50.0,high=50.0,value=0.0)
    totVolume = Range(low=.01,high=100.0,value=0.01)
    temperature = Range(low=-50.0,high=50.0,value=50.0)
    r_constant= Float(8.314472)
    plot_type = Enum("line", "scatter")

....

Creating the View

The main GUI window is created by defining a Traits View instance. This View contains all of the GUI elements, including the plot. To link a variable with a widget element on the GUI, we create a Traits Item instance with the same name as the variable and pass it as an argument of the Traits View instance declaration. The Traits UI User Guide discusses the View and Item objects in depth. In order to embed a Chaco plot into a Traits View, you need to import the ChacoPlotItem class, which can be passed as a parameter to View just like the Item objects. The first two arguments to ChacoPlotItem are the lists of X- and Y-coordinates for the graph. The attributes volume and pressure hold the lists of X- and Y-coordinates, and therefore are the first two arguments to Chaco2PlotItem. Other parameters have been provided to the plot for additional customization:

class Data(HasTraits):
    ....

    traits_view = View(ChacoPlotItem("volume", "pressure",
                               type_trait="plot_type",
                               resizable=True,
                               x_label="Volume",
                               y_label="Pressure",
                               x_bounds=(-10,120),
                               x_auto=False,
                               y_bounds=(-2000,4000),
                               y_auto=False,
                               color="blue",
                               bgcolor="white",
                               border_visible=True,
                               border_width=1,
                               title='Pressure vs. Volume',
                               padding_bg_color="lightgray"),
                       Item(name='attraction'),
                       Item(name='totVolume'),
                       Item(name='temperature'),
                       Item(name='r_constant', style='readonly'),
                       Item(name='plot_type'),
                       resizable = True,
                       buttons = ["OK"],
                       title='Van der Waal Equation',
                       width=900, height=800)
....

Updating the Plot

The power of Traits and Chaco enables the plot to update itself whenever the X- or Y-arrays are changed. So, we need a function to re-calculate the X- and Y-coordinate lists whenever the input parameters are changed by the user moving the sliders in the GUI.

The volume attribute is the independent variable and pressure is the dependent variable. The relationship between pressure and volume, as derived from the equation found on the wiki page, is:

            r_constant * Temperature       attraction
Pressure =  ------------------------   -   ----------
               Volume - totVolume          Volume**2

Next, there are two programing tasks to complete:

  1. Define trait listener methods for your input parameters. These methods are automatically called whenever the parameters are changed, since it will be time to recalculate the pressure array.
  2. Write a calculation method that updates your lists of X- and Y-coordinates for your plot.

The following is the code for these two needs:

# Re-calculate when attraction, totVolume, or temperature are changed.
@on_trait_change('attraction, totVolume, temperature')
def calc(self):
    """ Update the data based on the numbers specified by the user. """
    self.volume = arange(.1, 100)
    self.pressure = ((self.r_constant*self.temperature)
                     /(self.volume - self.totVolume)
                    -(self.attraction/(self.volume*self.volume)))
    return

The calc() function computes the pressure array using the current values of the independent variables. Meanwhile, the @on_trait_change() decorator (provided by Traits) tells Python to call calc() whenever any of the attributes attraction, totVolume, or temperature changes.

Testing your Program

The application is complete, and can be tested by instantiating a copy of the class and then creating the view by calling the configure_traits() method on the class. For a simple test, run these lines from an interpreter or a separate module:

from vanderwaals import Data
viewer = Data()
viewer.calc()            # Must calculate the initial (x,y) lists
viewer.configure_traits()

Clicking and dragging on the sliders in the GUI dynamically updates the pressure data array, and causes the plot to update, showing the new values.

Screenshots

Here is what the program looks like:

../_images/vanderwaals.png

But it could be better....

It seems inconvenient to have to call a calculation function manually before we call configure_traits(). Also, the pressure equation depends on the values of other variables. It would be nice to make the relationship between the dependant and independent variables clearer. There is another way we could define our variables that is easier for the user to understand, and provides better source documentation.

Since our X-values remain constant in this example, it is wasteful to keep recreating the volume array. The Y-array, pressure, is the single array that needs to be updated when the independent variables change. So, instead of defining pressure as an Array, we define it as a Property. Property is a Traits type that allows you to define a variable whose value is recalculated whenever it is requested. In addition, when the depends_on argument of a Property constructor is set to list of traits in your HasTraits class, the property’s trait events fire whenever any of the dependent trait’s change events fire. This means that the pressure attribute fires a trait change whenever our depends_on traits are changed. Meanwhile, the Chaco plot is automatically listening to the pressure attribute, so the plot display gets the new value of pressure whenever someone changes the input parameters!

When the value of a Property trait is requested, the _get_trait_name method is called to calculate and return its current value. So we define use the _get_pressure() method as our new calculation method. It is important to note that this implementation does have a weakness. Since we are calculating new pressures each time someone changes the value of the input variables, this could slow down the program if the calculation is long. When the user drags a slider widget, each stopping point along the slider requests a recompute.

For the new implementation, these are the necessary changes:

  1. Define the Y-coordinate array variable as a Property instead of an Array.
  2. Perform the calculations in the _get_trait_name method for the Y-coordinate array variable, which is _get_pressure() in this example.
  3. Define the _trait_default method to set the initial value of the X-coordinate array, so _get_pressure() does not have to keep recalculating it.
  4. Remove the previous @on_trait_change() decorator and calculation method.

The new pieces of code to add to the Data class are:

class Data(HasTraits):
    ...
    pressure = Property(Array, depends_on=['temperature',
                                           'attraction',
                                           'totVolume'])
    ...

    def _volume_default(self):
      return arange(.1, 100)

    # Pressure is recalculated whenever one of the elements the property
    # depends on changes.  No need to use @on_trait_change.
    def _get_pressure(self):
      return ((self.r_constant*self.temperature)
              /(self.volume - self.totVolume)
             -(self.attraction/(self.volume*self.volume)))

You now no longer have to call an inconvenient calculation function before the first call to configure_traits()!

Source Code

The final version on the program, vanderwaals.py

from enthought.traits.api \
    import HasTraits, Array, Range, Float, Enum, on_trait_change, Property
from enthought.traits.ui.api import View, Item
from enthought.chaco.chaco_plot_editor import ChacoPlotItem
from numpy import arange

class Data(HasTraits):
    volume = Array
    pressure = Property(Array, depends_on=['temperature', 'attraction',
                                       'totVolume'])
    attraction = Range(low=-50.0,high=50.0,value=0.0)
    totVolume = Range(low=.01,high=100.0,value=0.01)
    temperature = Range(low=-50.0,high=50.0,value=50.0)
    r_constant= Float(8.314472)
    plot_type = Enum("line", "scatter")

    traits_view = View(ChacoPlotItem("volume", "pressure",
                               type_trait="plot_type",
                               resizable=True,
                               x_label="Volume",
                               y_label="Pressure",
                               x_bounds=(-10,120),
                               x_auto=False,
                               y_bounds=(-2000,4000),
                               y_auto=False,
                               color="blue",
                               bgcolor="white",
                               border_visible=True,
                               border_width=1,
                               title='Pressure vs. Volume',
                               padding_bg_color="lightgray"),
                       Item(name='attraction'),
                       Item(name='totVolume'),
                       Item(name='temperature'),
                       Item(name='r_constant', style='readonly'),
                       Item(name='plot_type'),
                       resizable = True,
                       buttons = ["OK"],
                       title='Van der Waal Equation',
                       width=900, height=800)


    def _volume_default(self):
        """ Default handler for volume Trait Array. """
        return arange(.1, 100)

    def _get_pressure(self):
        """Recalculate when one a trait the property depends on changes."""
        return ((self.r_constant*self.temperature)
              /(self.volume - self.totVolume)
             -(self.attraction/(self.volume*self.volume)))

if __name__ == '__main__':
    viewer = Data()
    viewer.configure_traits()