# Tag: Software

### Plotting multivariate data with Matplotlib/Pylab: Edgar Anderson’s Iris flower data set

The problem of how to visualize multivariate data sets is something I often face in my work. When using numerical optimization we might have a single objective function and multiple design variables that can be represented by columnar data in the form {x1, x2, x3, … xn, y} a.k.a. NXY. With design spaces of more than a few dimensions it is difficult to visualize them in order to estimate the relationship between each independent variable and the objective, or perform a sensitivity study.

JensG / Pixabay

While perusing recent work in and tools for visualizing such data I stumbled across some nice examples of multivariate data plotting using a famous data set known as the “Iris data set”, also known as Fisher’s Iris data set or Edgar Anderson’s Iris flower data set. It contains data from 50 flowers each of three different flower species, collected in the Gaspé Peninsula. This set is not in the NXY form typical of optimization routines, but instead each flower has a number of parameters measured and tabulated; namely sepal length, sepal width, petal length and petal width. In other words there is no resultant Y data that is a function of the design space vector. Instead, it is interesting to plot relationships between the measured parameters to determine if they correlate with each other.

A quick internet search brings up a number of examples where the set has been plotted as a gridded set of subplots, using various software tools. For example, Mike Bostock’s blog post demonstrating his D3.js package, and the version on the wikipedia page.

I decided to try and code a Matplotlib script to generate a similar gridded multiplot from the data set. I did so within a Jupyter Notebook (formerly known as iPython Notebook) running Python 2.7. The data was imported using Pandas and made use of Matplotlib’s Pyplot module. Pandas was used to import the data but it could have been done in a number of different ways; it is just that Pandas is designed to work with csv files containing a mix of types.

The resulting image can be seen below.

Fisher’s Iris data set sometimes known as Anderson’s Iris data set, visualization by Simon Bance using Matplotlib/Pyplot. A multivariate data set introduced by Ronald Fisher in 1936 from data collected by Edgar Anderson on Iris flowers in the Gaspé Peninsula.

Here is the script:

```
"""
https://en.wikipedia.org/wiki/Iris_flower_data_set
A script for plotting multivariate tabular data as gridded scatter plots.
"""
import os
import pandas as pd
import matplotlib.pyplot as plt

inFile = r'iris.dat'

# Check if data file exists:
if not os.path.exists(inFile): sys.exit("File %s does not exist" % inFile)

rootFolder = os.path.dirname(os.path.abspath(inFile))

# Read in the data file
df.head(5) # Prints first n lines to check if we loaded the data file as expected.

# We also have n=4 distinct species in the Species column and I will
# list the species names so we can distinguish them later for plotting:
species = list(df.Species.unique()) # normal python list, thank you very much!
print type(species)

# Here we specify how many columns prepend and append the columns that we want to use.
# For Dakota this would include the objective function(s) column(s) appended to the end.
num_precols = 0
num_obj_fn = 1

# Work out the number of dimensions in each design vector:
num_dims = df.shape[1] - num_obj_fn # We know that there are 3 additional columns (and hope that it stays consistent in future)!
print "Our design vector has %s dimensions: %s" % (num_dims, headers[num_precols:-1])
gridshape = (num_dims, num_dims)
num_plots = num_dims**2
print "Our multivariate grid will therefore be of shape", gridshape, "with a total of", num_plots, "plots"

# Plot the data in a grid of subplots.
fig = plt.figure(figsize=(12, 12))

# Iterate over the correct number of plots.
n = 1

# Create an empty 2D list to store created axes. This alows us to edit them somehow.
axes = [[False for i in range(num_dims)] for j in range(num_dims)]

for j in range(num_dims):
for i in range(num_dims):

# e.g. plt.subplot(nx, ny, plotnumber)
ax = fig.add_subplot(num_dims, num_dims, n) # Plot numbering in this case starts from 1 not zero (MATLAB style indexing)!

# Choose your list of colours
colors = ['red', 'green', 'blue']

for index, s in enumerate(species):

# x axis: For each in the species list look at all rows with that value in the Species column.
# Use the ith column of that subset as the x series.
# y axis: Likewisem, but use the jth column.

if i != j:
ax.scatter(df.where(df['Species'] == s).ix[:,i], df.where(df['Species'] == s).ix[:,j], color=colors[index], label=s)
else:
# Put the variable name on the i=j subplots:
pass

# Set axis labels:

# Hide axes for all but the plots on the edge:
if j &lt; num_dims - 1: ax.xaxis.set_visible(False) if i &gt; 0:
ax.yaxis.set_visible(False)

if i == 1 and j == 0:
ax.legend(bbox_to_anchor=(3.5, 1), loc=2, borderaxespad=0., title="Species name:")

# Add this axis to the list.
axes[j][i] = ax

n += 1

plt.savefig("%s/iris.png" % rootFolder, dpi=300)
plt.show()

```

Further so-called “classic data sets” are listed at https://en.wikipedia.org/wiki/Data_set#Classic_data_sets.

### The new default colormap for matplotlib is called “viridis” and it’s great!

It’s probably not news to anyone in data visualization that the most-used “jet” colormap (sic) (sometimes referred to as “rainbow”) is a bad choice for many reasons.

• Doesn’t work when printed black & white
• Doesn’t work well for colourblind people
• Not linear in colour space, so it’s hard to estimate numerical values from the resulting image

The Matlab team recently developed a new colormap called “parula” but amazingly because Matlab is commercially-licensed software no-one else is allowed to use it!
The guys at Matplotlib have therefore developed their own version, based on the principles of colour theory (covered in my own BSc lecture courses on Visualization 🙂 ) that is actually an improvement on parula. The new Matplotlib default colormap is named “viridis” and you can learn all about it in the following lecture from the SciPy 2015 conference (YouTube ):

Viridis will be the new default colour map from Matplotlib 2.0 onwards, but users of v1.5.1 can also choose to use it using the `cmap=plt.cm.viridis` command.
I don’t know about you, but I like it a lot and will start using it immediately!

## Science via email

One thing scientists and engineers have to do daily is discuss collaborative work via email exchanges. This often includes the need to share and discuss mathematical equations and to represent variables with subscripts and superscripts or special characters; something that is tricky when you are emailing in plain text.

WikiImages / Pixabay

Of course it is possible to work around this problem! Email was invented by scientists, and for decades they have been communicating in this manner, using various conventions to convey the correct information using plaintext. However, if you are a Gmail user there is a nice extension that will make your equations look proper good.

## Tex for Gmail

TeX for Gmail is a Chrome browser extension that checks a Gmail email that you are writing for LaTeX markup and converts the markup to a visually prettier equation, using one of two modes. In Simple Math mode, subscripts and superscripts are correctly formatted but the current font is maintained and text remains ediatble. In Rich Math mode, the equation is rendered into TeX and replaced by an embedded image.  The email recipient doesn’t need the extension installed on their browser in order to read your nice equations!

### Example

Original markup:

\$E = mc^{2}\$

Simple Math mode:

E = mc2

Rich Math mode:
$\dpi{300}\inline E = mc^{2}$

## Issues

One problem; once the extension has converted my markup to formatted text, I cannot get the markup back. So editing a small mistake usually means re-doing all the curly brackets and other stuff that a TeX equation requires. The only workaround seems to be to stay vigilant and use Undo (Ctrl-z), but this doesn’t work when you notice a mistake in an equation that you wrote a while ago. One improvement could be the option to restore any equation to the original markup.

## Conclusions

Overall, a great little tool to improve the clarity of science and maths communications over email. With a few small improvements it could be even better but it is already very usable.

### 5 Tips for making finite element models with Salome

Salome is an open source software package used to create geometric models and finite element meshes for use in numerical simulations. It is also able to perform its own numerical simulations and has post-processing capabilities built in.

Here are my 5 tips for anyone who is interested in using Salome for model and mesh creation.

## 1. Practice manually first

This goes without saying. Although Salome has a powerful Python-based scripting capability, it is worth practicing with manual model generation. By that I mean, clicking with your mouse in the GUI. Manual practice lets you get familiar with the quirks of the Salome workflow, which has a different mentality to many other model generator programs.

## 2. Use the Notebook

In Salome the Notebook is a useful tool that allows you to set size parameters in the beginning as model variables. This means that later on you can edit the notebook variable values and re-build the model using different sizes; something that cannot be done normally, while typing size values in to construct geometric objects. The Notebook is like having some of the power of scripting while still making the model manually in the GUI. A great halfway step up to full scripting.

## 3. Learn to use scripting

Once you are familiar with Salome’s way of thinking, automation through scripting can become a critical component of being productive. Often it is necessary to compare many similar models where just one specific parameter (say the size of some part) is being changed.

In this recent paper we had to compare the effects of different soft magnetic defect thicknesses in a permanent magnetic grain.  By scripting the model generation I was able to rapidly generate similar models from one template script.

## 4. Small size adjustments can get you out of a rut

Sometimes with Salome (and actually with other modelling software too) you find an annoying problem that makes no sense. For example, you made the model with no problems but now you increased the size of part A and it doesn’t want to build anymore. These kind of problems can occur because designing such a powerful piece of software to work universally is hard. You might be attempting something that the software designers did not anticipate.

One trick that often works for me goes like this. Change the parameter again by a small, arbitrary amount. If size A is 100 nm large, try changing it to 100.001. The simulation result will be virtually identical but you might find the model generation can now function without problems.

I remember in an earlier version of GiD, doing a boolean volume operation on two objects would fail if the edges of the objects overlapped perfectly. So I always had to make sure to translate one of the objects by a tiny amount. Then the Boolean operation would usually work. The makers of GiD fixed this in later versions and most good model software can handle such things.

The same problem often occurs with meshing algorithms. Depending on the type, an algorithm may be trying to fill a certain volume with elements but is being constrained for element size. This can cause the algorithm to fail, but a small change in the specified mesh size can get it to work again.

## 5. Check your dumped scripts

When making a model using the GUI it is really cool to be able to dump the model as a Python script, which can then be edited and run using the script mode. As I highlighted in another post, it helps to take care that Explode functions do not reorder the exploded entities. The default behaviour is to reorder, and it is easy to forget this when using the script, leading to confusion when the wrong objects are subject to later operations.

### Cool code: plotting columns from many data files with Grace

Grace a.k.a. xmgrace is a really useful tool for plotting histograms from tabular data files. Its power comes from the command line control and being scriptable. Yes, there are other options which are sometimes more suitable for specific situations (e.g. GNUplot, Matplotlib/PyLab), but for quick, basic plotting I usually find myself relying on xmgrace.

Here is an example of a single line command to plot two columns from each of a large number of data files:

`for i in ./a*/field.log; do echo -n " -block \$i -bxy 10:44" ; done | xargs xmgrace`

The command searches all current subdirectories with names beginning “a” for files called field.log. For each field.log file found it uses an echo command to generate a commandline argument string that we normally use to make a 2D plot with the 10th (x axis) and 44th (y axis) columns using xmgrace. The -n option for echo makes sure there is no newline after each echo, generating one long collection of commands. We next want to pass this on to xmgrace…

xmgrace does not take input from stdin so we first pipe the total echo output to xargs, which is a tool used to construct command line parameters from stdin. xargs then passes these command line arguments to xmgrace.

This little code snippet saves a lot of typing, which grows of the order N for N data files. Now I need to work out how to name each data set on the fly too.