Analysing the output¶

The results.csv.bz2 file contains all of the population trajectories from the nine model runs. You can explore this using Python pandas, R, or Excel as you did before. Using ipython or Jupyter notebooks with pandas, we can load up the file;

>>> import pandas as pd
>>> df = pd.read_csv("output/results.csv.bz2")
>>> print(df)
     fingerprint  repeat  beta[2]  too_ill_to_move[2]  day  ...         S  E  I         R  IW
0            3_0       1      0.3                 0.0    0  ...  56082077  0  0         0   0
1            3_0       1      0.3                 0.0    1  ...  56082077  0  0         0   0
2            3_0       1      0.3                 0.0    2  ...  56082072  5  0         0   0
3            3_0       1      0.3                 0.0    3  ...  56082072  0  5         0   0
4            3_0       1      0.3                 0.0    4  ...  56082071  0  5         1   1
...          ...     ...      ...                 ...  ...  ...       ... .. ..       ...  ..
1764         5_5       1      0.5                 0.5  172  ...   6304109  0  5  49777963   0
1765         5_5       1      0.5                 0.5  173  ...   6304109  0  4  49777964   0
1766         5_5       1      0.5                 0.5  174  ...   6304109  0  3  49777965   0
1767         5_5       1      0.5                 0.5  175  ...   6304109  0  1  49777967   0
1768         5_5       1      0.5                 0.5  176  ...   6304109  0  0  49777968   0

[1769 rows x 11 columns]

This is very similar to before, except now we have extra columns giving the values of the variables that are being adjusted (columns beta[2] and too_ill_to_move[2]. We also now have a use for the fingerprint column, which contains a unique identifier for each pair of adjustable variables.

Note

The fingerprint is constructed by removing the leading 0. from the value of the adjustable variable, and the joining the values together using underscores. Thus 0.3 0.0 becomes 3_0, while 0.5 0.5 becomes 5_5.

Finding peaks¶

We can use .groupby to group the results with the same fingerprint together. Then the .max function can be used to show the maximum values of selected columns from each group, e.g.

>>> df.groupby("fingerprint")[["day", "E","I", "IW", "R"]].max()
              day        E         I    IW         R
 fingerprint
 3_0          204  1767303   8665472  8588  48105748
 3_25         205  1908160   9296754  8588  48076343
 3_5          215  1844377   9024418  8588  48036902
 4_0          192  1947245   9532789  8588  49042717
 4_25         210  1965166   9614400  8588  49009034
 4_5          200  2095342  10179621  8588  48975523
 5_0          175  2207896  10714530  8588  49857969
 5_25         183  2120481  10326984  8588  49821966
 5_5          176  2117730  10330952  8588  49777968

From this, we can see that higher peaks occured for higher values of beta, which is expected. However, different values of too_ill_to_move had little impact on the peaks.

Warning

Do not over-interpret the results of single runs, such as the above. There is a lot of random error in these calculations and multiple model runs must be averaged over to gain a good understanding.

Plotting the output¶

There are lots of plots you would likely want to draw, so it is recommended that you use a tool such as R, Pandas or Excel to create the plots that will let you explore the data in full. For a quick set of plots, you can again use metawards-plot to generate some overview plots. To do this type;

metawards-plot -i output/results.csv.bz2 --format jpg --dpi 150

Note

We have used the ‘jpg’ image format here are we want to create animations. You can choose from many different formats, e.g. ‘pdf’ for publication quality graphs, ‘png’ etc. Use the --dpi option to set the resolution when creating bitmap (png, jpg) images.

As there are multiple fingerprints, this will produce multiple overview graphs (one overview per fingerprint, and if you have run multiple repeats, then one average per fingerprint too).

The fingerprint value is included in the graph name, and they will all be plotted on the same axes. This means that they could be joined together into an animation. As well as plotting, metawards-plot has an animation mode that can be used to join images together. To run this, use;

metawards-plot --animate output/overview*.jpg

Note

You can only animate image files (e.g. jpg, png). You can’t animate pdfs (yet - although pull requests welcome)

Here is the animation.

Animated overview graphs from the parameter sweep

Jupyter notebook¶

In addition, to the metawards-plot command, we also have a Jupyter notebook which you can look at which breaks down exactly how metawards-plot uses pandas and matplotlib to render multi-fingerprint graphs.