AUTO is a software for continuation and bifurcation problems in ordinary differential equations

this is a relatively complex tool, with more or less excellent documentation[pdf].. but in places is a little bit rough around the edges.. that said, for such a specialised area there's really not much to complain about.. and anyway, the edges are pretty easy to tidy up

anyway, the main issues I came up against..

enabling the ipython interface

if you've installed everything somewhat sensibly then auto -i should open up AUTO with the ipython interface, which is very handy, tab-completion and all the other good things ipython brings are a must for working with AUTO

in the latest release however, it doesn't work with versions of ipython > 11.0, and AUTO complains about ipython not having been installed.. fortunately this has already been fixed in the dev version

replacing ~/auto/07p/python/ with this should sort it

plotting in matplotlib

there's lots of dependencies required to make this work, and in fairness, most of them are mentioned in the docs

however, the main culprit for this problem is the contents of ~/auto/07p/pythongraphics/

#!/usr/bin/env python
    import Tkinter
    import tkSimpleDialog
    import tkFileDialog
except ImportError:
    import tkinter as Tkinter # Python 3
    from tkinter import simpledialog as tkSimpleDialog
    from tkinter import filedialog as tkFileDialog

where the try/except buries any issues with importing the stuff required for fancy plotting and drops you into the old school Tkinter interface.. (which is awful)... commenting out the try/except and dealing with the errors arising from the first 3 imports led me to realise I was missing the tk-dev package (on ubuntu 12.04), which appears to be an unmentioned dependency

max/min, plots

generally, when following limit cycles people tend to plot just the maxima of the cycle.. if you also want to plot the minima (to overlay with numerics for example) you can use the IPLT flag.. in the following run I'm following a Hopf bifurcation and monitoring the max/min of U(1).. for max/min of U(2) you would set IPLT=-2 etc

AUTO In [3]: r3 = run(r2('HB1'),c='yam.2',UZR={-2:3},ISW=1,IPS=2,ILP=0,IPLT=-1)
Starting yam ...

  BR    PT  TY  LAB    PAR(2)        MIN U(1)      MAX U(1)      MAX U(2)      MAX U(3)
  13   100       19   7.18230E+00   1.38549E-01   5.52980E+00   1.47324E-01   1.17757E-01
  13   200       20   6.33871E+00   1.93734E-02   7.18718E+00   1.92397E-01   1.41228E-01
  13   300       21   5.68379E+00   3.50677E-03   7.75285E+00   2.11506E-01   1.48706E-01
  13   400       22   5.18226E+00   7.23511E-04   7.88476E+00   2.20634E-01   1.51414E-01
  13   500       23   4.79096E+00   1.65134E-04   7.80820E+00   2.24777E-01   1.52480E-01
  13   600       24   4.47883E+00   4.13158E-05   7.61930E+00   2.26042E-01   1.52923E-01
  13   700       25   4.22482E+00   1.12902E-05   7.36622E+00   2.25495E-01   1.53115E-01
  13   800       26   4.01451E+00   3.36259E-06   7.07585E+00   2.23743E-01   1.53200E-01

now, you can use the in built matplotlib plotting tools if you're preparing a figure for publication, but if you want to overlay results on numerical simulations or do some type complex plot in plain matplotlib.. then your best bet is to get the data out of AUTO and far away as fast as possible....

a crude regex that i've been using (for example)

AUTO In [4]: !tail -n +17 fort.7 | awk '{print $2","$5","$7","$8}' \
                                 | sed -e '1s/^/st,js,i1,i2\n/'    \
                                 | sed 's/\([0-9]\)-\([0-9]\)/\1E-\2/g' > hopf.sol

here you get out information about the stability of the equilibrium/limit cycle from the sign of $2 (negative for stable, positive for unstable), and you can then pick out whichever other columns are useful.. (note, this isn't something you'll need to be doing regularly, but it's still useful to know how)

now, this bifurcation information is contained in the file hopf.sol..

my strategy for plotting data I've exported from AUTO then goes something like..

from pylab import *
import pandas as pd

hp = pd.read_csv('hopf.sol')

stable_hp = hp[ hp['st'] < 0 ]
unstable_hp = hp[ hp['st'] > 0 ]

plot( stable_hp['js'], stable_hp['i1'], 'b-')
plot( unstable_hp['js'], unstable_hp['i1'], 'b--')


obviously the plotting tools built in to AUTO are just wrappers of matplotlib anyway, but if you're preparing something for publication or similar, it's useful to be able to break out of the limitations it imposes