#Python and C tools for studying Dynamical Systems
##Requirements These tools require a C compiler, Python (version >= 2.7), and the following Python modules:
##Installation and Building We recommend installing the first two Python modules with the Python Package Index pip. For graph_tool, see here. For OS X users we recommend using homebrew to install graph_tool. We also caution that graph_tool is large, and sometimes quite difficult to install. As it is only used in our Morse Decomposition program, the user may find graph_tool unnecessary.
If you don't have a C compiler, we again recommend using homebrew (OS X) or apt-get (Linux) to get one. To build all, simply type:
cd chaos
make
If you are on Windows, you may have to change the individual makefiles so that they make .so files instead of .dylibs. This also means that you will have to change libraries.txt in the root directory. ##Tools For the sake of speed, each Python tool (xx)run.py uses one or more compiled C libraries through Python's ctypes module. Included are the following tools:
- A C Program to run 4th Order Runge Kutta in 2 Dimensions (rk4/rk4.c)
- A C implementation of a Sparse Matrix for efficient graph storage (sparse_matrix_table/smtable.c)
- A C Program with a corrected real number modulus (usefulfunctions/functions.c)
- A C Program to compute the probability of Cantori switches (invariantdynamics/switch.c)
- A Python Program to compute Invariant Sets (invariantdynamics/irun.py)
- A Python Program to compute Birkhoff Partitions (invariantdynamics/bprun.py)
- A Python Program to differentiate Quasiperiodic and Chaotic Sets (invariantdynamics/qrun.py)
- A Python Program to compute Recurrence Plots (invariantdynamics/rprun.py)
- A Python Program to compute Stickiness Rates along trajectories (invariantdynamics/srun.py)
- A Python Program to compute Morse Decompositions of Invariant Sets (invariantdynamics/morse_analysis.py)
- A Python Program to compute Sticky Regions in Chaotic Sets (invariantdynamics/sticky_analysis.py)
- A Python Program to track the evolution of a region (figurefactory/frun.py)
##Usage The parameters of each Python tool are explained in their comments. If the user wishes to add custom maps or flows, they must alter the corresponding C programs. Namely,
- irun.py calls invariant4.c and smtable.c
- bprun.py calls birkhoff_partition.c
- qrun.py calls quasiperiodicity.c
- rprun.py calls stick.c
- srun.py calls sticky.c
- rk4.c contains the differential equation governing any flow
To use one of the Python tools, simply alter it's parameters as needs be and type
python (xx)run.py
The two analysis tools don't have easily editable parameters, but are well commented if the user wishes to modify them.
irun.py can also produce a graph file ('outputs/graph_save.p') if the user runs
python irun.py -g
This output is needed by morse_analysis.py (don't run morse_analysis.py unless you have produced a graph). Similarly, sticky_analysis.py requires the outputs of qrun.py and srun.py (run these first).
Finally, the program frun.py requires a directory named for the map being studied, and for the map to be specified in factory.c.
The outputs of the Python tools are as follows:
- frun.py => (map)diffs/diff_(n).png and (map)figs/result_(n).png
- irun.py => outputs/invariant_result.ps and outputs/imatrix.txt and outputs/graph_save.p
- qrun.py => outputs/convergence_result.ps and outputs/convergence_histogram.ps and outputs/conv_matrix.p
- bprun.py => outputs/birkhoff_result.ps
- rprun.py => outputs/rp_result.ps
- srun.py => outputs/rr_result.ps and outputs/stickypoints.txt
- morse_analyis.py => outputs/graph.ps and outputs/condensation_graph.ps
- sticky_analysis.py => outputs/sticky_result.ps
##Examples Website Read more examples and usage information here