| cpldosc_codegen.cpp | This C++ program uses ginac to create an assortment of C subroutines. |
| ginac_linalg_funcs.cpp | Some ginac-related functions | ginac_linalg_funcs.h | Header file that must be included in any file that uses functions in ginac_linalg_func.cpp |
| ginac_write_code.cpp | Functions that write C code based on ginac expression, vectors or matrices. |
| Makefile_codegen | Makefile for cpldosc_codegen |
To run this program, save the files in a directory, and run the commands
$ make -f Makefile_codegen $ ./cpldosc_codegenThe program will create several C files.
| cpldosc_slowvf_main.c | The main routine for a program that computes solutions to the slow vector field, and stops when it reaches a fold. |
| evt_stepsize.c | The step size function that helps to ensure that sign changes are detected. |
| Makefile_slowvf | Makefile for the cpldosc_slowvf_main program. |
To run this program, you must first download and run the code generator. Then save these files in the same directory, and run (for example)
$ make -f Makefile_slowvf $ ./cpldosc_slowvf_main 1.0 1.5 3 1.25 0.05 10 > data $ gnuplot gnuplot> set xlabel "v1" gnuplot> set ylabel "v2" gnuplot> plot "data" using 2:3 with linespoints gnuplot> quitThe command line arguments for the executable cpldosc_slowvf_main are: v1, v2, sigma1, sigma2, omega, stoptime. (The solution will stop when it reaches a fold or at time stoptime, which ever happens first.)
| cpldosc_fastvf_main.c | The main routine for a program that computes solutions to the fast vector field, and stops when it reaches an equilibrium point. |
| cpldosc_fast_gvf.c | The C function that defines the fast vector field and its Jacobian, to be used with the GSL ODE suite. |
| cpldosc_fast_proto.h | Header file that give the function prototypes for the functions defined in cpldosc_fast_gvf.c |
| Makefile_fastvf | Makefile for the cpldosc_fastvf_main program. |
To run this program, save these files, and run (for example)
$ make -f Makefile_fastvf $ ./cpldosc_fastvf_main 1.0 1.2 0.9 0.25 3 1.25 0.05 100 > data $ gnuplot gnuplot> set xlabel "t" gnuplot> plot "data" using 1:2 with linespoints, "data" using 1:3 with linespoints gnuplot> quitThe command line arguments for the executable cpldosc_fastvf_main are: v1, v2, q1, q2, sigma1, sigma2, omega, stoptime. (The solution will stop when it "reaches" an equilibrium point, or when stoptime is reached, which ever occurs first.)
In the version, the code that actually solves the differential
equations has been put into a separate function that is called
by the main program. You must run the cpldosc_codegen program
first, and you also need evt_stepsize.c.
| cpldosc_slowvf_main2.c | The main routine. This puts the command-line arguments into appropriate arrays, and calls cpldosc_slowvf_solve. |
| cpldosc_slowvf_solve.c | This file contains the function that actually calls the GSL ODE solver to solve the differential equations. |
| Makefile_slowvf2 | Makefile for the cpldosc_slowvf_main2 program. |
To run this program, you must first download and run the code generator. You must also get evt_stepsize.c. If you put the files from the previous examples all in one directory, then you can just add these three new files to the same directory. Run the commands:
$ make -f Makefile_slowvf2 $ ./cpldosc_slowvf_main2 1.0 1.5 3 1.25 0.05 10 > data $ gnuplot gnuplot> set xlabel "v1" gnuplot> set ylabel "v2" gnuplot> plot "data" using 2:3 with linespoints gnuplot> quitThe command line arguments for the executable cpldosc_slowvf_main2 are: v1, v2, sigma1, sigma2, omega, stoptime. (The solution will stop when it reaches a fold or at time stoptime, which ever happens first.)
| cpldosc_computefold2.c | A program that computes pieces of the fold curve. |
| Makefile_computefold2 | Makefile for the cpldosc_computefold2 program. |
| cf | A shell script that runs cpldosc_computefold2 to compute the fold curves for sigma1=3.00, sigma2=1.25, omega=0.05 |
| plotfold.gnuplot | A gnuplot script that plots the files generated by the cf script. |
This code computes pieces of the fold curve. Save the files in the same directory with the previous programs. To compile and run it, first run the cpldosc_codegen program (if you haven't already), then
$ make -f Makefile_computefold2
The executable is called cpldosc_computefold2, and its arguments are v1 v2 sigma1 sigma2 omega delta N, where (v1,v2) is a guess for the starting point, (sigma1, sigma2, omega) are the parameter values, delta is the (maximum) step size, and N is the number of points to compute. Change the sign of delta to change the direction of the computed curve. The program will use the magnitude of the gradient of the fold function to adapt the step size; where the gradient is small, the step size will be small.
Here is an example of running the program and plotting the results.
$ ./cpldosc_computefold2 -0.4 -1.5 3.0 1.25 0.05 .02 350 > fold3.00-1.25-0.05-1.dat $ gnuplot > plot "fold3.00-1.25-0.05-1.dat" u 2:3 w lines
To use the cf and plotcurve.gnuplot scripts, do this:
$ sh cf $ gnuplot > load "plotcurve.gnuplot"Here is the result: fold.png.
| cpldosc_fast_eigvec0.c | A function that computes an eigenvector associated with the zero eigenvalue of the Jacobian of the fast subsystem. |
double v[2]; double p[5]; double vf[2]; /* * Some code here should set the values in v and p... */ /* * Compute the vector field at v and put it in vf. */ cpldosc_fast_vf(0.0, v, vf, (void *) p);(The first argument is 0.0, which is the time. Since the differential equations are autonomous, it doesn't matter what value we use.)
| cpldosc_fhat.m | Matlab function that computes the critical manifold q=cpldosc_fhat(v,p), where q = (q1,q2), v=(v1,v2) and p=(sigma1,sigma2,omega). |
| cpldosc_fhat_q1.m | Matlab function that computes the q1 coordinate of the critical manifold as a function of (v1,v2). That is, q1=cpldosc_fhat_q1(v,p), where v=(v1,v2) and p=(sigma1,sigma2,omega). |
| cpldosc_fhat_q2.m | Matlab function that computes the q2 coordinate of the critical manifold as a function of (v1,v2). That is, q2=cpldosc_fhat_q2(v,p), where v=(v1,v2) and p=(sigma1,sigma2,omega). |
| q2plot.m | A Matlab script that plots the critical manifold in (v1,v2,q2) coordinates, and also plots two curves, one slow and one fast. |
| slow.dat | Data used by q2plot.m. |
| fast.dat | Data used by q2plot.m. |
Here is the output of the Matlab script q2plot: q2plot.png.
| slowfast_plot.m | Matlab script to plot a curve with alternating blue and red, depending on whether a column of data is 0 or 1. |
