An installation instruction of the program realising the proof of the existence of invariant tori in forced pendulum and the Michelson system
as described in the paper
D. Wilczak, R. Barrio, Systematic ComputerAssisted Proof of branches of stable elliptic periodic orbits and surrounding invariant tori.
IMPORTANT:
The program requires a compiler that supports C++11 standard, for instance gcc4.8 or newer. Earlier versions of gcc are not supported.
Installation instruction under linux on PC
 please unzip the archive and enter directory
tar xvfz invtori.tgz
cd invtori

call 'make' program in the main directory.
make CAPD=PATH
where
PATH is absolute or relative path to the installation directory of the CAPD library on your computer. For example:
make CAPD=/home/daniel/capdbuild/bin/
The latest command generates four executables in the current directory: pendulum, msystem, hhsystem1 and hhsystem2.
Start computation
In order to start computation we must provide three obligatory parameters (in the given order)
 numberOfThreads  we specify how many cores can be used by the program. It is strongly recommended to run the program on a multicore remote computer.
 minSize  minimal step size in parameter range and minimal set size for the interval Newton method. These are parameters h_{min} and s_{min} defined in Section 3 of the article.
 degree  number of coefficients in the normal form to be computed. It is recommended to use value 1 and after several subdivisions switch to 2.
The fourth parameter is optional. It can be used to restart computation with different parameters from a completed earlier computation.
 inputDataFile  an file with output data from previous computation
Example:
 Primary computation with 64 CPUs, minimal size set to 1e5 and 1 coefficients in the normal form

 ./pendulum 64 1e5 1
 Restart computation with different minimal size
 ./pendulum 64 1e6 1 boundspendulum1e5
 Restart computation with two coefficients in the normal form and different minimal size
 ./pendulum 64 1e7 2 boundspendulum1e6
OUTPUT of the programs:
Each program creates three output files. The names of these files contain two parts dependent on the program and one of its parameters:
 $1  program description
 $2  value of the parameter minSize used when run the program
The three files created are:
 'gamma$1$2': contains a rigorous bound for the coefficients gamma_{1} and/or gamma_{2}
 'log$1$2': log file from the computation. Can be used to observe progress in computation.
 'bounds$1$2': contains detailed data on subdivisions of the parameter range and computed coefficients in normal form.
Comments:
 The file 'bounds$1$2' can be huge  (even few GB)
 The file 'bounds$1$2' can be used as the fourth argument of the program to restart computation as presented in the section Start computation
Example: the command
./pendulum 64 1e5 1
creates three files
 'gammapendulum1e05'
 'logpendulum1e05'
 'boundspendulum1e05'
NOTE:
More informations about libraries can be found on the web page of CAPD group:
http://capd.ii.uj.edu.pl.