Computation of Morse decompositions. More...

#include <algorithm>
#include <new>
#include <iostream>
#include <iomanip>
#include <ios>
#include <string>
#include <fstream>
#include <sstream>
#include <cstdio>
#include "chomp/system/textfile.h"
#include "chomp/cubes/pointset.h"
#include "chomp/struct/digraph.h"
#include "chomp/struct/multitab.h"
#include "chomp/struct/hashsets.h"
#include "chomp/system/timeused.h"
#include "config.h"
#include "typedefs.h"
#include "conindex.h"
#include "morsedec.h"
#include "typedyns.h"
#include "indcache.h"
#include "invpart.h"
#include "utils.h"
#include "spacewrap.h"
#include "procmdec.h"
#include "morsecache.h"
#include "eigenval.h"
#include "dotgraph.h"
#include "datatext.h"

Classes
class	TConnTable
	A simple class for storing connections in an array that uses the "multitable" class. More...

class	TConnMorse
	A simple class for storing connections in an array that uses the "multitable" class. More...

Functions
void	setDummyIndex (theMorseDecompositionType &morseDec, int n, int nonzero=-1)
	This small auxiliary procedure sets a dummy Conley index to the given Morse set. More...

int	computeConleyIndex (theMorseDecompositionType &morseDec, int n, const double offset, const double width, int subdivDepth, const theMapType &theMap, const theCubMapType &theCubMap0, const theCubMapType &theCubMap1, int &subdivNonemptyInv, int &noIsolation, int &attractor)
	Verifies that the provided Morse set can be used as a basis for a Conley index pair and computes the Conley index. More...

template<class typeCubes >
void	chainRecurrentSet (const typeCubes &X, typeCubes &result, const chomp::homology::diGraph<> &g)
	Computes the chain recurrent set of X. More...

template<class typeCubes , class typeMorseDec >
void	invMorseDec (const typeCubes &X, const chomp::homology::diGraph<> &g, typeMorseDec &morseDec, const double offset, const double width, int subdivDepth, const theMapType &theMap, const theCubMapType &theCubMap0, const theCubMapType &theCubMap1, int_t skipIndices, const std::string &cacheFileName, bool &morseDecComputed, std::vector< int > &wrongIndices, std::vector< int > &skippedIndices, std::vector< int > &attractors, bool connOrbits, const double leftMapParam, const double rightMapParam, int paramCount, chomp::homology::timeused &timeSubdiv)
	Computes a Conley-Morse decomposition of ChainRecSet (X). More...

theMorseDecompositionType *	computeMorseDecomposition (theMapType &theMap, const theCubMapType theCubMap0, const theCubMapType theCubMap1, const double offset, const double width, int_t skipIndices, const std::string &cacheFileName, const std::string &pictureFileName, const std::string &cubesFilePrefix, const std::string &morseDecFileName, const std::string &graphFileName, const std::string &procFilePrefix, const std::string &mapOptFileName, bool &morseDecComputed, std::vector< int > &wrongIndices, std::vector< int > &skippedIndices, std::vector< int > &attractors, bool connOrbits, const double leftMapParam, const double rightMapParam, int paramCount)
	Computes the Morse decomposition using all the pre- and postprocessing. More...

Detailed Description

Computation of Morse decompositions.

This file contains the definition of a function for the computation of a Morse decomposition for a given map, as well as several auxiliary procedures necessary to compute this Morse decomposition in an efficient way by restricting the phase space to the invariant part computed with respect to a coarser grid. The computed Morse decomposition is processed further in order to eliminate spurious Morse sets wherever possible.

Author: Pawel Pilarczyk

Definition in file compmdec.h.

Function Documentation

◆ chainRecurrentSet()

template<class typeCubes >

void chainRecurrentSet	(	const typeCubes &	X,
		typeCubes &	result,
		const chomp::homology::diGraph<> &	g
	)

Computes the chain recurrent set of X.

Note: The resulting set may be taken the same as X if one wants to replace the set with its chain recurrent set.

Definition at line 379 of file compmdec.h.

Referenced by computeMorseDecomposition().

◆ computeConleyIndex()

int computeConleyIndex	(	theMorseDecompositionType &	morseDec,
		int	n,
		const double *	offset,
		const double *	width,
		int	subdivDepth,
		const theMapType &	theMap,
		const theCubMapType &	theCubMap0,
		const theCubMapType &	theCubMap1,
		int &	subdivNonemptyInv,
		int &	noIsolation,
		int &	attractor
	)

inline

Verifies that the provided Morse set can be used as a basis for a Conley index pair and computes the Conley index.

If this verification fails then subdivides the Morse set and repeats the procedure restricted to the invariant part of the set. Returns 0 if succeeds or -1 in the case of failure. Makes a note of having reached the subdivision limit or having come across empty invariant part in the provided variable which is set to 1 in the former case and 0 in the latter (otherwise it is not modified). If a problem with isolation is encountered then sets "noIsolation" to 1. If the index pair is computed then sets the value of the variable which remembers if this is an attractor (empty exit set) or not.

Definition at line 210 of file compmdec.h.

References custom::difference::ignoreIsolationForConleyIndex, invariantPart(), custom::difference::maxImageDiameter, custom::difference::maxImageVolume, custom::difference::maxRefineSize0, custom::difference::maxRefineSize1, custom::difference::refineDepth, setDummyIndex(), and subdivideCubes().

Referenced by invMorseDec().

◆ computeMorseDecomposition()

theMorseDecompositionType * computeMorseDecomposition	(	theMapType &	theMap,
		const theCubMapType	theCubMap0,
		const theCubMapType	theCubMap1,
		const double *	offset,
		const double *	width,
		int_t	skipIndices,
		const std::string &	cacheFileName,
		const std::string &	pictureFileName,
		const std::string &	cubesFilePrefix,
		const std::string &	morseDecFileName,
		const std::string &	graphFileName,
		const std::string &	procFilePrefix,
		const std::string &	mapOptFileName,
		bool &	morseDecComputed,
		std::vector< int > &	wrongIndices,
		std::vector< int > &	skippedIndices,
		std::vector< int > &	attractors,
		bool	connOrbits,
		const double *	leftMapParam,
		const double *	rightMapParam,
		int	paramCount
	)

inline

Computes the Morse decomposition using all the pre- and postprocessing.

The target Morse decomposition object must be already initialized with the right map which is to be used to compute the Conley indices of the Morse sets. If a file name prefix is nonempty then an attempt is being made to read cached Morse decomposition information from a file.

Definition at line 996 of file compmdec.h.

References chainRecurrentSet(), checkIsolation(), computeMapGraph(), CONFIG_ENHANCEINV, data2text(), double2string(), enhanceCubes(), fileExists(), custom::difference::finalDepth, custom::difference::initialDepth, invariantPart(), invMorseDec(), loadMorseDecCache(), custom::difference::maxImageDiameter, custom::difference::maxImageVolume, moveSomeToFront(), custom::difference::paramCount, custom::procMorseDecExit::processMorseDec(), resetRounding(), saveMorseDecCache(), custom::difference::spaceDim, subdivideCubes(), text2data(), and writeDotGraph().

Referenced by Worker::Process(), and runSingleComp().

◆ invMorseDec()

template<class typeCubes , class typeMorseDec >

void invMorseDec	(	const typeCubes &	X,
		const chomp::homology::diGraph<> &	g,
		typeMorseDec &	morseDec,
		const double *	offset,
		const double *	width,
		int	subdivDepth,
		const theMapType &	theMap,
		const theCubMapType &	theCubMap0,
		const theCubMapType &	theCubMap1,
		int_t	skipIndices,
		const std::string &	cacheFileName,
		bool &	morseDecComputed,
		std::vector< int > &	wrongIndices,
		std::vector< int > &	skippedIndices,
		std::vector< int > &	attractors,
		bool	connOrbits,
		const double *	leftMapParam,
		const double *	rightMapParam,
		int	paramCount,
		chomp::homology::timeused &	timeSubdiv
	)

Computes a Conley-Morse decomposition of ChainRecSet (X).

The combinatorial cubical multivalued map F is encoded in the directed graph provided. The Morse decomposition structure must be initially empty. The arguments "offset", "width", "subdivDepth" and "theMap" are only necessary for the purpose of refining trivial Morse sets. The global constants "refineDepth", "maxRefineSize0" and "maxRefineSize1" determine, respectively, the maximal allowed refinement depth, and the maximal size of a cubical set which is refined if necessary. Further simplification of the computed Morse decomposition is done by joining Morse sets (see the description in "morsedec.h" for details). If requested, the Conley indices of Morse sets which have at least the given number of boxes are not computed (they are set to be trivial). If a file name prefix is nonempty then an attempt is being made to read cached Morse decomposition information from a file.

Definition at line 440 of file compmdec.h.

References checkEmptyInv(), checkIsolation(), computeConleyIndex(), cubesVolume(), fileExists(), custom::difference::finalDepth, custom::difference::maxJoinConnection, custom::difference::maxJoinDistance, custom::difference::maxJoinSize, custom::difference::maxRefineSize0, custom::difference::paramCount, custom::noKnownIndices::setConleyIndex(), setDummyIndex(), and showRealCoords().