#include <morsedec.h>
Public Types | |
| typedef mapcomp | MapCompType |
| The type of the map computation class. | |
| typedef cubetype | CubeType |
| The type of a single cube. | |
| typedef cubsettype | CubSetType |
| The type of a set of cubes used to store each Morse set. | |
| typedef IndexPair < mapcomp, cubetype, cubsettype > | PairType |
| The type of the index pair. | |
| typedef ConleyIndex < PairType > | IndexType |
| The type of the Conley index. | |
Public Member Functions | |
| MorseDecomposition (const mapcomp &_M=mapcomp()) | |
| The default constructor. | |
| ~MorseDecomposition () | |
| The destructor. | |
| MorseDecomposition (const MorseDecomposition &m) | |
| The copy constructor. | |
| MorseDecomposition < mapcomp, cubetype, cubsettype > & | operator= (const MorseDecomposition< mapcomp, cubetype, cubsettype > &m) |
| The assignment operator. | |
| int | setnumber (int n) |
| Changes (increases or decreases) the number of Morse sets. | |
| int | add (int n, const cubetype &q) |
| Adds a cube to the given Morse set and increases the number of Morse sets if necessary. | |
| int | count () const |
| Returns the number of Morse sets. | |
| const cubsettype & | operator[] (int n) const |
| Returns the n-th Morse set. | |
| int | distance (int n, int m) const |
| Returns the approximate distance between the two Morse sets. | |
| int | addconn (int n, int m) |
| Adds a connection between the given Morse sets without adding any cubes to this connection (like in a direct connection). | |
| int | addconn (int n, int m, const cubetype &q) |
| Adds a cube to the connecting orbit between the given Morse sets. | |
| bool | connected (int n, int m) const |
| Checks whether there exists a connection between given sets. | |
| const cubsettype & | connection (int n, int m) const |
| Returns the connection between the given sets. | |
| int | distance (int n, int m, int k) const |
| Returns the approximate maximal distance of a cube in the orbit that connects the sets n and m (in either direction) from the k-th Morse set, i.e., how far the orbit is from the set. | |
| int | conndistance (int n, int m) const |
| Returns the appropriate maximal distance between cubes that are contained in the Morse set n and the connecting orbit n-m or m-n. | |
| int | makegraph (chomp::homology::diGraph<> &g) const |
| Creates a graph representation of the Morse decomposition. | |
| const IndexType & | compute (int n) |
| Computes the Conley index of the given Morse set. | |
| int | compute () |
| Computes the Conley indices of all the Morse sets. | |
| bool | computed (int n) const |
| Verifies if the Conley index for the given Morse set has been already computed. | |
| const IndexType & | index (int n) const |
| Retrieves the previously computed Conley index of the given Morse set. | |
| const IndexType & | setindex (int n, const typename MorseDecomposition< mapcomp, cubetype, cubsettype >::IndexType &ind) |
| Sets the index of the given Morse set to the apriori known one. | |
| bool | trivial (int n) const |
| Returns true if the Conley index of the given Morse set is trivial, and false if either nontrivial or not yet computed. | |
| void | intersection (const MorseDecomposition< mapcomp, cubetype, cubsettype > &m, const MorseDecomposition< mapcomp, cubetype, cubsettype > &n) |
| Computes the set-wise intersection of two Morse decompositions. | |
| int | join (int n, int m) |
| Joins the two given Morse sets. | |
| int | passthru (int n) |
| Make connecting orbits pass through the given Morse set, because its invariant part is in fact empty. | |
| int | jointrivial (int maxsetsize, int maxconnsize, int maxdistance) |
| Joins small Morse sets with trivial indices with Morse sets whose indices are nontrivial. | |
| int | savetofiles (const char *prefix=0) |
| Save the Morse sets and connecting orbits to files. | |
| int | loadfromfiles (const char *prefix=0) |
| Load the Morse sets and connecting orbits from files. | |
Public Attributes | |
| const mapcomp & | M |
| The map computation class. | |
Private Types | |
| typedef chomp::homology::mvmap < cubetype, cubetype > | cubmaptype |
| The type of a combinatorial cubical multivalued map. | |
Private Member Functions | |
| void | deleteall (int firstnumber, int lastnumber) |
| Release the memory (used in the destructor and copy constructor). | |
| void | copyall (const MorseDecomposition &m) |
| Copy all the data (used in the copy constructor and operator =). | |
| void | addone () |
| Add one Morse set and initialize its data. | |
| bool | adjacent (int n, int m, int margin=0) const |
| Verifies if two Morse sets are adjacent to each other. | |
Static Private Member Functions | |
| static int | cubsetdistance (const cubsettype &X, const cubsettype &Y, bool minimum) |
| Returns the approximate distance between the two cubical sets. | |
Private Attributes | |
| int | nsets |
| The number of Morse sets. | |
| chomp::homology::multitable < cubsettype * > | sets |
| The Morse sets. | |
| chomp::homology::multitable < IndexType * > | indices |
| The Conley indices of the Morse sets. | |
| chomp::homology::multitable < int > | nontrivial |
| The table that stores the information on whether the indices are trivial or not: -1 = unknown, 0 = trivial, 1 = nontrivial. | |
| chomp::homology::multitable < chomp::homology::multitable < cubsettype * > > | conn |
| Connecting orbits from one set to another. | |
| chomp::homology::multitable < chomp::homology::multitable < int > > | dist |
| Tabulated distances between the Morse sets. | |
| chomp::homology::multitable < chomp::homology::multitable < int > > | distconn |
| Tabulated values of the function "conndistance". | |
This is a template whose parameters define a class used to compute the combinatorial cubical multivalued map on Morse sets, a class which corresponds to a single cube, and a class which is used to keep sets of cubes (the hashed set by default).
Definition at line 67 of file morsedec.h.
typedef chomp::homology::mvmap<cubetype,cubetype> MorseDecomposition< mapcomp, cubetype, cubsettype >::cubmaptype [private] |
| typedef mapcomp MorseDecomposition< mapcomp, cubetype, cubsettype >::MapCompType |
| typedef cubetype MorseDecomposition< mapcomp, cubetype, cubsettype >::CubeType |
| typedef cubsettype MorseDecomposition< mapcomp, cubetype, cubsettype >::CubSetType |
| typedef IndexPair<mapcomp,cubetype,cubsettype> MorseDecomposition< mapcomp, cubetype, cubsettype >::PairType |
| typedef ConleyIndex<PairType> MorseDecomposition< mapcomp, cubetype, cubsettype >::IndexType |
| MorseDecomposition< mapcomp, cubetype, cubsettype >::MorseDecomposition | ( | const mapcomp & | _M = mapcomp () |
) | [inline] |
| MorseDecomposition< mapcomp, cubetype, cubsettype >::~MorseDecomposition | ( | ) | [inline] |
| MorseDecomposition< mapcomp, cubetype, cubsettype >::MorseDecomposition | ( | const MorseDecomposition< mapcomp, cubetype, cubsettype > & | m | ) | [inline] |
| MorseDecomposition< mapcomp, cubetype, cubsettype > & MorseDecomposition< mapcomp, cubetype, cubsettype >::operator= | ( | const MorseDecomposition< mapcomp, cubetype, cubsettype > & | m | ) | [inline] |
| int MorseDecomposition< mapcomp, cubetype, cubsettype >::setnumber | ( | int | n | ) | [inline] |
Changes (increases or decreases) the number of Morse sets.
Definition at line 613 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::addone(), MorseDecomposition< mapcomp, cubetype, cubsettype >::deleteall(), and MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets.
| int MorseDecomposition< mapcomp, cubetype, cubsettype >::add | ( | int | n, | |
| const cubetype & | q | |||
| ) | [inline] |
Adds a cube to the given Morse set and increases the number of Morse sets if necessary.
Definition at line 626 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::addone(), MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets, and MorseDecomposition< mapcomp, cubetype, cubsettype >::sets.
Referenced by MorseDecomposition< mapcomp, cubetype, cubsettype >::compute().
| int MorseDecomposition< mapcomp, cubetype, cubsettype >::count | ( | ) | const [inline] |
Returns the number of Morse sets.
Definition at line 666 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets.
| const cubsettype & MorseDecomposition< mapcomp, cubetype, cubsettype >::operator[] | ( | int | n | ) | const [inline] |
Returns the n-th Morse set.
Throws an exception in case of a wrong number.
Definition at line 673 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets, and MorseDecomposition< mapcomp, cubetype, cubsettype >::sets.
| int MorseDecomposition< mapcomp, cubetype, cubsettype >::distance | ( | int | n, | |
| int | m | |||
| ) | const [inline] |
Returns the approximate distance between the two Morse sets.
Warning: This computation may take some time for large sets. Note: The values returned by this function are tabulated, and are not updated when the Morse sets are modified with the 'add' function. Call with (-1,-1) to reset the tabulation.
Definition at line 682 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::cubsetdistance(), MorseDecomposition< mapcomp, cubetype, cubsettype >::dist, MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets, and MorseDecomposition< mapcomp, cubetype, cubsettype >::sets.
Referenced by MorseDecomposition< mapcomp, cubetype, cubsettype >::conndistance(), and MorseDecomposition< mapcomp, cubetype, cubsettype >::jointrivial().
| int MorseDecomposition< mapcomp, cubetype, cubsettype >::addconn | ( | int | n, | |
| int | m | |||
| ) | [inline] |
Adds a connection between the given Morse sets without adding any cubes to this connection (like in a direct connection).
Definition at line 640 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::addone(), MorseDecomposition< mapcomp, cubetype, cubsettype >::conn, and MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets.
| int MorseDecomposition< mapcomp, cubetype, cubsettype >::addconn | ( | int | n, | |
| int | m, | |||
| const cubetype & | q | |||
| ) | [inline] |
Adds a cube to the connecting orbit between the given Morse sets.
Definition at line 653 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::addone(), MorseDecomposition< mapcomp, cubetype, cubsettype >::conn, and MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets.
| bool MorseDecomposition< mapcomp, cubetype, cubsettype >::connected | ( | int | n, | |
| int | m | |||
| ) | const [inline] |
Checks whether there exists a connection between given sets.
Returns true if yes, false if no or wrong numbers.
Definition at line 739 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::conn, and MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets.
| const cubsettype & MorseDecomposition< mapcomp, cubetype, cubsettype >::connection | ( | int | n, | |
| int | m | |||
| ) | const [inline] |
Returns the connection between the given sets.
Throws an exception if there is no connection or wrong numbers.
Definition at line 747 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::conn, and MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets.
| int MorseDecomposition< mapcomp, cubetype, cubsettype >::distance | ( | int | n, | |
| int | m, | |||
| int | k | |||
| ) | const [inline] |
Returns the approximate maximal distance of a cube in the orbit that connects the sets n and m (in either direction) from the k-th Morse set, i.e., how far the orbit is from the set.
Note: This computation may take some time for large sets.
Definition at line 757 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::conn, MorseDecomposition< mapcomp, cubetype, cubsettype >::cubsetdistance(), MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets, and MorseDecomposition< mapcomp, cubetype, cubsettype >::sets.
| int MorseDecomposition< mapcomp, cubetype, cubsettype >::conndistance | ( | int | n, | |
| int | m | |||
| ) | const [inline] |
Returns the appropriate maximal distance between cubes that are contained in the Morse set n and the connecting orbit n-m or m-n.
Note: The values returned by this function are tabulated, and are not updated when the Morse sets are modified with the 'add' function or when the connecting orbits are modified with the 'addconn' function. Call with (-1,-1) to reset the tabulation.
Definition at line 770 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::distance(), MorseDecomposition< mapcomp, cubetype, cubsettype >::distconn, and MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets.
Referenced by MorseDecomposition< mapcomp, cubetype, cubsettype >::jointrivial().
| int MorseDecomposition< mapcomp, cubetype, cubsettype >::makegraph | ( | chomp::homology::diGraph<> & | g | ) | const [inline] |
Creates a graph representation of the Morse decomposition.
Each Morse set corresponds to a vertex, and each connecting orbit gives rise to a corresponding edge. The graph given as an argument must be initially empty.
Definition at line 813 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::conn, and MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets.
| const MorseDecomposition< mapcomp, cubetype, cubsettype >::IndexType & MorseDecomposition< mapcomp, cubetype, cubsettype >::compute | ( | int | n | ) | [inline] |
Computes the Conley index of the given Morse set.
Definition at line 832 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::add(), MorseDecomposition< mapcomp, cubetype, cubsettype >::compute(), MorseDecomposition< mapcomp, cubetype, cubsettype >::indices, MorseDecomposition< mapcomp, cubetype, cubsettype >::M, MorseDecomposition< mapcomp, cubetype, cubsettype >::nontrivial, MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets, MorseDecomposition< mapcomp, cubetype, cubsettype >::sets, and MorseDecomposition< mapcomp, cubetype, cubsettype >::trivial().
| int MorseDecomposition< mapcomp, cubetype, cubsettype >::compute | ( | ) | [inline] |
Computes the Conley indices of all the Morse sets.
Definition at line 865 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets.
Referenced by MorseDecomposition< mapcomp, cubetype, cubsettype >::compute(), and MorseDecomposition< mapcomp, cubetype, cubsettype >::jointrivial().
| bool MorseDecomposition< mapcomp, cubetype, cubsettype >::computed | ( | int | n | ) | const [inline] |
Verifies if the Conley index for the given Morse set has been already computed.
Definition at line 873 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::indices, and MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets.
| const MorseDecomposition< mapcomp, cubetype, cubsettype >::IndexType & MorseDecomposition< mapcomp, cubetype, cubsettype >::index | ( | int | n | ) | const [inline] |
Retrieves the previously computed Conley index of the given Morse set.
Throws an exception if the index has not yet been computed. Note that if the Morse set is chaned, then its index should be computed again using one of the functions above.
Definition at line 882 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::indices, and MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets.
| const MorseDecomposition< mapcomp, cubetype, cubsettype >::IndexType & MorseDecomposition< mapcomp, cubetype, cubsettype >::setindex | ( | int | n, | |
| const typename MorseDecomposition< mapcomp, cubetype, cubsettype >::IndexType & | ind | |||
| ) | [inline] |
Sets the index of the given Morse set to the apriori known one.
Does not compute it, but verifies if it is nontrivial.
Definition at line 892 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::indices, MorseDecomposition< mapcomp, cubetype, cubsettype >::nontrivial, MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets, and MorseDecomposition< mapcomp, cubetype, cubsettype >::trivial().
| bool MorseDecomposition< mapcomp, cubetype, cubsettype >::trivial | ( | int | n | ) | const [inline] |
Returns true if the Conley index of the given Morse set is trivial, and false if either nontrivial or not yet computed.
Definition at line 909 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::nontrivial, and MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets.
Referenced by MorseDecomposition< mapcomp, cubetype, cubsettype >::compute(), and MorseDecomposition< mapcomp, cubetype, cubsettype >::setindex().
| void MorseDecomposition< mapcomp, cubetype, cubsettype >::intersection | ( | const MorseDecomposition< mapcomp, cubetype, cubsettype > & | m, | |
| const MorseDecomposition< mapcomp, cubetype, cubsettype > & | n | |||
| ) | [inline] |
Computes the set-wise intersection of two Morse decompositions.
The Morse decomposition must be initially empty and different from the objects passed as arguments.
Definition at line 918 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::addone(), MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets, and MorseDecomposition< mapcomp, cubetype, cubsettype >::sets.
| int MorseDecomposition< mapcomp, cubetype, cubsettype >::join | ( | int | n, | |
| int | m | |||
| ) | [inline] |
Joins the two given Morse sets.
Updates the connecting orbits. Resets the Conley index. The new Morse set replaces the n-th one, and the numbers of Morse sets beyond the m-th one are shifted downwards.
Definition at line 940 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::conn, MorseDecomposition< mapcomp, cubetype, cubsettype >::deleteall(), MorseDecomposition< mapcomp, cubetype, cubsettype >::dist, MorseDecomposition< mapcomp, cubetype, cubsettype >::distconn, MorseDecomposition< mapcomp, cubetype, cubsettype >::indices, MorseDecomposition< mapcomp, cubetype, cubsettype >::nontrivial, MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets, and MorseDecomposition< mapcomp, cubetype, cubsettype >::sets.
Referenced by MorseDecomposition< mapcomp, cubetype, cubsettype >::jointrivial().
| int MorseDecomposition< mapcomp, cubetype, cubsettype >::passthru | ( | int | n | ) | [inline] |
Make connecting orbits pass through the given Morse set, because its invariant part is in fact empty.
The Morse set is deleted and its contents is included in connecting orbits.
Definition at line 1017 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::conn, MorseDecomposition< mapcomp, cubetype, cubsettype >::deleteall(), MorseDecomposition< mapcomp, cubetype, cubsettype >::distconn, MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets, and MorseDecomposition< mapcomp, cubetype, cubsettype >::sets.
| int MorseDecomposition< mapcomp, cubetype, cubsettype >::jointrivial | ( | int | maxsetsize, | |
| int | maxconnsize, | |||
| int | maxdistance | |||
| ) | [inline] |
Joins small Morse sets with trivial indices with Morse sets whose indices are nontrivial.
Only sets whose size, as well as the size of the connecting orbit is below the given limits are joined, provided their distance is also limited.
Definition at line 1080 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::compute(), MorseDecomposition< mapcomp, cubetype, cubsettype >::conn, MorseDecomposition< mapcomp, cubetype, cubsettype >::conndistance(), MorseDecomposition< mapcomp, cubetype, cubsettype >::dist, MorseDecomposition< mapcomp, cubetype, cubsettype >::distance(), MorseDecomposition< mapcomp, cubetype, cubsettype >::join(), MorseDecomposition< mapcomp, cubetype, cubsettype >::nontrivial, MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets, and MorseDecomposition< mapcomp, cubetype, cubsettype >::sets.
| int MorseDecomposition< mapcomp, cubetype, cubsettype >::savetofiles | ( | const char * | prefix = 0 |
) | [inline] |
Save the Morse sets and connecting orbits to files.
Set numbers are attached to the given prefix. Connections are numbered N-M.
Definition at line 1266 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::conn, MorseDecomposition< mapcomp, cubetype, cubsettype >::indices, MorseDecomposition< mapcomp, cubetype, cubsettype >::nontrivial, MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets, and MorseDecomposition< mapcomp, cubetype, cubsettype >::sets.
| int MorseDecomposition< mapcomp, cubetype, cubsettype >::loadfromfiles | ( | const char * | prefix = 0 |
) | [inline] |
Load the Morse sets and connecting orbits from files.
Definition at line 1331 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::addone(), MorseDecomposition< mapcomp, cubetype, cubsettype >::conn, MorseDecomposition< mapcomp, cubetype, cubsettype >::indices, MorseDecomposition< mapcomp, cubetype, cubsettype >::nontrivial, MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets, and MorseDecomposition< mapcomp, cubetype, cubsettype >::sets.
| void MorseDecomposition< mapcomp, cubetype, cubsettype >::deleteall | ( | int | firstnumber, | |
| int | lastnumber | |||
| ) | [inline, private] |
Release the memory (used in the destructor and copy constructor).
Optionally, delete only Morse decompositions data for Morse sets whose numbers are greater or equal the given number.
Definition at line 295 of file morsedec.h.
Referenced by MorseDecomposition< mapcomp, cubetype, cubsettype >::join(), MorseDecomposition< mapcomp, cubetype, cubsettype >::passthru(), and MorseDecomposition< mapcomp, cubetype, cubsettype >::setnumber().
| void MorseDecomposition< mapcomp, cubetype, cubsettype >::copyall | ( | const MorseDecomposition< mapcomp, cubetype, cubsettype > & | m | ) | [inline, private] |
Copy all the data (used in the copy constructor and operator =).
Definition at line 391 of file morsedec.h.
| void MorseDecomposition< mapcomp, cubetype, cubsettype >::addone | ( | ) | [inline, private] |
Add one Morse set and initialize its data.
Definition at line 455 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::conn, MorseDecomposition< mapcomp, cubetype, cubsettype >::dist, MorseDecomposition< mapcomp, cubetype, cubsettype >::distconn, MorseDecomposition< mapcomp, cubetype, cubsettype >::indices, MorseDecomposition< mapcomp, cubetype, cubsettype >::nontrivial, MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets, and MorseDecomposition< mapcomp, cubetype, cubsettype >::sets.
Referenced by MorseDecomposition< mapcomp, cubetype, cubsettype >::add(), MorseDecomposition< mapcomp, cubetype, cubsettype >::addconn(), MorseDecomposition< mapcomp, cubetype, cubsettype >::intersection(), MorseDecomposition< mapcomp, cubetype, cubsettype >::loadfromfiles(), and MorseDecomposition< mapcomp, cubetype, cubsettype >::setnumber().
| bool MorseDecomposition< mapcomp, cubetype, cubsettype >::adjacent | ( | int | n, | |
| int | m, | |||
| int | margin = 0 | |||
| ) | const [inline, private] |
Verifies if two Morse sets are adjacent to each other.
Note: If both sets are large, then this can be time-consuming.
Definition at line 490 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets, and MorseDecomposition< mapcomp, cubetype, cubsettype >::sets.
| int MorseDecomposition< mapcomp, cubetype, cubsettype >::cubsetdistance | ( | const cubsettype & | X, | |
| const cubsettype & | Y, | |||
| bool | minimum | |||
| ) | [inline, static, private] |
Returns the approximate distance between the two cubical sets.
If minimum is set to true, then computes the minimal distance between any pair of cubes, one taken from X, the other from Y. If minimum is set to false, then computes the maximal distance of any cube in X from the set Y, that is, how far X is from Y (warning: the latter relation is not symmetric!) Note: This computation may take some time for large sets.
Definition at line 563 of file morsedec.h.
References MorseDecomposition< mapcomp, cubetype, cubsettype >::dist.
Referenced by MorseDecomposition< mapcomp, cubetype, cubsettype >::distance().
| const mapcomp& MorseDecomposition< mapcomp, cubetype, cubsettype >::M |
The map computation class.
Definition at line 103 of file morsedec.h.
Referenced by MorseDecomposition< mapcomp, cubetype, cubsettype >::compute().
int MorseDecomposition< mapcomp, cubetype, cubsettype >::nsets [private] |
The number of Morse sets.
Definition at line 232 of file morsedec.h.
Referenced by MorseDecomposition< mapcomp, cubetype, cubsettype >::add(), MorseDecomposition< mapcomp, cubetype, cubsettype >::addconn(), MorseDecomposition< mapcomp, cubetype, cubsettype >::addone(), MorseDecomposition< mapcomp, cubetype, cubsettype >::adjacent(), MorseDecomposition< mapcomp, cubetype, cubsettype >::compute(), MorseDecomposition< mapcomp, cubetype, cubsettype >::computed(), MorseDecomposition< mapcomp, cubetype, cubsettype >::conndistance(), MorseDecomposition< mapcomp, cubetype, cubsettype >::connected(), MorseDecomposition< mapcomp, cubetype, cubsettype >::connection(), MorseDecomposition< mapcomp, cubetype, cubsettype >::count(), MorseDecomposition< mapcomp, cubetype, cubsettype >::distance(), MorseDecomposition< mapcomp, cubetype, cubsettype >::index(), MorseDecomposition< mapcomp, cubetype, cubsettype >::intersection(), MorseDecomposition< mapcomp, cubetype, cubsettype >::join(), MorseDecomposition< mapcomp, cubetype, cubsettype >::jointrivial(), MorseDecomposition< mapcomp, cubetype, cubsettype >::loadfromfiles(), MorseDecomposition< mapcomp, cubetype, cubsettype >::makegraph(), MorseDecomposition< mapcomp, cubetype, cubsettype >::operator[](), MorseDecomposition< mapcomp, cubetype, cubsettype >::passthru(), MorseDecomposition< mapcomp, cubetype, cubsettype >::savetofiles(), MorseDecomposition< mapcomp, cubetype, cubsettype >::setindex(), MorseDecomposition< mapcomp, cubetype, cubsettype >::setnumber(), and MorseDecomposition< mapcomp, cubetype, cubsettype >::trivial().
chomp::homology::multitable<cubsettype *> MorseDecomposition< mapcomp, cubetype, cubsettype >::sets [private] |
The Morse sets.
Definition at line 235 of file morsedec.h.
Referenced by MorseDecomposition< mapcomp, cubetype, cubsettype >::add(), MorseDecomposition< mapcomp, cubetype, cubsettype >::addone(), MorseDecomposition< mapcomp, cubetype, cubsettype >::adjacent(), MorseDecomposition< mapcomp, cubetype, cubsettype >::compute(), MorseDecomposition< mapcomp, cubetype, cubsettype >::distance(), MorseDecomposition< mapcomp, cubetype, cubsettype >::intersection(), MorseDecomposition< mapcomp, cubetype, cubsettype >::join(), MorseDecomposition< mapcomp, cubetype, cubsettype >::jointrivial(), MorseDecomposition< mapcomp, cubetype, cubsettype >::loadfromfiles(), MorseDecomposition< mapcomp, cubetype, cubsettype >::operator[](), MorseDecomposition< mapcomp, cubetype, cubsettype >::passthru(), and MorseDecomposition< mapcomp, cubetype, cubsettype >::savetofiles().
chomp::homology::multitable<IndexType *> MorseDecomposition< mapcomp, cubetype, cubsettype >::indices [private] |
The Conley indices of the Morse sets.
Definition at line 238 of file morsedec.h.
Referenced by MorseDecomposition< mapcomp, cubetype, cubsettype >::addone(), MorseDecomposition< mapcomp, cubetype, cubsettype >::compute(), MorseDecomposition< mapcomp, cubetype, cubsettype >::computed(), MorseDecomposition< mapcomp, cubetype, cubsettype >::index(), MorseDecomposition< mapcomp, cubetype, cubsettype >::join(), MorseDecomposition< mapcomp, cubetype, cubsettype >::loadfromfiles(), MorseDecomposition< mapcomp, cubetype, cubsettype >::savetofiles(), and MorseDecomposition< mapcomp, cubetype, cubsettype >::setindex().
chomp::homology::multitable<int> MorseDecomposition< mapcomp, cubetype, cubsettype >::nontrivial [private] |
The table that stores the information on whether the indices are trivial or not: -1 = unknown, 0 = trivial, 1 = nontrivial.
Definition at line 242 of file morsedec.h.
Referenced by MorseDecomposition< mapcomp, cubetype, cubsettype >::addone(), MorseDecomposition< mapcomp, cubetype, cubsettype >::compute(), MorseDecomposition< mapcomp, cubetype, cubsettype >::join(), MorseDecomposition< mapcomp, cubetype, cubsettype >::jointrivial(), MorseDecomposition< mapcomp, cubetype, cubsettype >::loadfromfiles(), MorseDecomposition< mapcomp, cubetype, cubsettype >::savetofiles(), MorseDecomposition< mapcomp, cubetype, cubsettype >::setindex(), and MorseDecomposition< mapcomp, cubetype, cubsettype >::trivial().
chomp::homology::multitable<chomp::homology::multitable<cubsettype *> > MorseDecomposition< mapcomp, cubetype, cubsettype >::conn [private] |
Connecting orbits from one set to another.
There is no connection iff the pointer is zero.
Definition at line 247 of file morsedec.h.
Referenced by MorseDecomposition< mapcomp, cubetype, cubsettype >::addconn(), MorseDecomposition< mapcomp, cubetype, cubsettype >::addone(), MorseDecomposition< mapcomp, cubetype, cubsettype >::connected(), MorseDecomposition< mapcomp, cubetype, cubsettype >::connection(), MorseDecomposition< mapcomp, cubetype, cubsettype >::distance(), MorseDecomposition< mapcomp, cubetype, cubsettype >::join(), MorseDecomposition< mapcomp, cubetype, cubsettype >::jointrivial(), MorseDecomposition< mapcomp, cubetype, cubsettype >::loadfromfiles(), MorseDecomposition< mapcomp, cubetype, cubsettype >::makegraph(), MorseDecomposition< mapcomp, cubetype, cubsettype >::passthru(), and MorseDecomposition< mapcomp, cubetype, cubsettype >::savetofiles().
chomp::homology::multitable<chomp::homology::multitable<int> > MorseDecomposition< mapcomp, cubetype, cubsettype >::dist [mutable, private] |
Tabulated distances between the Morse sets.
Definition at line 251 of file morsedec.h.
Referenced by MorseDecomposition< mapcomp, cubetype, cubsettype >::addone(), MorseDecomposition< mapcomp, cubetype, cubsettype >::cubsetdistance(), MorseDecomposition< mapcomp, cubetype, cubsettype >::distance(), MorseDecomposition< mapcomp, cubetype, cubsettype >::join(), and MorseDecomposition< mapcomp, cubetype, cubsettype >::jointrivial().
chomp::homology::multitable<chomp::homology::multitable<int> > MorseDecomposition< mapcomp, cubetype, cubsettype >::distconn [mutable, private] |
Tabulated values of the function "conndistance".
Definition at line 255 of file morsedec.h.
Referenced by MorseDecomposition< mapcomp, cubetype, cubsettype >::addone(), MorseDecomposition< mapcomp, cubetype, cubsettype >::conndistance(), MorseDecomposition< mapcomp, cubetype, cubsettype >::join(), and MorseDecomposition< mapcomp, cubetype, cubsettype >::passthru().
1.5.3