Detailed Description

Calculates number of partitions of (A,Z,M)

Created by KVClassFactory on Thu Sep 30 16:48:24 2010 Author: John Frankland,,,,

These functions calculate the total number of partitions and the number of partitions per multiplicity either for a single component system (corresponding to the partition function of number theory, i.e. the number of ways to decompose an integer into distinct sums of other integers), or for a system made of two kinds of objects, i.e. protons and neutrons, with A=N+Z.

These are exact results, the numbers correspond to each and every partition appearing once and only once.

Single component system

The method

Double_t PartFunc(Int_t A, Int_t M)

Int_t

int Int_t

Double_t

double Double_t

KVPartitionFunction::PartFunc

Double_t PartFunc(int A, int M)

Definition KVPartitionFunction.cpp:48

calculates the total number of ways to partition an integer A into the sum of M integers ( \(1\leq M\leq A\)). We use the recursion relation given by J.P. Bondorf in Nucl. Phys. A443, 321 (1985), Eq. (2.6).

The method

Double_t PartSum(Int_t A)

KVPartitionFunction::PartSum

Double_t PartSum(int A)

Definition KVPartitionFunction.cpp:83

returns the total number of partitions summed over all multiplicities.

Two component system

The method

Double_t PartFunc(Int_t A, Int_t Z, Int_t M)

calculates the total number of ways to partition Z protons and (A-Z) neutrons into M fragments, using the method given by K. Sneppen in Nucl. Phys. A470, 213 (1987), Eqs. (4)-(6).

The method

Double_t PartSum(Int_t A, Int_t Z)

returns the total number of partitions summed over all multiplicities.

Definition at line 55 of file KVPartitionFunction.h.

#include <KVPartitionFunction.h>

Inheritance diagram for KVPartitionFunction:

[legend]

Public Member Functions
	KVPartitionFunction ()
	Default constructor.

virtual	~KVPartitionFunction ()
	Destructor.

Double_t	GetMaxValueNclass () const

Double_t	GetMaxValueNp () const

Double_t	MeanA (int A0)

Double_t	MeanM (int A0)

Double_t	MeanNA (int A0, int A)

Double_t	MeanNA (int A0, int Z0, int A)

Double_t	MeanNA_M (int A0, int A, int M)

Double_t	MeanNAZ (int A0, int Z0, int A, int Z)

Double_t	MeanNZ (int A0, int Z0, int Z)

Double_t	PartFunc (int A, int M)

Double_t	PartFunc (int A, int Z, int M)

Double_t	PartSum (int A)

Double_t	PartSum (int A, int Z)

Public Member Functions inherited from TObject
	TObject ()

	TObject (const TObject &object)

virtual	~TObject ()

void	AbstractMethod (const char *method) const

virtual void	AppendPad (Option_t *option="")

virtual void	Browse (TBrowser *b)

ULong_t	CheckedHash ()

virtual const char *	ClassName () const

virtual void	Clear (Option_t *="")

virtual TObject *	Clone (const char *newname="") const

virtual Int_t	Compare (const TObject *obj) const

virtual void	Copy (TObject &object) const

virtual void	Delete (Option_t *option="")

virtual Int_t	DistancetoPrimitive (Int_t px, Int_t py)

virtual void	Draw (Option_t *option="")

virtual void	DrawClass () const

virtual TObject *	DrawClone (Option_t *option="") const

virtual void	Dump () const

virtual void	Error (const char method, const char msgfmt,...) const

virtual void	Execute (const char method, const char params, Int_t *error=nullptr)

virtual void	Execute (TMethod method, TObjArray params, Int_t *error=nullptr)

virtual void	ExecuteEvent (Int_t event, Int_t px, Int_t py)

virtual void	Fatal (const char method, const char msgfmt,...) const

virtual TObject *	FindObject (const char *name) const

virtual TObject *	FindObject (const TObject *obj) const

virtual Option_t *	GetDrawOption () const

virtual const char *	GetIconName () const

virtual const char *	GetName () const

virtual char *	GetObjectInfo (Int_t px, Int_t py) const

virtual Option_t *	GetOption () const

virtual const char *	GetTitle () const

virtual UInt_t	GetUniqueID () const

virtual Bool_t	HandleTimer (TTimer *timer)

virtual ULong_t	Hash () const

Bool_t	HasInconsistentHash () const

virtual void	Info (const char method, const char msgfmt,...) const

virtual Bool_t	InheritsFrom (const char *classname) const

virtual Bool_t	InheritsFrom (const TClass *cl) const

virtual void	Inspect () const

void	InvertBit (UInt_t f)

virtual TClass *	IsA () const

Bool_t	IsDestructed () const

virtual Bool_t	IsEqual (const TObject *obj) const

virtual Bool_t	IsFolder () const

R__ALWAYS_INLINE Bool_t	IsOnHeap () const

virtual Bool_t	IsSortable () const

R__ALWAYS_INLINE Bool_t	IsZombie () const

virtual void	ls (Option_t *option="") const

void	MayNotUse (const char *method) const

virtual Bool_t	Notify ()

void	Obsolete (const char method, const char asOfVers, const char *removedFromVers) const

void	operator delete (void *ptr)

void	operator delete (void ptr, void vp)

void	operator delete[] (void *ptr)

void	operator delete[] (void ptr, void vp)

void *	operator new (size_t sz)

void *	operator new (size_t sz, void *vp)

void *	operator new[] (size_t sz)

void *	operator new[] (size_t sz, void *vp)

TObject &	operator= (const TObject &rhs)

virtual void	Paint (Option_t *option="")

virtual void	Pop ()

virtual void	Print (Option_t *option="") const

virtual Int_t	Read (const char *name)

virtual void	RecursiveRemove (TObject *obj)

void	ResetBit (UInt_t f)

virtual void	SaveAs (const char filename="", Option_t option="") const

virtual void	SavePrimitive (std::ostream &out, Option_t *option="")

void	SetBit (UInt_t f)

void	SetBit (UInt_t f, Bool_t set)

virtual void	SetDrawOption (Option_t *option="")

virtual void	SetUniqueID (UInt_t uid)

virtual void	Streamer (TBuffer &)

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

virtual void	SysError (const char method, const char msgfmt,...) const

R__ALWAYS_INLINE Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

virtual void	UseCurrentStyle ()

virtual void	Warning (const char method, const char msgfmt,...) const

virtual Int_t	Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0)

virtual Int_t	Write (const char *name=nullptr, Int_t option=0, Int_t bufsize=0) const

Private Member Functions
Double_t	calc_sneppen_Nclass (int A, int Z, int M, int B)
	calculates Eqs. 5a-d

Double_t	calc_sneppen_Np (int A, int Z, int M)
	calculates Eq. 4

Double_t	get_value (Int_t A, Int_t Z, Int_t M, Int_t B=-1)

const Char_t *	name_value (Int_t A, Int_t Z, Int_t M, Int_t B=-1)

Double_t	sneppen_Nclass (int A, int Z, int M, int B)

Double_t	sneppen_Np (int A, int Z, int M)

void	store_value (Double_t val, Int_t A, Int_t Z, Int_t M, Int_t B=-1)

Private Attributes
THashTable	fTable

Double_t	maxvalueNclass

Double_t	maxvalueNp

Double_t	NvalsNcl

Double_t	NvalsNp

Additional Inherited Members
Public Types inherited from TObject
enum	EDeprecatedStatusBits

enum	EStatusBits

Static Public Member Functions inherited from TObject
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

static Longptr_t	GetDtorOnly ()

static Bool_t	GetObjectStat ()

static void	SetDtorOnly (void *obj)

static void	SetObjectStat (Bool_t stat)

Public Attributes inherited from TObject
	kBitMask

	kCanDelete

	kCannotPick

	kHasUUID

	kInconsistent

	kInvalidObject

	kIsOnHeap

	kIsReferenced

	kMustCleanup

	kNoContextMenu

	kNotDeleted

	kObjInCanvas

	kOverwrite

	kSingleKey

	kWriteDelete

	kZombie

Protected Member Functions inherited from TObject
virtual void	DoError (int level, const char location, const char fmt, va_list va) const

void	MakeZombie ()

Protected Attributes inherited from TObject
	kOnlyPrepStep

Constructor & Destructor Documentation

◆ KVPartitionFunction()

KVPartitionFunction::KVPartitionFunction ( )

Default constructor.

Definition at line 15 of file KVPartitionFunction.cpp.

◆ ~KVPartitionFunction()

KVPartitionFunction::~KVPartitionFunction ( )

virtual

Destructor.

Definition at line 26 of file KVPartitionFunction.cpp.

Member Function Documentation

◆ calc_sneppen_Nclass()

Double_t KVPartitionFunction::calc_sneppen_Nclass	(	int	A,
		int	Z,
		int	M,
		int	B
	)

private

calculates Eqs. 5a-d

Definition at line 137 of file KVPartitionFunction.cpp.

◆ calc_sneppen_Np()

Double_t KVPartitionFunction::calc_sneppen_Np	(	int	A,
		int	Z,
		int	M
	)

private

calculates Eq. 4

Definition at line 184 of file KVPartitionFunction.cpp.

◆ get_value()

Double_t KVPartitionFunction::get_value	(	Int_t	A,
		Int_t	Z,
		Int_t	M,
		Int_t	B = `-1`
	)

inlineprivate

Definition at line 82 of file KVPartitionFunction.h.

◆ GetMaxValueNclass()

Double_t KVPartitionFunction::GetMaxValueNclass ( ) const

inline

Definition at line 105 of file KVPartitionFunction.h.

◆ GetMaxValueNp()

Double_t KVPartitionFunction::GetMaxValueNp ( ) const

inline

Definition at line 101 of file KVPartitionFunction.h.

◆ MeanA()

Double_t KVPartitionFunction::MeanA ( int A0 )

Calculate the mean size of clusters in all partitions of a single-component system of mass A0.

Definition at line 429 of file KVPartitionFunction.cpp.

◆ MeanM()

Double_t KVPartitionFunction::MeanM ( int A0 )

Calculate the mean multiplicity of all partitions of a single-component system of mass A0.

Definition at line 407 of file KVPartitionFunction.cpp.

◆ MeanNA() [1/2]

Double_t KVPartitionFunction::MeanNA	(	int	A0,
		int	A
	)

Calculate the mean number of clusters of size A when a system of size A0 fragments in all possible ways with equal probability Using Eq. (3) of K. Sneppen Nucl. Phys. A470, 213 (1987)

Correction for A=A0: there is always exactly 1 partition of M=1 composed of one fragment with A=A0 the mean multiplicity of A=A0 is therefore 1/PartSum(A0)

Definition at line 254 of file KVPartitionFunction.cpp.

◆ MeanNA() [2/2]

Double_t KVPartitionFunction::MeanNA	(	int	A0,
		int	Z0,
		int	A
	)

Calculate the mean number of clusters of mass A when a two-component system (A0,Z0) fragments in all possible ways with equal probability This is just the sum of MeanNAZ(A0,Z0,A,Z) with 0<=Z<= min(A,Z0)

Definition at line 372 of file KVPartitionFunction.cpp.

◆ MeanNA_M()

Double_t KVPartitionFunction::MeanNA_M	(	int	A0,
		int	A,
		int	M
	)

Calculate the mean number of clusters of size A when a system of size A0 breaks up into M fragments, each partition having equal probability Using Eqs. (2b) & (3) of K. Sneppen Nucl. Phys. A470, 213 (1987)

Correction for M=1: if A==A0, mean multiplicity is 1; otherwise 0. Correction for M=2 and even values of A0: when an odd-A0 splits into M=2, there are PartFunc(A0,M) partitions in which each A between 1 and A0-1 occurs once only, therefore the mean multiplicity for any A is 1/PartFunc(A0,M) when an even-A0 splits into M=2, one of the PartFunc(A0,M) partitions is the symmetric split (A0/2, A0/2). Therefore the mean multiplicity of A=A0/2 is twice that of the other A, i.e. 2/PartFunc(A0,M) Correction for M=A0: in this case only one partition exists, made of M=A0 monomers A=1 therefore mean multiplicity of A=1 is M, for all other A it is 0.

Definition at line 295 of file KVPartitionFunction.cpp.

◆ MeanNAZ()

Double_t KVPartitionFunction::MeanNAZ	(	int	A0,
		int	Z0,
		int	A,
		int	Z
	)

Calculate the mean number of clusters of mass A and charge Z when a two-component system (A0,Z0) fragments in all possible ways with equal probability Using Eq. (7) of K. Sneppen Nucl. Phys. A470, 213 (1987)

Definition at line 348 of file KVPartitionFunction.cpp.

◆ MeanNZ()

Double_t KVPartitionFunction::MeanNZ	(	int	A0,
		int	Z0,
		int	Z
	)

Calculate the mean number of clusters of charge Z when a two-component system (A0,Z0) fragments in all possible ways with equal probability This is just the sum of MeanNAZ(A0,Z0,A,Z) with Z<=A<=(Z+A0-Z0)

Definition at line 390 of file KVPartitionFunction.cpp.

◆ name_value()

const Char_t * KVPartitionFunction::name_value	(	Int_t	A,
		Int_t	Z,
		Int_t	M,
		Int_t	B = `-1`
	)

inlineprivate

Definition at line 68 of file KVPartitionFunction.h.

◆ PartFunc() [1/2]

Double_t KVPartitionFunction::PartFunc	(	int	A,
		int	M
	)

recursive calculation of number of partitions of A nucleons into M fragments of size 1, 2, ..., A from Eq. (2.6) of Bondorf et al., Nucl. Phys. A443, 321 (1985): "We now consider the division of the partition space into the subsets characterized by having a common multiplicity. Let P(A,, M) be the number of partitions in one of such subsets. To compute P(A,, M) it is sufficient to observe that it should be equal to the number of partitions having at least one fragment composed of just one nucleon (which number is immediately shown to equal P(A0 - 1, M - 1)) plus those not having any unitary fragment. The number of this last portion can be computed by observing that, if we take one nucleon from each of its fragments one has the set of all partitions of A0 - M nucleons into M fragments. We thus arrive at P(A0,M) = P(A0-1,M-l) + P(A0-M, M) Eq. (2.5)" The expression below follows from recursive use of this relation.

Definition at line 48 of file KVPartitionFunction.cpp.

◆ PartFunc() [2/2]

Double_t KVPartitionFunction::PartFunc	(	int	A,
		int	Z,
		int	M
	)

Returns the total number of partitions of Z protons and (A-Z) neutrons into M fragments, using the method given by K. Sneppen in Nucl. Phys. A470, 213 (1987), Eqs. (4)-(6).

Definition at line 211 of file KVPartitionFunction.cpp.

◆ PartSum() [1/2]

Double_t KVPartitionFunction::PartSum ( int A )

calculate total number of partitions of A nucleons into 1, 2, ..., A fragments. from Eq. (2.7) of Bondorf et al., Nucl. Phys. A443, 321 (1985)

Definition at line 83 of file KVPartitionFunction.cpp.

◆ PartSum() [2/2]

Double_t KVPartitionFunction::PartSum	(	int	A,
		int	Z
	)

Returns the total number of partitions of Z protons and (A-Z) neutrons summed over all multiplicities, using the method given by K. Sneppen in Nucl. Phys. A470, 213 (1987), Eqs. (4)-(6).

Definition at line 230 of file KVPartitionFunction.cpp.

◆ sneppen_Nclass()

Double_t KVPartitionFunction::sneppen_Nclass	(	int	A,
		int	Z,
		int	M,
		int	B
	)

private

Definition at line 99 of file KVPartitionFunction.cpp.

◆ sneppen_Np()

Double_t KVPartitionFunction::sneppen_Np	(	int	A,
		int	Z,
		int	M
	)

private

Definition at line 117 of file KVPartitionFunction.cpp.

◆ store_value()

void KVPartitionFunction::store_value	(	Double_t	val,
		Int_t	A,
		Int_t	Z,
		Int_t	M,
		Int_t	B = `-1`
	)

inlineprivate

Definition at line 74 of file KVPartitionFunction.h.

Member Data Documentation

◆ fTable

THashTable KVPartitionFunction::fTable

private

Definition at line 56 of file KVPartitionFunction.h.

◆ maxvalueNclass

Double_t KVPartitionFunction::maxvalueNclass

private

Definition at line 59 of file KVPartitionFunction.h.

◆ maxvalueNp

Double_t KVPartitionFunction::maxvalueNp

private

Definition at line 58 of file KVPartitionFunction.h.

◆ NvalsNcl

Double_t KVPartitionFunction::NvalsNcl

private

Definition at line 61 of file KVPartitionFunction.h.

◆ NvalsNp

Double_t KVPartitionFunction::NvalsNp

private

Definition at line 60 of file KVPartitionFunction.h.

Detailed Description

Single component system

Two component system

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ KVPartitionFunction()

◆ ~KVPartitionFunction()

Member Function Documentation

◆ calc_sneppen_Nclass()

◆ calc_sneppen_Np()

◆ get_value()

◆ GetMaxValueNclass()

◆ GetMaxValueNp()

◆ MeanA()

◆ MeanM()

◆ MeanNA() [1/2]

◆ MeanNA() [2/2]

◆ MeanNA_M()

◆ MeanNAZ()

◆ MeanNZ()

◆ name_value()

◆ PartFunc() [1/2]

◆ PartFunc() [2/2]

◆ PartSum() [1/2]

◆ PartSum() [2/2]

◆ sneppen_Nclass()

◆ sneppen_Np()

◆ store_value()

Member Data Documentation

◆ fTable

◆ maxvalueNclass

◆ maxvalueNp

◆ NvalsNcl

◆ NvalsNp