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class TDecompSparse: public TDecompBase


Sparse Symmetric Decomposition class

Solve a sparse symmetric system of linear equations using a method
based on Gaussian elimination as discussed in Duff and Reid,
ACM Trans. Math. Software 9 (1983), 302-325.

Function Members (Methods)

public:

	TDecompSparse()
	TDecompSparse(const TDecompSparse& another)
	TDecompSparse(const TMatrixDSparse& a, Int_t verbose)
	TDecompSparse(Int_t nRows, Int_t nr_nonZeros, Int_t verbose)
	TDecompSparse(Int_t row_lwb, Int_t row_upb, Int_t nr_nonZeros, Int_t verbose)
virtual	~TDecompSparse()
void	TObject::AbstractMethod(const char* method) const
virtual void	TObject::AppendPad(Option_t* option = "")
virtual void	TObject::Browse(TBrowser* b)
static TClass*	Class()
virtual const char*	TObject::ClassName() const
virtual void	TObject::Clear(Option_t* = "")
virtual TObject*	TObject::Clone(const char* newname = "") const
virtual Int_t	TObject::Compare(const TObject* obj) const
virtual Double_t	TDecompBase::Condition()
virtual void	TObject::Copy(TObject& object) const
virtual Bool_t	Decompose()
virtual void	TObject::Delete(Option_t* option = "")MENU
virtual void	Det(Double_t&, Double_t&)
virtual Int_t	TObject::DistancetoPrimitive(Int_t px, Int_t py)
virtual void	TObject::Draw(Option_t* option = "")
virtual void	TObject::DrawClass() constMENU
virtual TObject*	TObject::DrawClone(Option_t* option = "") constMENU
virtual void	TObject::Dump() constMENU
virtual void	TObject::Error(const char* method, const char* msgfmt) const
virtual void	TObject::Execute(const char* method, const char* params, Int_t* error = 0)
virtual void	TObject::Execute(TMethod* method, TObjArray* params, Int_t* error = 0)
virtual void	TObject::ExecuteEvent(Int_t event, Int_t px, Int_t py)
virtual void	TObject::Fatal(const char* method, const char* msgfmt) const
virtual TObject*	TObject::FindObject(const char* name) const
virtual TObject*	TObject::FindObject(const TObject* obj) const
Int_t	TDecompBase::GetColLwb() const
Double_t	TDecompBase::GetCondition() const
Double_t	TDecompBase::GetDet1() const
Double_t	TDecompBase::GetDet2() const
virtual Option_t*	TObject::GetDrawOption() const
static Long_t	TObject::GetDtorOnly()
virtual const char*	TObject::GetIconName() const
virtual const char*	TObject::GetName() const
virtual Int_t	GetNcols() const
virtual Int_t	GetNrows() const
virtual char*	TObject::GetObjectInfo(Int_t px, Int_t py) const
static Bool_t	TObject::GetObjectStat()
virtual Option_t*	TObject::GetOption() const
Int_t	TDecompBase::GetRowLwb() const
virtual const char*	TObject::GetTitle() const
Double_t	TDecompBase::GetTol() const
virtual UInt_t	TObject::GetUniqueID() const
virtual Bool_t	TObject::HandleTimer(TTimer* timer)
virtual ULong_t	TObject::Hash() const
virtual void	TObject::Info(const char* method, const char* msgfmt) const
virtual Bool_t	TObject::InheritsFrom(const char* classname) const
virtual Bool_t	TObject::InheritsFrom(const TClass* cl) const
virtual void	TObject::Inspect() constMENU
void	TObject::InvertBit(UInt_t f)
virtual TClass*	IsA() const
virtual Bool_t	TObject::IsEqual(const TObject* obj) const
virtual Bool_t	TObject::IsFolder() const
Bool_t	TObject::IsOnHeap() const
virtual Bool_t	TObject::IsSortable() const
Bool_t	TObject::IsZombie() const
virtual void	TObject::ls(Option_t* option = "") const
void	TObject::MayNotUse(const char* method) const
virtual Bool_t	TDecompBase::MultiSolve(TMatrixD& B)
virtual Bool_t	TObject::Notify()
void	TObject::Obsolete(const char* method, const char* asOfVers, const char* removedFromVers) const
static void	TObject::operator delete(void* ptr)
static void	TObject::operator delete(void* ptr, void* vp)
static void	TObject::operator delete[](void* ptr)
static void	TObject::operator delete[](void* ptr, void* vp)
void*	TObject::operator new(size_t sz)
void*	TObject::operator new(size_t sz, void* vp)
void*	TObject::operator new[](size_t sz)
void*	TObject::operator new[](size_t sz, void* vp)
TDecompSparse&	operator=(const TDecompSparse& source)
virtual void	TObject::Paint(Option_t* option = "")
virtual void	TObject::Pop()
virtual void	Print(Option_t* opt = "") constMENU
virtual Int_t	TObject::Read(const char* name)
virtual void	TObject::RecursiveRemove(TObject* obj)
void	TObject::ResetBit(UInt_t f)
virtual void	TObject::SaveAs(const char* filename = "", Option_t* option = "") constMENU
virtual void	TObject::SavePrimitive(ostream& out, Option_t* option = "")
void	TObject::SetBit(UInt_t f)
void	TObject::SetBit(UInt_t f, Bool_t set)
virtual void	TObject::SetDrawOption(Option_t* option = "")MENU
static void	TObject::SetDtorOnly(void* obj)
virtual void	SetMatrix(const TMatrixDSparse& a)
static void	TObject::SetObjectStat(Bool_t stat)
Double_t	TDecompBase::SetTol(Double_t newTol)
virtual void	TObject::SetUniqueID(UInt_t uid)
void	SetVerbose(Int_t v)
virtual void	ShowMembers(TMemberInspector& insp)
virtual Bool_t	Solve(TVectorD& b)
virtual Bool_t	Solve(TMatrixDColumn&)
virtual TVectorD	Solve(const TVectorD& b, Bool_t& ok)
virtual void	Streamer(TBuffer& b)
void	StreamerNVirtual(TBuffer& b)
virtual void	TObject::SysError(const char* method, const char* msgfmt) const
Bool_t	TObject::TestBit(UInt_t f) const
Int_t	TObject::TestBits(UInt_t f) const
virtual Bool_t	TransSolve(TVectorD& b)
virtual Bool_t	TransSolve(TMatrixDColumn&)
virtual TVectorD	TransSolve(const TVectorD& b, Bool_t& ok)
virtual void	TObject::UseCurrentStyle()
virtual void	TObject::Warning(const char* method, const char* msgfmt) const
virtual Int_t	TObject::Write(const char* name = 0, Int_t option = 0, Int_t bufsize = 0)
virtual Int_t	TObject::Write(const char* name = 0, Int_t option = 0, Int_t bufsize = 0) const

protected:

static void	CopyUpperTriang(const TMatrixDSparse& a, Double_t* b)
static void	TDecompBase::DiagProd(const TVectorD& diag, Double_t tol, Double_t& d1, Double_t& d2)
virtual void	TObject::DoError(int level, const char* location, const char* fmt, va_list va) const
Int_t	ErrorFlag()
static void	Factor(const Int_t n, const Int_t nz, TArrayI& Airn, TArrayI& Aicn, TArrayD& Aa, TArrayI& Aiw, TArrayI& Aikeep, const Int_t nsteps, Int_t& maxfrt, TArrayI& Aiw1, Int_t* icntl, Double_t* cntl, Int_t* info)
static void	Factor_sub1(const Int_t n, const Int_t nz, Int_t& nz1, Double_t* a, const Int_t la, Int_t* irn, Int_t* icn, Int_t* iw, const Int_t liw, Int_t* perm, Int_t* iw2, Int_t* icntl, Int_t* info)
static void	Factor_sub2(const Int_t n, const Int_t nz, Double_t* a, const Int_t la, Int_t* iw, const Int_t liw, Int_t* perm, Int_t* nstk, const Int_t nsteps, Int_t& maxfrt, Int_t* nelim, Int_t* iw2, Int_t* icntl, Double_t* cntl, Int_t* info)
static void	Factor_sub3(Double_t* a, Int_t* iw, Int_t& j1, Int_t& j2, const Int_t itop, const Int_t ireal, Int_t& ncmpbr, Int_t& ncmpbi)
virtual const TMatrixDBase&	GetDecompMatrix() const
Double_t	GetThresholdPivoting()
Double_t	GetTreatAsZero()
Int_t	TDecompBase::Hager(Double_t& est, Int_t iter = 5)
static Int_t	IDiag(Int_t ix, Int_t iy)
Int_t	IError()
void	InitParam()
static void	InitPivot(const Int_t n, const Int_t nz, TArrayI& Airn, TArrayI& Aicn, TArrayI& Aiw, TArrayI& Aikeep, TArrayI& Aiw1, Int_t& nsteps, const Int_t iflag, Int_t* icntl, Double_t* cntl, Int_t* info, Double_t& ops)
static void	InitPivot_sub1(const Int_t n, const Int_t nz, Int_t* irn, Int_t* icn, Int_t* iw, Int_t* ipe, Int_t* iq, Int_t* flag, Int_t& iwfr, Int_t* icntl, Int_t* info)
static void	InitPivot_sub2(const Int_t n, Int_t* ipe, Int_t* iw, const Int_t lw, Int_t& iwfr, Int_t* nv, Int_t* nxt, Int_t* lst, Int_t* ipd, Int_t* flag, const Int_t iovflo, Int_t& ncmpa, const Double_t fratio)
static void	InitPivot_sub2a(const Int_t n, Int_t* ipe, Int_t* iw, const Int_t lw, Int_t& iwfr, Int_t& ncmpa)
static void	InitPivot_sub3(const Int_t n, const Int_t nz, Int_t* irn, Int_t* icn, Int_t* perm, Int_t* iw, Int_t* ipe, Int_t* iq, Int_t* flag, Int_t& iwfr, Int_t* icntl, Int_t* info)
static void	InitPivot_sub4(const Int_t n, Int_t* ipe, Int_t* iw, const Int_t lw, Int_t& iwfr, Int_t* ips, Int_t* ipv, Int_t* nv, Int_t* flag, Int_t& ncmpa)
static void	InitPivot_sub5(const Int_t n, Int_t* ipe, Int_t* nv, Int_t* ips, Int_t* ne, Int_t* na, Int_t* nd, Int_t& nsteps, const Int_t nemin)
static void	InitPivot_sub6(const Int_t n, const Int_t nz, Int_t* irn, Int_t* icn, Int_t* perm, Int_t* na, Int_t* ne, Int_t* nd, const Int_t nsteps, Int_t* lstki, Int_t* lstkr, Int_t* iw, Int_t* info, Double_t& ops)
void	TObject::MakeZombie()
Int_t	MinIntWorkspace()
Int_t	MinRealWorkspace()
static Int_t	NonZerosUpperTriang(const TMatrixDSparse& a)
void	TDecompBase::ResetStatus()
void	SetThresholdPivoting(Double_t piv)
void	SetTreatAsZero(Double_t tol)
static void	Solve(const Int_t n, TArrayD& Aa, TArrayI& Aiw, TArrayD& Aw, const Int_t maxfrt, TVectorD& b, TArrayI& Aiw1, const Int_t nsteps, Int_t* icntl, Int_t* info)
static void	Solve_sub1(const Int_t n, Double_t* a, Int_t* iw, Double_t* w, Double_t* rhs, Int_t* iw2, const Int_t nblk, Int_t& latop, Int_t* icntl)
static void	Solve_sub2(const Int_t n, Double_t* a, Int_t* iw, Double_t* w, Double_t* rhs, Int_t* iw2, const Int_t nblk, const Int_t latop, Int_t* icntl)

Data Members

public:

enum TDecompBase::EMatrixDecompStat {	kInit
	kPatternSet
	kValuesSet
	kMatrixSet
	kDecomposed
	kDetermined
	kCondition
	kSingular
};
enum TDecompBase::[unnamed] {	kWorkMax
};
enum TObject::EStatusBits {	kCanDelete
	kMustCleanup
	kObjInCanvas
	kIsReferenced
	kHasUUID
	kCannotPick
	kNoContextMenu
	kInvalidObject
};
enum TObject::[unnamed] {	kIsOnHeap
	kNotDeleted
	kZombie
	kBitMask
	kSingleKey
	kOverwrite
	kWriteDelete
};

protected:

TMatrixDSparse	fA	original matrix; needed for the iterative solving procedure
Double_t	fCntl[6]	float control numbers
TArrayI	fColFact
Int_t	TDecompBase::fColLwb	Column lower bound of decomposed matrix
Double_t	TDecompBase::fCondition	matrix condition number
Double_t	TDecompBase::fDet1	determinant mantissa
Double_t	TDecompBase::fDet2	determinant exponent for powers of 2
TArrayD	fFact	size of fFact array; may be increased during the numerical factorization
Double_t	fIPessimism	amounts by which to increase allocated factorization space when
Int_t	fIcntl[31]	integer control numbers
TArrayI	fIkeep	pivot sequence and temporary storage information
Int_t	fInfo[21]	array used for communication between programs
TArrayI	fIw
TArrayI	fIw1
TArrayI	fIw2
Int_t	fMaxfrt
Int_t	fNnonZeros
Int_t	fNrows
Int_t	fNsteps
Double_t	fPrecision	precision we demand from the linear system solver. If it isn't
Double_t	fRPessimism	inadequate space is detected. fIPessimism is for array "fIw",
TArrayI	fRowFact
Int_t	TDecompBase::fRowLwb	Row lower bound of decomposed matrix
Double_t	TDecompBase::fTol	sqrt(epsilon); epsilon is smallest number number so that 1+epsilon > 1
Int_t	fVerbose
TArrayD	fW	temporary storage for the factorization

Class Charts

Inheritance Inherited Members Includes Libraries

Function documentation

TDecompSparse()

 Default constructor

TDecompSparse(Int_t nRows, Int_t nr_nonZeros, Int_t verbose)

 Constructor for a matrix with nrows and unspecified number of columns .
 nr_nonZeros is the total number of non-zero entries in the matrix .

TDecompSparse(Int_t row_lwb, Int_t row_upb, Int_t nr_nonZeros, Int_t verbose)

 Constructor for a matrix with row range, [row_lwb..row_upb] and unspecified column
 range . nr_nonZeros is the total number of non-zero entries in the matrix .

TDecompSparse(const TMatrixDSparse& a, Int_t verbose)

 Constructor for matrix A .

TDecompSparse(const TDecompSparse& another)

 Copy constructor

Int_t NonZerosUpperTriang(const TMatrixDSparse& a)

 Static function, returning the number of non-zero entries in the upper triangular matrix .

void CopyUpperTriang(const TMatrixDSparse& a, Double_t* b)

 Static function, copying the non-zero entries in the upper triangle to
 array b . User should allocate enough memory for array b .

void SetMatrix(const TMatrixDSparse& a)

 Set matrix to be decomposed .

Bool_t Decompose()

 Decomposition engine .
 If the decomposition succeeds, bit kDecomposed is set .

Bool_t Solve(TVectorD& b)

 Solve Ax=b . Solution returned in b.

void InitParam()

 initializing control parameters

void InitPivot(const Int_t n, const Int_t nz, TArrayI& Airn, TArrayI& Aicn, TArrayI& Aiw, TArrayI& Aikeep, TArrayI& Aiw1, Int_t& nsteps, const Int_t iflag, Int_t* icntl, Double_t* cntl, Int_t* info, Double_t& ops)

 Setup Pivoting variables

void Factor(const Int_t n, const Int_t nz, TArrayI& Airn, TArrayI& Aicn, TArrayD& Aa, TArrayI& Aiw, TArrayI& Aikeep, const Int_t nsteps, Int_t& maxfrt, TArrayI& Aiw1, Int_t* icntl, Double_t* cntl, Int_t* info)

 Factorization routine, the workhorse for the decompostion step

void Solve(const Int_t n, TArrayD& Aa, TArrayI& Aiw, TArrayD& Aw, const Int_t maxfrt, TVectorD& b, TArrayI& Aiw1, const Int_t nsteps, Int_t* icntl, Int_t* info)

 Main routine for solving Ax=b

void InitPivot_sub1(const Int_t n, const Int_t nz, Int_t* irn, Int_t* icn, Int_t* iw, Int_t* ipe, Int_t* iq, Int_t* flag, Int_t& iwfr, Int_t* icntl, Int_t* info)

 Help routine for pivoting setup

void InitPivot_sub2(const Int_t n, Int_t* ipe, Int_t* iw, const Int_t lw, Int_t& iwfr, Int_t* nv, Int_t* nxt, Int_t* lst, Int_t* ipd, Int_t* flag, const Int_t iovflo, Int_t& ncmpa, const Double_t fratio)

 Help routine for pivoting setup

void InitPivot_sub2a(const Int_t n, Int_t* ipe, Int_t* iw, const Int_t lw, Int_t& iwfr, Int_t& ncmpa)

 Help routine for pivoting setup

void InitPivot_sub3(const Int_t n, const Int_t nz, Int_t* irn, Int_t* icn, Int_t* perm, Int_t* iw, Int_t* ipe, Int_t* iq, Int_t* flag, Int_t& iwfr, Int_t* icntl, Int_t* info)

 Help routine for pivoting setup

void InitPivot_sub4(const Int_t n, Int_t* ipe, Int_t* iw, const Int_t lw, Int_t& iwfr, Int_t* ips, Int_t* ipv, Int_t* nv, Int_t* flag, Int_t& ncmpa)

 Help routine for pivoting setup

void InitPivot_sub5(const Int_t n, Int_t* ipe, Int_t* nv, Int_t* ips, Int_t* ne, Int_t* na, Int_t* nd, Int_t& nsteps, const Int_t nemin)

 Help routine for pivoting setup

void InitPivot_sub6(const Int_t n, const Int_t nz, Int_t* irn, Int_t* icn, Int_t* perm, Int_t* na, Int_t* ne, Int_t* nd, const Int_t nsteps, Int_t* lstki, Int_t* lstkr, Int_t* iw, Int_t* info, Double_t& ops)

 Help routine for pivoting setup

void Factor_sub1(const Int_t n, const Int_t nz, Int_t& nz1, Double_t* a, const Int_t la, Int_t* irn, Int_t* icn, Int_t* iw, const Int_t liw, Int_t* perm, Int_t* iw2, Int_t* icntl, Int_t* info)

 Help routine for factorization

void Factor_sub2(const Int_t n, const Int_t nz, Double_t* a, const Int_t la, Int_t* iw, const Int_t liw, Int_t* perm, Int_t* nstk, const Int_t nsteps, Int_t& maxfrt, Int_t* nelim, Int_t* iw2, Int_t* icntl, Double_t* cntl, Int_t* info)

 Help routine for factorization

void Factor_sub3(Double_t* a, Int_t* iw, Int_t& j1, Int_t& j2, const Int_t itop, const Int_t ireal, Int_t& ncmpbr, Int_t& ncmpbi)

 Help routine for factorization

void Solve_sub1(const Int_t n, Double_t* a, Int_t* iw, Double_t* w, Double_t* rhs, Int_t* iw2, const Int_t nblk, Int_t& latop, Int_t* icntl)

 Help routine for solving

void Solve_sub2(const Int_t n, Double_t* a, Int_t* iw, Double_t* w, Double_t* rhs, Int_t* iw2, const Int_t nblk, const Int_t latop, Int_t* icntl)

 Help routine for solving

void Print(Option_t* opt = "") const

 Print class members

TDecompSparse & operator=(const TDecompSparse& source)

 Assignment operator

void Solve(const Int_t n, TArrayD& Aa, TArrayI& Aiw, TArrayD& Aw, const Int_t maxfrt, TVectorD& b, TArrayI& Aiw1, const Int_t nsteps, Int_t* icntl, Int_t* info)

Int_t IDiag(Int_t ix, Int_t iy)

{ return ((iy-1)*(2*ix-iy+2))/2; }

Int_t IError()

{ return fInfo[2]; }

Int_t MinRealWorkspace()

{ return fInfo[5]; }

Int_t MinIntWorkspace()

{ return fInfo[6]; }

Int_t ErrorFlag()

{ return fInfo[1]; }

Double_t GetThresholdPivoting()

 Takes values in the range [0,1]. Larger values enforce greater stability in
 the factorization as they insist on larger pivots. Smaller values preserve
 sparsity at the cost of using smaller pivots.

{ return fCntl[1]; }

Double_t GetTreatAsZero()

{ return fCntl[3]; }

void SetThresholdPivoting(Double_t piv)

 The factorization will not accept a pivot whose absolute value is less than fCntl[3] as
 a 1x1 pivot or as the off-diagonal in a 2x2 pivot.

{ fCntl[1] = piv; }

void SetTreatAsZero(Double_t tol)

{ fCntl[3] = tol; }

const TMatrixDBase & GetDecompMatrix() const

{ MayNotUse("GetDecompMatrix()"); return fA; }

virtual ~TDecompSparse()

{}

void SetVerbose(Int_t v)

Int_t GetNrows() const

{ return fA.GetNrows(); }

Int_t GetNcols() const

{ return fA.GetNcols(); }

Bool_t Solve(TVectorD& b)

Bool_t TransSolve(TVectorD& b)

{ return Solve(b); }

TVectorD TransSolve(const TVectorD& b, Bool_t& ok)

{ TVectorD x = b; ok = Solve(x); return x; }

Bool_t TransSolve(TMatrixDColumn& )

{ MayNotUse("TransSolve(TMatrixDColumn &)"); return kFALSE; }

void Det(Double_t& , Double_t& )

{ MayNotUse("Det(Double_t&,Double_t&)"); }