template<class Element>
class TMatrixTBase< Element >

Linear Algebra Package.

Linear Algebra Package

The present package implements all the basic algorithms dealing with vectors, matrices, matrix columns, rows, diagonals, etc. In addition eigen-Vector analysis and several matrix decomposition have been added (LU,QRH,Cholesky,Bunch-Kaufman and SVD) . The decompositions are used in matrix inversion, equation solving.

For a dense matrix, elements are arranged in memory in a ROW-wise fashion . For (n x m) matrices where n*m <=kSizeMax (=25 currently) storage space is available on the stack, thus avoiding expensive allocation/deallocation of heap space . However, this introduces of course kSizeMax overhead for each matrix object . If this is an issue recompile with a new appropriate value (>=0) for kSizeMax

Sparse matrices are also stored in row-wise fashion but additional row/column information is stored, see TMatrixTSparse source for additional details .

Another way to assign and store matrix data is through Use see for instance stressLinear.cxx file .

Unless otherwise specified, matrix and vector indices always start with 0, spanning up to the specified limit-1. However, there are constructors to which one can specify aribtrary lower and upper bounds, e.g. TMatrixD m(1,10,1,5) defines a matrix that ranges from 1..10, 1..5 (a(1,1)..a(10,5)).

The present package provides all facilities to completely AVOID returning matrices. Use "TMatrixD A(TMatrixD::kTransposed,B);" and other fancy constructors as much as possible. If one really needs to return a matrix, return a TMatrixTLazy object instead. The conversion is completely transparent to the end user, e.g. "TMatrixT m = THaarMatrixT(5);" and is efficient.

Since TMatrixT et al. are fully integrated in ROOT, they of course can be stored in a ROOT database.

For usage examples see $ROOTSYS/test/stressLinear.cxx

Acknowledgements

Oleg E. Kiselyov First implementations were based on the his code . We have diverged quite a bit since then but the ideas/code for lazy matrix and "nested function" are 100% his . You can see him and his code in action at http://okmij.org/ftp
Chris R. Birchenhall, We adapted his idea of the implementation for the decomposition classes instead of our messy installation of matrix inversion His installation of matrix condition number, using an iterative scheme using the Hage algorithm is worth looking at ! Chris has a nice writeup (matdoc.ps) on his matrix classes at ftp://ftp.mcc.ac.uk/pub/matclass/
Mark Fischler and Steven Haywood of CLHEP They did the slave labor of spelling out all sub-determinants for Cramer inversion of (4x4),(5x5) and (6x6) matrices The stack storage for small matrices was also taken from them
Roldan Pozo of TNT (http://math.nist.gov/tnt/) He converted the EISPACK routines for the eigen-vector analysis to C++ . We started with his implementation
Siegmund Brandt (http://siux00.physik.uni-siegen.de/~brandt/datan We adapted his (very-well) documented SVD routines

How to efficiently use this package

1. Never return complex objects (matrices or vectors)

Danger: For example, when the following snippet:

TMatrixD foo(int n)
{
  TMatrixD foom(n,n); fill_in(foom); return foom;
}
TMatrixD m = foo(5);

runs, it constructs matrix foo:foom, copies it onto stack as a return value and destroys foo:foom. Return value (a matrix) from foo() is then copied over to m (via a copy constructor), and the return value is destroyed. So, the matrix constructor is called 3 times and the destructor 2 times. For big matrices, the cost of multiple constructing/copying/destroying of objects may be very large. Some optimized compilers can cut down on 1 copying/destroying, but still it leaves at least two calls to the constructor. Note, TMatrixDLazy (see below) can construct TMatrixD m "inplace", with only a single call to the constructor.

2. Use "two-address instructions"

"void TMatrixD::operator += (const TMatrixD &B);"

as much as possible. That is, to add two matrices, it's much more efficient to write

A += B;

ROOT::Math::Cephes::B

static double B[]

Definition: SpecFuncCephes.cxx:178

ROOT::Math::Cephes::A

static double A[]

Definition: SpecFuncCephes.cxx:170

than

TMatrixD C = A + B;

ROOT::Math::Cephes::C

static double C[]

Definition: SpecFuncCephes.cxx:187

(if both operand should be preserved, TMatrixD C = A; C += B; is still better).

3. Use glorified constructors when returning of an object seems inevitable:

"TMatrixD A(TMatrixD::kTransposed,B);"

"TMatrixD C(A,TMatrixD::kTransposeMult,B);"

like in the following snippet (from $ROOTSYS/test/vmatrix.cxx) that verifies that for an orthogonal matrix T, T'T = TT' = E.

TMatrixD haar = THaarMatrixD(5);
TMatrixD unit(TMatrixD::kUnit,haar);
TMatrixD haar_t(TMatrixD::kTransposed,haar);
TMatrixD hth(haar,TMatrixD::kTransposeMult,haar);
TMatrixD hht(haar,TMatrixD::kMult,haar_t);
TMatrixD hht1 = haar; hht1 *= haar_t;
VerifyMatrixIdentity(unit,hth);
VerifyMatrixIdentity(unit,hht);
VerifyMatrixIdentity(unit,hht1);

4. Accessing row/col/diagonal of a matrix without much fuss

(and without moving a lot of stuff around):

TMatrixD m(n,n); TVectorD v(n); TMatrixDDiag(m) += 4;
v = TMatrixDRow(m,0);
TMatrixDColumn m1(m,1); m1(2) = 3; // the same as m(2,1)=3;

Note, constructing of, say, TMatrixDDiag does not involve any copying of any elements of the source matrix.

5. It's possible (and encouraged) to use "nested" functions

For example, creating of a Hilbert matrix can be done as follows:

void foo(const TMatrixD &m)
{
 TMatrixD m1(TMatrixD::kZero,m);
 struct MakeHilbert : public TElementPosActionD {
    void Operation(Double_t &element)
       { element = 1./(fI+fJ-1); }
 };
 m1.Apply(MakeHilbert());
}

of course, using a special method THilbertMatrixD() is still more optimal, but not by a whole lot. And that's right, class MakeHilbert is declared within a function and local to that function. It means one can define another MakeHilbert class (within another function or outside of any function, that is, in the global scope), and it still will be OK. Note, this currently is not yet supported by the interpreter CINT.

Another example is applying of a simple function to each matrix element:

void foo(TMatrixD &m,TMatrixD &m1)
{
 typedef  double (*dfunc_t)(double);
 class ApplyFunction : public TElementActionD {
    dfunc_t fFunc;
    void Operation(Double_t &element)
         { element=fFunc(element); }
  public:
    ApplyFunction(dfunc_t func):fFunc(func) {}
 };
 ApplyFunction x(TMath::Sin);
 m.Apply(x);
}

Validation code $ROOTSYS/test/vmatrix.cxx and vvector.cxx contain a few more examples of that kind.

6. Lazy matrices:

instead of returning an object return a "recipe" how to make it. The full matrix would be rolled out only when and where it's needed:

TMatrixD haar = THaarMatrixD(5);

THaarMatrixD() is a class, not a simple function. However similar this looks to a returning of an object (see note #1 above), it's dramatically different. THaarMatrixD() constructs a TMatrixDLazy, an object of just a few bytes long. A special "TMatrixD(const TMatrixDLazy &recipe)" constructor follows the recipe and makes the matrix haar() right in place. No matrix element is moved whatsoever!

Definition at line 85 of file TMatrixTBase.h.

Public Member Functions
	TMatrixTBase ()

virtual	~TMatrixTBase ()

virtual TMatrixTBase< Element > &	Abs ()
	Take an absolute value of a matrix, i.e. apply Abs() to each element. More...

virtual TMatrixTBase< Element > &	Apply (const TElementActionT< Element > &action)
	Apply action to each matrix element. More...

virtual TMatrixTBase< Element > &	Apply (const TElementPosActionT< Element > &action)
	Apply action to each element of the matrix. More...

TClass *	Class ()

virtual void	Clear (Option_t *option="")=0

virtual Element	ColNorm () const
	Column matrix norm, MAX{ SUM{ \|M(i,j)\|, over i}, over j}. More...

virtual Double_t	Determinant () const

virtual void	Determinant (Double_t &d1, Double_t &d2) const

void	Draw (Option_t *option="")
	Draw this matrix The histogram is named "TMatrixT" by default and no title. More...

virtual Element	E2Norm () const
	Square of the Euclidian norm, SUM{ m(i,j)^2 }. More...

virtual void	ExtractRow (Int_t row, Int_t col, Element *v, Int_t n=-1) const
	Store in array v, n matrix elements of row rown starting at column coln. More...

virtual const Int_t *	GetColIndexArray () const =0

virtual Int_t *	GetColIndexArray ()=0

Int_t	GetColLwb () const

Int_t	GetColUpb () const

virtual void	GetMatrix2Array (Element data, Option_t option="") const
	Copy matrix data to array . More...

virtual const Element *	GetMatrixArray () const =0

virtual Element *	GetMatrixArray ()=0

Int_t	GetNcols () const

Int_t	GetNoElements () const

Int_t	GetNrows () const

virtual const Int_t *	GetRowIndexArray () const =0

virtual Int_t *	GetRowIndexArray ()=0

Int_t	GetRowLwb () const

Int_t	GetRowUpb () const

virtual TMatrixTBase< Element > &	GetSub (Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb, TMatrixTBase< Element > &target, Option_t *option="S") const =0

Element	GetTol () const

virtual TMatrixTBase< Element > &	InsertRow (Int_t row, Int_t col, const Element *v, Int_t n=-1)
	Copy n elements from array v to row rown starting at column coln. More...

void	Invalidate ()

Bool_t	IsOwner () const

virtual Bool_t	IsSymmetric () const
	Check whether matrix is symmetric. More...

Bool_t	IsValid () const

void	MakeValid ()

virtual Element	Max () const
	return maximum vector element value More...

virtual Element	Min () const
	return minimum matrix element value More...

virtual Int_t	NonZeros () const
	Compute the number of elements != 0.0. More...

Element	Norm1 () const

virtual TMatrixTBase< Element > &	NormByDiag (const TVectorT< Element > &v, Option_t *option="D")
	option: More...

Element	NormInf () const

Bool_t	operator!= (Element val) const
	Are all matrix elements not equal to val? More...

virtual Element	operator() (Int_t rown, Int_t coln) const =0

virtual Element &	operator() (Int_t rown, Int_t coln)=0

Bool_t	operator< (Element val) const
	Are all matrix elements < val? More...

Bool_t	operator<= (Element val) const
	Are all matrix elements <= val? More...

Bool_t	operator== (Element val) const
	Are all matrix elements equal to val? More...

Bool_t	operator> (Element val) const
	Are all matrix elements > val? More...

Bool_t	operator>= (Element val) const
	Are all matrix elements >= val? More...

void	Print (Option_t *name="") const
	Print the matrix as a table of elements. More...

virtual TMatrixTBase< Element > &	Randomize (Element alpha, Element beta, Double_t &seed)
	Randomize matrix element values. More...

virtual TMatrixTBase< Element > &	ResizeTo (Int_t nrows, Int_t ncols, Int_t nr_nonzeros=-1)=0

virtual TMatrixTBase< Element > &	ResizeTo (Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb, Int_t nr_nonzeros=-1)=0

virtual Element	RowNorm () const
	Row matrix norm, MAX{ SUM{ \|M(i,j)\|, over j}, over i}. More...

virtual TMatrixTBase< Element > &	SetColIndexArray (Int_t *data)=0

virtual TMatrixTBase< Element > &	SetMatrixArray (const Element data, Option_t option="")
	Copy array data to matrix . More...

virtual TMatrixTBase< Element > &	SetRowIndexArray (Int_t *data)=0

virtual TMatrixTBase< Element > &	SetSub (Int_t row_lwb, Int_t col_lwb, const TMatrixTBase< Element > &source)=0

Element	SetTol (Element tol)

virtual TMatrixTBase< Element > &	Shift (Int_t row_shift, Int_t col_shift)
	Shift the row index by adding row_shift and the column index by adding col_shift, respectively. More...

virtual TMatrixTBase< Element > &	Sqr ()
	Square each element of the matrix. More...

virtual TMatrixTBase< Element > &	Sqrt ()
	Take square root of all elements. More...

virtual Element	Sum () const
	Compute sum of elements. More...

virtual TMatrixTBase< Element > &	UnitMatrix ()
	Make a unit matrix (matrix need not be a square one). More...

virtual TMatrixTBase< Element > &	Zero ()
	Set matrix elements to zero. More...

Public Member Functions inherited from TObject
	TObject ()
	TObject constructor. More...

	TObject (const TObject &object)
	TObject copy ctor. More...

virtual	~TObject ()
	TObject destructor. More...

void	AbstractMethod (const char *method) const
	Use this method to implement an "abstract" method that you don't want to leave purely abstract. More...

virtual void	AppendPad (Option_t *option="")
	Append graphics object to current pad. More...

virtual void	Browse (TBrowser *b)
	Browse object. May be overridden for another default action. More...

ULong_t	CheckedHash ()
	Check and record whether this class has a consistent Hash/RecursiveRemove setup (*) and then return the regular Hash value for this object. More...

virtual const char *	ClassName () const
	Returns name of class to which the object belongs. More...

virtual void	Clear (Option_t *="")

virtual TObject *	Clone (const char *newname="") const
	Make a clone of an object using the Streamer facility. More...

virtual Int_t	Compare (const TObject *obj) const
	Compare abstract method. More...

virtual void	Copy (TObject &object) const
	Copy this to obj. More...

virtual void	Delete (Option_t *option="")
	Delete this object. More...

virtual Int_t	DistancetoPrimitive (Int_t px, Int_t py)
	Computes distance from point (px,py) to the object. More...

virtual void	Draw (Option_t *option="")
	Default Draw method for all objects. More...

virtual void	DrawClass () const
	Draw class inheritance tree of the class to which this object belongs. More...

virtual TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current selected pad for instance with: `gROOT->SetSelectedPad(gPad)`. More...

virtual void	Dump () const
	Dump contents of object on stdout. More...

virtual void	Error (const char method, const char msgfmt,...) const
	Issue error message. More...

virtual void	Execute (const char method, const char params, Int_t *error=0)
	Execute method on this object with the given parameter string, e.g. More...

virtual void	Execute (TMethod method, TObjArray params, Int_t *error=0)
	Execute method on this object with parameters stored in the TObjArray. More...

virtual void	ExecuteEvent (Int_t event, Int_t px, Int_t py)
	Execute action corresponding to an event at (px,py). More...

virtual void	Fatal (const char method, const char msgfmt,...) const
	Issue fatal error message. More...

virtual TObject *	FindObject (const char *name) const
	Must be redefined in derived classes. More...

virtual TObject *	FindObject (const TObject *obj) const
	Must be redefined in derived classes. More...

virtual Option_t *	GetDrawOption () const
	Get option used by the graphics system to draw this object. More...

virtual const char *	GetIconName () const
	Returns mime type name of object. More...

virtual const char *	GetName () const
	Returns name of object. More...

virtual char *	GetObjectInfo (Int_t px, Int_t py) const
	Returns string containing info about the object at position (px,py). More...

virtual Option_t *	GetOption () const

virtual const char *	GetTitle () const
	Returns title of object. More...

virtual UInt_t	GetUniqueID () const
	Return the unique object id. More...

virtual Bool_t	HandleTimer (TTimer *timer)
	Execute action in response of a timer timing out. More...

virtual ULong_t	Hash () const
	Return hash value for this object. More...

Bool_t	HasInconsistentHash () const
	Return true is the type of this object is known to have an inconsistent setup for Hash and RecursiveRemove (i.e. More...

virtual void	Info (const char method, const char msgfmt,...) const
	Issue info message. More...

virtual Bool_t	InheritsFrom (const char *classname) const
	Returns kTRUE if object inherits from class "classname". More...

virtual Bool_t	InheritsFrom (const TClass *cl) const
	Returns kTRUE if object inherits from TClass cl. More...

virtual void	Inspect () const
	Dump contents of this object in a graphics canvas. More...

void	InvertBit (UInt_t f)

virtual Bool_t	IsEqual (const TObject *obj) const
	Default equal comparison (objects are equal if they have the same address in memory). More...

virtual Bool_t	IsFolder () const
	Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). More...

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
	The ls function lists the contents of a class on stdout. More...

void	MayNotUse (const char *method) const
	Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary). More...

virtual Bool_t	Notify ()
	This method must be overridden to handle object notification. More...

void	Obsolete (const char method, const char asOfVers, const char *removedFromVers) const
	Use this method to declare a method obsolete. More...

void	operator delete (void *ptr)
	Operator delete. More...

void	operator delete[] (void *ptr)
	Operator delete []. More...

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)
	TObject assignment operator. More...

virtual void	Paint (Option_t *option="")
	This method must be overridden if a class wants to paint itself. More...

virtual void	Pop ()
	Pop on object drawn in a pad to the top of the display list. More...

virtual void	Print (Option_t *option="") const
	This method must be overridden when a class wants to print itself. More...

virtual Int_t	Read (const char *name)
	Read contents of object with specified name from the current directory. More...

virtual void	RecursiveRemove (TObject *obj)
	Recursively remove this object from a list. More...

void	ResetBit (UInt_t f)

virtual void	SaveAs (const char filename="", Option_t option="") const
	Save this object in the file specified by filename. More...

virtual void	SavePrimitive (std::ostream &out, Option_t *option="")
	Save a primitive as a C++ statement(s) on output stream "out". More...

void	SetBit (UInt_t f)

void	SetBit (UInt_t f, Bool_t set)
	Set or unset the user status bits as specified in f. More...

virtual void	SetDrawOption (Option_t *option="")
	Set drawing option for object. More...

virtual void	SetUniqueID (UInt_t uid)
	Set the unique object id. More...

virtual void	SysError (const char method, const char msgfmt,...) const
	Issue system error message. More...

R__ALWAYS_INLINE Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

virtual void	UseCurrentStyle ()
	Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked. More...

virtual void	Warning (const char method, const char msgfmt,...) const
	Issue warning message. More...

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory. More...

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const
	Write this object to the current directory. More...

Static Public Member Functions
static Element &	NaNValue ()

Static Public Member Functions inherited from TObject
static Long_t	GetDtorOnly ()
	Return destructor only flag. More...

static Bool_t	GetObjectStat ()
	Get status of object stat flag. More...

static void	SetDtorOnly (void *obj)
	Set destructor only flag. More...

static void	SetObjectStat (Bool_t stat)
	Turn on/off tracking of objects in the TObjectTable. More...

Protected Types
enum	{ kSizeMax = 25 }

enum	{ kWorkMax = 100 }

enum	EMatrixStatusBits { kStatus = BIT(14) }

Static Protected Member Functions
static void	DoubleLexSort (Int_t n, Int_t first, Int_t second, Element *data)
	default kTRUE, when Use array kFALSE More...

static void	IndexedLexSort (Int_t n, Int_t first, Int_t swapFirst, Int_t second, Int_t swapSecond, Int_t *index)
	Lexical sort on array data using indices first and second. More...

Protected Attributes
Int_t	fColLwb

Bool_t	fIsOwner

Int_t	fNcols

Int_t	fNelems

Int_t	fNrowIndex

Int_t	fNrows

Int_t	fRowLwb

Element	fTol

Private Member Functions
Element *	GetElements ()

Additional Inherited Members
Public Types inherited from TObject
enum	{ kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 , kBitMask = 0x00ffffff }

enum	{ kSingleKey = BIT(0) , kOverwrite = BIT(1) , kWriteDelete = BIT(2) }

enum	EDeprecatedStatusBits { kObjInCanvas = BIT(3) }

enum	EStatusBits { kCanDelete = BIT(0) , kMustCleanup = BIT(3) , kIsReferenced = BIT(4) , kHasUUID = BIT(5) , kCannotPick = BIT(6) , kNoContextMenu = BIT(8) , kInvalidObject = BIT(13) }

Protected Member Functions inherited from TObject
virtual void	DoError (int level, const char location, const char fmt, va_list va) const
	Interface to ErrorHandler (protected). More...

void	MakeZombie ()

#include <TMatrixTBase.h>

Inheritance diagram for TMatrixTBase< Element >:

[legend]

Member Enumeration Documentation

◆ anonymous enum

template<class Element >

anonymous enum

protected

Enumerator
kSizeMax

Definition at line 107 of file TMatrixTBase.h.

◆ anonymous enum

template<class Element >

anonymous enum

protected

Enumerator
kWorkMax

Definition at line 108 of file TMatrixTBase.h.

◆ EMatrixStatusBits

template<class Element >

enum TMatrixTBase::EMatrixStatusBits

protected

Enumerator
kStatus

Definition at line 110 of file TMatrixTBase.h.

Constructor & Destructor Documentation

◆ TMatrixTBase()

template<class Element >

TMatrixTBase< Element >::TMatrixTBase ( )

inline

Definition at line 116 of file TMatrixTBase.h.

◆ ~TMatrixTBase()

template<class Element >

virtual TMatrixTBase< Element >::~TMatrixTBase ( )

inlinevirtual

Definition at line 120 of file TMatrixTBase.h.

Member Function Documentation

◆ Abs()

template<class Element >

TMatrixTBase< Element > & TMatrixTBase< Element >::Abs

virtual

Take an absolute value of a matrix, i.e. apply Abs() to each element.

Definition at line 559 of file TMatrixTBase.cxx.

◆ Apply() [1/2]

template<class Element >

TMatrixTBase< Element > & TMatrixTBase< Element >::Apply ( const TElementActionT< Element > & action )

virtual

Apply action to each matrix element.

Reimplemented in TMatrixTSym< Double_t >, and TMatrixTSym< Element >.

Definition at line 997 of file TMatrixTBase.cxx.

◆ Apply() [2/2]

template<class Element >

TMatrixTBase< Element > & TMatrixTBase< Element >::Apply ( const TElementPosActionT< Element > & action )

virtual

Apply action to each element of the matrix.

To action the location of the current element is passed.

Reimplemented in TMatrixTSym< Double_t >, and TMatrixTSym< Element >.

Definition at line 1014 of file TMatrixTBase.cxx.

◆ Class()

TClass * TMatrixTBase< double >::Class ( )

◆ Clear()

template<class Element >

virtual void TMatrixTBase< Element >::Clear ( Option_t * option = "" )

pure virtual

Reimplemented from TObject.

Implemented in TMatrixT< Element >, TMatrixT< Double_t >, TMatrixTSparse< Element >, TMatrixTSparse< Double_t >, TMatrixTSym< Element >, and TMatrixTSym< Double_t >.

◆ ColNorm()

template<class Element >

Element TMatrixTBase< Element >::ColNorm

virtual

Column matrix norm, MAX{ SUM{ |M(i,j)|, over i}, over j}.

The norm is induced by the 1 vector norm.

Reimplemented in TMatrixTSparse< Element >, and TMatrixTSparse< Double_t >.

Definition at line 713 of file TMatrixTBase.cxx.

◆ Determinant() [1/2]

template<class Element >

virtual Double_t TMatrixTBase< Element >::Determinant ( ) const

inlinevirtual

Reimplemented in TMatrixT< Element >, TMatrixT< Double_t >, TMatrixTSym< Element >, and TMatrixTSym< Double_t >.

Definition at line 163 of file TMatrixTBase.h.

◆ Determinant() [2/2]

template<class Element >

virtual void TMatrixTBase< Element >::Determinant	(	Double_t &	d1,
		Double_t &	d2
	)		const

inlinevirtual

Reimplemented in TMatrixT< Element >, TMatrixT< Double_t >, TMatrixTSym< Element >, and TMatrixTSym< Double_t >.

Definition at line 164 of file TMatrixTBase.h.

◆ DoubleLexSort()

template<class Element >

void TMatrixTBase< Element >::DoubleLexSort	(	Int_t	n,
		Int_t *	first,
		Int_t *	second,
		Element *	data
	)

staticprotected

default kTRUE, when Use array kFALSE

Lexical sort on array data using indices first and second.

Definition at line 238 of file TMatrixTBase.cxx.

◆ Draw()

template<class Element >

void TMatrixTBase< Element >::Draw ( Option_t * option = "" )

virtual

Draw this matrix The histogram is named "TMatrixT" by default and no title.

Reimplemented from TObject.

Definition at line 819 of file TMatrixTBase.cxx.

◆ E2Norm()

template<class Element >

Element TMatrixTBase< Element >::E2Norm

virtual

Square of the Euclidian norm, SUM{ m(i,j)^2 }.

Definition at line 740 of file TMatrixTBase.cxx.

◆ ExtractRow()

template<class Element >

void TMatrixTBase< Element >::ExtractRow	(	Int_t	row,
		Int_t	col,
		Element *	v,
		Int_t	n = `-1`
	)		const

virtual

Store in array v, n matrix elements of row rown starting at column coln.

Reimplemented in TMatrixTSparse< Double_t >, and TMatrixTSparse< Element >.

Definition at line 501 of file TMatrixTBase.cxx.

◆ GetColIndexArray() [1/2]

template<class Element >

virtual const Int_t * TMatrixTBase< Element >::GetColIndexArray ( ) const

pure virtual

Implemented in TMatrixT< Element >, TMatrixT< Double_t >, TMatrixTSparse< Element >, TMatrixTSparse< Double_t >, TMatrixTSym< Element >, and TMatrixTSym< Double_t >.

◆ GetColIndexArray() [2/2]

template<class Element >

virtual Int_t * TMatrixTBase< Element >::GetColIndexArray ( )

pure virtual

Implemented in TMatrixT< Element >, TMatrixT< Double_t >, TMatrixTSparse< Element >, TMatrixTSparse< Double_t >, TMatrixTSym< Element >, and TMatrixTSym< Double_t >.

◆ GetColLwb()

template<class Element >

Int_t TMatrixTBase< Element >::GetColLwb ( ) const

inline

Definition at line 125 of file TMatrixTBase.h.

◆ GetColUpb()

template<class Element >

Int_t TMatrixTBase< Element >::GetColUpb ( ) const

inline

Definition at line 126 of file TMatrixTBase.h.

◆ GetElements()

template<class Element >

Element * TMatrixTBase< Element >::GetElements ( )

private

◆ GetMatrix2Array()

template<class Element >

void TMatrixTBase< Element >::GetMatrix2Array	(	Element *	data,
		Option_t *	option = `""`
	)		const

virtual

Copy matrix data to array .

It is assumed that array is of size >= fNelems (=)))) fNrows*fNcols option indicates how the data is stored in the array: option =

'F' : column major (Fortran) array[i+j*fNrows] = m[i][j]
else : row major (C) array[i*fNcols+j] = m[i][j] (default)

Reimplemented in TMatrixTSparse< Double_t >, and TMatrixTSparse< Element >.

Definition at line 441 of file TMatrixTBase.cxx.

◆ GetMatrixArray() [1/2]

template<class Element >

virtual const Element * TMatrixTBase< Element >::GetMatrixArray ( ) const

pure virtual

Implemented in TMatrixT< Element >, TMatrixT< Double_t >, TMatrixTSparse< Element >, TMatrixTSparse< Double_t >, TMatrixTSym< Element >, and TMatrixTSym< Double_t >.

◆ GetMatrixArray() [2/2]

template<class Element >

virtual Element * TMatrixTBase< Element >::GetMatrixArray ( )

pure virtual

Implemented in TMatrixT< Element >, TMatrixT< Double_t >, TMatrixTSparse< Element >, TMatrixTSparse< Double_t >, TMatrixTSym< Element >, and TMatrixTSym< Double_t >.

◆ GetNcols()

template<class Element >

Int_t TMatrixTBase< Element >::GetNcols ( ) const

inline

Definition at line 127 of file TMatrixTBase.h.

◆ GetNoElements()

template<class Element >

Int_t TMatrixTBase< Element >::GetNoElements ( ) const

inline

Definition at line 128 of file TMatrixTBase.h.

◆ GetNrows()

template<class Element >

Int_t TMatrixTBase< Element >::GetNrows ( ) const

inline

Definition at line 124 of file TMatrixTBase.h.

◆ GetRowIndexArray() [1/2]

template<class Element >

virtual const Int_t * TMatrixTBase< Element >::GetRowIndexArray ( ) const

pure virtual

Implemented in TMatrixT< Element >, TMatrixT< Double_t >, TMatrixTSparse< Element >, TMatrixTSparse< Double_t >, TMatrixTSym< Element >, and TMatrixTSym< Double_t >.

◆ GetRowIndexArray() [2/2]

template<class Element >

virtual Int_t * TMatrixTBase< Element >::GetRowIndexArray ( )

pure virtual

Implemented in TMatrixT< Element >, TMatrixT< Double_t >, TMatrixTSparse< Element >, TMatrixTSparse< Double_t >, TMatrixTSym< Element >, and TMatrixTSym< Double_t >.

◆ GetRowLwb()

template<class Element >

Int_t TMatrixTBase< Element >::GetRowLwb ( ) const

inline

Definition at line 122 of file TMatrixTBase.h.

◆ GetRowUpb()

template<class Element >

Int_t TMatrixTBase< Element >::GetRowUpb ( ) const

inline

Definition at line 123 of file TMatrixTBase.h.

◆ GetSub()

template<class Element >

virtual TMatrixTBase< Element > & TMatrixTBase< Element >::GetSub	(	Int_t	row_lwb,
		Int_t	row_upb,
		Int_t	col_lwb,
		Int_t	col_upb,
		TMatrixTBase< Element > &	target,
		Option_t *	option = `"S"`
	)		const

pure virtual

Implemented in TMatrixT< Double_t >, TMatrixTSparse< Double_t >, TMatrixTSym< Double_t >, TMatrixT< Element >, TMatrixTSparse< Element >, and TMatrixTSym< Element >.

◆ GetTol()

template<class Element >

Element TMatrixTBase< Element >::GetTol ( ) const

inline

Definition at line 129 of file TMatrixTBase.h.

◆ IndexedLexSort()

template<class Element >

void TMatrixTBase< Element >::IndexedLexSort	(	Int_t	n,
		Int_t *	first,
		Int_t	swapFirst,
		Int_t *	second,
		Int_t	swapSecond,
		Int_t *	index
	)

staticprotected

Lexical sort on array data using indices first and second.

Definition at line 277 of file TMatrixTBase.cxx.

◆ InsertRow()

template<class Element >

TMatrixTBase< Element > & TMatrixTBase< Element >::InsertRow	(	Int_t	row,
		Int_t	col,
		const Element *	v,
		Int_t	n = `-1`
	)

virtual

Copy n elements from array v to row rown starting at column coln.

Reimplemented in TMatrixTSparse< Double_t >, and TMatrixTSparse< Element >.

Definition at line 467 of file TMatrixTBase.cxx.

◆ Invalidate()

template<class Element >

void TMatrixTBase< Element >::Invalidate ( )

inline

Definition at line 145 of file TMatrixTBase.h.

◆ IsOwner()

template<class Element >

Bool_t TMatrixTBase< Element >::IsOwner ( ) const

inline

Definition at line 148 of file TMatrixTBase.h.

◆ IsSymmetric()

template<class Element >

Bool_t TMatrixTBase< Element >::IsSymmetric

virtual

Check whether matrix is symmetric.

Reimplemented in TMatrixTSparse< Element >, TMatrixTSparse< Double_t >, TMatrixTSym< Element >, and TMatrixTSym< Double_t >.

Definition at line 412 of file TMatrixTBase.cxx.

◆ IsValid()

template<class Element >

Bool_t TMatrixTBase< Element >::IsValid ( ) const

inline

Definition at line 147 of file TMatrixTBase.h.

◆ MakeValid()

template<class Element >

void TMatrixTBase< Element >::MakeValid ( )

inline

Definition at line 146 of file TMatrixTBase.h.

◆ Max()

template<class Element >

Element TMatrixTBase< Element >::Max

virtual

return maximum vector element value

Definition at line 805 of file TMatrixTBase.cxx.

◆ Min()

template<class Element >

Element TMatrixTBase< Element >::Min

virtual

return minimum matrix element value

Definition at line 792 of file TMatrixTBase.cxx.

◆ NaNValue()

template<class Element >

Element & TMatrixTBase< Element >::NaNValue

static

Definition at line 1282 of file TMatrixTBase.cxx.

◆ NonZeros()

template<class Element >

Int_t TMatrixTBase< Element >::NonZeros

virtual

Compute the number of elements != 0.0.

Reimplemented in TMatrixTSparse< Element >, and TMatrixTSparse< Double_t >.

Definition at line 758 of file TMatrixTBase.cxx.

◆ Norm1()

template<class Element >

Element TMatrixTBase< Element >::Norm1 ( ) const

inline

Definition at line 178 of file TMatrixTBase.h.

◆ NormByDiag()

template<class Element >

TMatrixTBase< Element > & TMatrixTBase< Element >::NormByDiag	(	const TVectorT< Element > &	v,
		Option_t *	option = `"D"`
	)

virtual

option:

"D" : b(i,j) = a(i,j)/sqrt(abs*(v(i)*v(j))) (default)
else : b(i,j) = a(i,j)*sqrt(abs*(v(i)*v(j))) (default)

Reimplemented in TMatrixTSparse< Element >.

Definition at line 632 of file TMatrixTBase.cxx.

◆ NormInf()

template<class Element >

Element TMatrixTBase< Element >::NormInf ( ) const

inline

Definition at line 177 of file TMatrixTBase.h.

◆ operator!=()

template<class Element >

Bool_t TMatrixTBase< Element >::operator!= ( Element val ) const

Are all matrix elements not equal to val?

Definition at line 909 of file TMatrixTBase.cxx.

◆ operator()() [1/2]

template<class Element >

virtual Element TMatrixTBase< Element >::operator()	(	Int_t	rown,
		Int_t	coln
	)		const

pure virtual

Implemented in TMatrixT< Element >, TMatrixT< Double_t >, TMatrixTSparse< Element >, TMatrixTSparse< Double_t >, TMatrixTSym< Element >, and TMatrixTSym< Double_t >.

◆ operator()() [2/2]

template<class Element >

virtual Element & TMatrixTBase< Element >::operator()	(	Int_t	rown,
		Int_t	coln
	)

pure virtual

Implemented in TMatrixT< Element >, TMatrixT< Double_t >, TMatrixTSparse< Element >, TMatrixTSparse< Double_t >, TMatrixTSym< Element >, and TMatrixTSym< Double_t >.

◆ operator<()

template<class Element >

Bool_t TMatrixTBase< Element >::operator< ( Element val ) const

Are all matrix elements < val?

Definition at line 929 of file TMatrixTBase.cxx.

◆ operator<=()

template<class Element >

Bool_t TMatrixTBase< Element >::operator<= ( Element val ) const

Are all matrix elements <= val?

Definition at line 946 of file TMatrixTBase.cxx.

◆ operator==()

template<class Element >

Bool_t TMatrixTBase< Element >::operator== ( Element val ) const

Are all matrix elements equal to val?

Definition at line 889 of file TMatrixTBase.cxx.

◆ operator>()

template<class Element >

Bool_t TMatrixTBase< Element >::operator> ( Element val ) const

Are all matrix elements > val?

Definition at line 963 of file TMatrixTBase.cxx.

◆ operator>=()

template<class Element >

Bool_t TMatrixTBase< Element >::operator>= ( Element val ) const

Are all matrix elements >= val?

Definition at line 980 of file TMatrixTBase.cxx.

◆ Print()

template<class Element >

void TMatrixTBase< Element >::Print ( Option_t * option = "" ) const

virtual

Print the matrix as a table of elements.

By default the format "%11.4g" is used to print one element. One can specify an alternative format with eg option ="f= %6.2f "

Reimplemented from TObject.

Definition at line 832 of file TMatrixTBase.cxx.

◆ Randomize()

template<class Element >

TMatrixTBase< Element > & TMatrixTBase< Element >::Randomize	(	Element	alpha,
		Element	beta,
		Double_t &	seed
	)

virtual

Randomize matrix element values.

Reimplemented in TMatrixTSparse< Double_t >, TMatrixTSym< Double_t >, TMatrixTSparse< Element >, and TMatrixTSym< Element >.

Definition at line 1032 of file TMatrixTBase.cxx.

◆ ResizeTo() [1/2]

template<class Element >

virtual TMatrixTBase< Element > & TMatrixTBase< Element >::ResizeTo	(	Int_t	nrows,
		Int_t	ncols,
		Int_t	nr_nonzeros = `-1`
	)

pure virtual

Implemented in TMatrixTSparse< Element >, TMatrixTSparse< Double_t >, TMatrixT< Element >, TMatrixT< Double_t >, TMatrixTSym< Element >, and TMatrixTSym< Double_t >.

◆ ResizeTo() [2/2]

template<class Element >

virtual TMatrixTBase< Element > & TMatrixTBase< Element >::ResizeTo	(	Int_t	row_lwb,
		Int_t	row_upb,
		Int_t	col_lwb,
		Int_t	col_upb,
		Int_t	nr_nonzeros = `-1`
	)

pure virtual

Implemented in TMatrixTSparse< Element >, TMatrixTSparse< Double_t >, TMatrixT< Element >, TMatrixT< Double_t >, TMatrixTSym< Element >, and TMatrixTSym< Double_t >.

◆ RowNorm()

template<class Element >

Element TMatrixTBase< Element >::RowNorm

virtual

Row matrix norm, MAX{ SUM{ |M(i,j)|, over j}, over i}.

The norm is induced by the infinity vector norm.

Reimplemented in TMatrixTSparse< Element >, and TMatrixTSparse< Double_t >.

Definition at line 686 of file TMatrixTBase.cxx.

◆ SetColIndexArray()

template<class Element >

virtual TMatrixTBase< Element > & TMatrixTBase< Element >::SetColIndexArray ( Int_t * data )

pure virtual

Implemented in TMatrixT< Element >, TMatrixT< Double_t >, TMatrixTSym< Element >, TMatrixTSym< Double_t >, TMatrixTSparse< Element >, and TMatrixTSparse< Double_t >.

◆ SetMatrixArray()

template<class Element >

TMatrixTBase< Element > & TMatrixTBase< Element >::SetMatrixArray	(	const Element *	data,
		Option_t *	option = `""`
	)

virtual

Copy array data to matrix .

It is assumed that array is of size >= fNelems (=)))) fNrows*fNcols option indicates how the data is stored in the array: option =

'F' : column major (Fortran) m[i][j] = array[i+j*fNrows]
else : row major (C) m[i][j] = array[i*fNcols+j] (default)

Reimplemented in TMatrixTSym< Double_t >, TMatrixTSparse< Element >, and TMatrixTSym< Element >.

Definition at line 384 of file TMatrixTBase.cxx.

◆ SetRowIndexArray()

template<class Element >

virtual TMatrixTBase< Element > & TMatrixTBase< Element >::SetRowIndexArray ( Int_t * data )

pure virtual

Implemented in TMatrixT< Element >, TMatrixT< Double_t >, TMatrixTSym< Element >, TMatrixTSym< Double_t >, TMatrixTSparse< Element >, and TMatrixTSparse< Double_t >.

◆ SetSub()

template<class Element >

virtual TMatrixTBase< Element > & TMatrixTBase< Element >::SetSub	(	Int_t	row_lwb,
		Int_t	col_lwb,
		const TMatrixTBase< Element > &	source
	)

pure virtual

Implemented in TMatrixT< Double_t >, TMatrixTSparse< Double_t >, TMatrixTSym< Double_t >, TMatrixT< Element >, TMatrixTSparse< Element >, and TMatrixTSym< Element >.

◆ SetTol()

template<class Element >

Element TMatrixTBase< Element >::SetTol ( Element tol )

inline

Definition at line 220 of file TMatrixTBase.h.

◆ Shift()

template<class Element >

TMatrixTBase< Element > & TMatrixTBase< Element >::Shift	(	Int_t	row_shift,
		Int_t	col_shift
	)

virtual

Shift the row index by adding row_shift and the column index by adding col_shift, respectively.

So [rowLwb..rowUpb][colLwb..colUpb] becomes [rowLwb+row_shift..rowUpb+row_shift][colLwb+col_shift..colUpb+col_shift]

Reimplemented in TMatrixTSym< Element >, and TMatrixTSym< Double_t >.

Definition at line 535 of file TMatrixTBase.cxx.

◆ Sqr()

template<class Element >

TMatrixTBase< Element > & TMatrixTBase< Element >::Sqr

virtual

Square each element of the matrix.

Definition at line 577 of file TMatrixTBase.cxx.

◆ Sqrt()

template<class Element >

TMatrixTBase< Element > & TMatrixTBase< Element >::Sqrt

virtual

Take square root of all elements.

Definition at line 595 of file TMatrixTBase.cxx.

◆ Sum()

template<class Element >

Element TMatrixTBase< Element >::Sum

virtual

Compute sum of elements.

Definition at line 775 of file TMatrixTBase.cxx.

◆ UnitMatrix()

template<class Element >

TMatrixTBase< Element > & TMatrixTBase< Element >::UnitMatrix

virtual

Make a unit matrix (matrix need not be a square one).

Reimplemented in TMatrixTSparse< Element >, and TMatrixTSparse< Double_t >.

Definition at line 613 of file TMatrixTBase.cxx.

◆ Zero()

template<class Element >

TMatrixTBase< Element > & TMatrixTBase< Element >::Zero

virtual

Set matrix elements to zero.

Reimplemented in TMatrixTSparse< Element >, and TMatrixTSparse< Double_t >.

Definition at line 547 of file TMatrixTBase.cxx.

Member Data Documentation

◆ fColLwb

template<class Element >

Int_t TMatrixTBase< Element >::fColLwb

protected

Definition at line 94 of file TMatrixTBase.h.

◆ fIsOwner

template<class Element >

Bool_t TMatrixTBase< Element >::fIsOwner

protected

Definition at line 101 of file TMatrixTBase.h.

◆ fNcols

template<class Element >

Int_t TMatrixTBase< Element >::fNcols

protected

Definition at line 92 of file TMatrixTBase.h.

◆ fNelems

template<class Element >

Int_t TMatrixTBase< Element >::fNelems

protected

Definition at line 95 of file TMatrixTBase.h.

◆ fNrowIndex

template<class Element >

Int_t TMatrixTBase< Element >::fNrowIndex

protected

Definition at line 96 of file TMatrixTBase.h.

◆ fNrows

template<class Element >

Int_t TMatrixTBase< Element >::fNrows

protected

Definition at line 91 of file TMatrixTBase.h.

◆ fRowLwb

template<class Element >

Int_t TMatrixTBase< Element >::fRowLwb

protected

Definition at line 93 of file TMatrixTBase.h.

◆ fTol

template<class Element >

Element TMatrixTBase< Element >::fTol

protected

Definition at line 98 of file TMatrixTBase.h.

Libraries for TMatrixTBase< Element >:

[legend]

Linear Algebra Package

Acknowledgements

How to efficiently use this package

1. Never return complex objects (matrices or vectors)

2. Use "two-address instructions"

3. Use glorified constructors when returning of an object seems inevitable:

4. Accessing row/col/diagonal of a matrix without much fuss

5. It's possible (and encouraged) to use "nested" functions

6. Lazy matrices:

Public Member Functions

Static Public Member Functions

Protected Types

Static Protected Member Functions

Protected Attributes

Private Member Functions

Additional Inherited Members

Member Enumeration Documentation

◆ anonymous enum

◆ anonymous enum

◆ EMatrixStatusBits

Constructor & Destructor Documentation

◆ TMatrixTBase()

◆ ~TMatrixTBase()

Member Function Documentation

◆ Abs()

◆ Apply() [1/2]

◆ Apply() [2/2]

◆ Class()

◆ Clear()

◆ ColNorm()

◆ Determinant() [1/2]

◆ Determinant() [2/2]

◆ DoubleLexSort()

◆ Draw()

◆ E2Norm()

◆ ExtractRow()

◆ GetColIndexArray() [1/2]

◆ GetColIndexArray() [2/2]

◆ GetColLwb()

◆ GetColUpb()

◆ GetElements()

◆ GetMatrix2Array()

◆ GetMatrixArray() [1/2]

◆ GetMatrixArray() [2/2]

◆ GetNcols()

◆ GetNoElements()

◆ GetNrows()

◆ GetRowIndexArray() [1/2]

◆ GetRowIndexArray() [2/2]

◆ GetRowLwb()

◆ GetRowUpb()

◆ GetSub()

◆ GetTol()

◆ IndexedLexSort()

◆ InsertRow()

◆ Invalidate()

◆ IsOwner()

◆ IsSymmetric()

◆ IsValid()

◆ MakeValid()

◆ Max()

◆ Min()

◆ NaNValue()

◆ NonZeros()

◆ Norm1()

◆ NormByDiag()

◆ NormInf()

◆ operator!=()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator<()

◆ operator<=()

◆ operator==()

◆ operator>()

◆ operator>=()

◆ Print()

◆ Randomize()

◆ ResizeTo() [1/2]

◆ ResizeTo() [2/2]

◆ RowNorm()