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;

than

TMatrixD C = A + B;

(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 25 of file TMatrixDBasefwd.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...

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...

Static Public Member Functions
static Element &	NaNValue ()

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 ()

#include <TMatrixDBasefwd.h>

Inheritance diagram for TMatrixTBase< Element >:

[legend]

Member Enumeration Documentation

◆ anonymous enum

template<class Element>

anonymous enum

protected

Enumerator
kSizeMax

Definition at line 105 of file TMatrixTBase.h.

◆ anonymous enum

template<class Element>

anonymous enum

protected

Enumerator
kWorkMax

Definition at line 106 of file TMatrixTBase.h.

◆ EMatrixStatusBits

template<class Element>

enum TMatrixTBase::EMatrixStatusBits

protected

Enumerator
kStatus

Definition at line 108 of file TMatrixTBase.h.

Constructor & Destructor Documentation

◆ TMatrixTBase()

template<class Element>

TMatrixTBase< Element >::TMatrixTBase ( )

inline

Definition at line 114 of file TMatrixTBase.h.

◆ ~TMatrixTBase()

template<class Element>

virtual TMatrixTBase< Element >::~TMatrixTBase ( )

inlinevirtual

Definition at line 118 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< 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< Element >.

Definition at line 1014 of file TMatrixTBase.cxx.

◆ Clear()

template<class Element>

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

pure virtual

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 ( ) const

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 161 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 162 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 = "" )

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

Definition at line 819 of file TMatrixTBase.cxx.

◆ E2Norm()

template<class Element >

Element TMatrixTBase< Element >::E2Norm ( ) const

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< 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 123 of file TMatrixTBase.h.

◆ GetColUpb()

template<class Element>

Int_t TMatrixTBase< Element >::GetColUpb ( ) const

inline

Definition at line 124 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)

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< Element >.

Definition at line 467 of file TMatrixTBase.cxx.

◆ Invalidate()

template<class Element>

void TMatrixTBase< Element >::Invalidate ( )

inline

Definition at line 143 of file TMatrixTBase.h.

◆ IsOwner()

template<class Element>

Bool_t TMatrixTBase< Element >::IsOwner ( ) const

inline

Definition at line 146 of file TMatrixTBase.h.

◆ IsSymmetric()

template<class Element >

Bool_t TMatrixTBase< Element >::IsSymmetric ( ) const

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 145 of file TMatrixTBase.h.

◆ MakeValid()

template<class Element>

void TMatrixTBase< Element >::MakeValid ( )

inline

Definition at line 144 of file TMatrixTBase.h.

◆ Max()

template<class Element >

Element TMatrixTBase< Element >::Max ( ) const

virtual

return maximum vector element value

Definition at line 805 of file TMatrixTBase.cxx.

◆ Min()

template<class Element >

Element TMatrixTBase< Element >::Min ( ) const

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 ( ) const

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 176 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 175 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 TMatrixTSparse< Element >, TMatrixTSparse< Double_t >, TMatrixT< Element >, TMatrixT< 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
	)

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 "

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

◆ RowNorm()

template<class Element >

Element TMatrixTBase< Element >::RowNorm ( ) const

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

◆ SetTol()

template<class Element >

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

inline

Definition at line 218 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.

template<class Element>

Element TMatrixTBase< Element >::fTol

protected

Definition at line 96 of file TMatrixTBase.h.

Libraries for TMatrixTBase< Element >:

[legend]

The documentation for this class was generated from the following files:

math/matrix/inc/TMatrixDBasefwd.h
math/matrix/inc/TMatrixTBase.h
math/matrix/src/TMatrixTBase.cxx

template<class Element> class TMatrixTBase< Element >

Linear Algebra Package

Acknowledgements

How to efficiently use this package

1. Never return complex objects (matrices or vectors)

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

Member Enumeration Documentation

◆ anonymous enum

◆ anonymous enum

◆ EMatrixStatusBits

Constructor & Destructor Documentation

◆ TMatrixTBase()

◆ ~TMatrixTBase()

Member Function Documentation

◆ Abs()

◆ Apply() [1/2]

◆ Apply() [2/2]

◆ 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()

◆ SetColIndexArray()

◆ SetMatrixArray()

◆ SetRowIndexArray()

template<class Element>
class TMatrixTBase< Element >