 ROOT   6.19/01 Reference Guide TMatrixTBase< Element > Class Template Referenceabstract

### 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 1. 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 2. 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/ 3. 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 4. 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 5. 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 hht(haar,TMatrixD::kMult,haar_t);
TMatrixD hht1 = haar; hht1 *= haar_t;

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

(and without moving a lot of stuff around):

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)
{
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:

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...

template<>
TClassClass ()

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_tGetColIndexArray () const =0

virtual Int_tGetColIndexArray ()=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_tGetRowIndexArray () const =0

virtual Int_tGetRowIndexArray ()=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...

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

virtual TObjectDrawClone (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 TObjectFindObject (const char *name) const
Must be redefined in derived classes. More...

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

virtual Option_tGetDrawOption () 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_tGetOption () 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...

voidoperator new (size_t sz)

voidoperator new (size_t sz, void *vp)

voidoperator new[] (size_t sz)

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

TObjectoperator= (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 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, Bool_t set)
Set or unset the user status bits as specified in f. More...

void SetBit (UInt_t f)

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...

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 () Public Types inherited from TObject
enum  {
kIsOnHeap = 0x01000000, kNotDeleted = 0x02000000, kZombie = 0x04000000, kInconsistent = 0x08000000,
}

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 <TMatrixDBasefwd.h>

Inheritance diagram for TMatrixTBase< Element >:
[legend]

## ◆ 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>
 protected
Enumerator
kStatus

Definition at line 110 of file TMatrixTBase.h.

## ◆ 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.

## ◆ 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.

## ◆ Class()

template<>
 TClass * TMatrixTBase< double >::Class ( )

## ◆ Clear()

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

Reimplemented from TObject.

## ◆ 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

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

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 ( ) 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

## ◆ GetColIndexArray() [2/2]

template<class Element>
 virtual Int_t* TMatrixTBase< Element >::GetColIndexArray ( )
pure virtual

## ◆ 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< Element >.

Definition at line 441 of file TMatrixTBase.cxx.

## ◆ GetMatrixArray() [1/2]

template<class Element>
 virtual const Element* TMatrixTBase< Element >::GetMatrixArray ( ) const
pure virtual

## ◆ GetMatrixArray() [2/2]

template<class Element>
 virtual Element* TMatrixTBase< Element >::GetMatrixArray ( )
pure virtual

## ◆ 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

## ◆ GetRowIndexArray() [2/2]

template<class Element>
 virtual Int_t* TMatrixTBase< Element >::GetRowIndexArray ( )
pure virtual

## ◆ 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& 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

## ◆ 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< 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 ( ) 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 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 ( ) 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 178 of file TMatrixTBase.h.

## ◆ NormByDiag()

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

option:

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

## ◆ operator()() [2/2]

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

## ◆ 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< Element >, and TMatrixTSym< Element >.

Definition at line 1032 of file TMatrixTBase.cxx.

## ◆ ResizeTo() [1/2]

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

## ◆ ResizeTo() [2/2]

template<class Element>
 virtual TMatrixTBase& 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

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

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

## ◆ SetSub()

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

## ◆ 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 ( ) const
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.

## ◆ 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.

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