class TMatrixTBase<float>: public TObject


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
w/column information is stored, see TMatrixTSparse source f
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
he constructor. Note, TMatrixDLazy (see below) can construc
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
bove), it's dramatically different. THaarMatrixD() constructs 
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!


Function Members (Methods)

 
    This is an abstract class, constructors will not be documented.
    Look at the header to check for available constructors.

public:
virtual~TMatrixTBase<float>()
virtual TMatrixTBase<float>&Abs()
voidTObject::AbstractMethod(const char* method) const
virtual voidTObject::AppendPad(Option_t* option = "")
virtual TMatrixTBase<float>&Apply(const TElementActionT<float>& action)
virtual TMatrixTBase<float>&Apply(const TElementPosActionT<float>& action)
virtual voidTObject::Browse(TBrowser* b)
static TClass*Class()
virtual const char*TObject::ClassName() const
virtual voidClear(Option_t* option = "")
virtual TObject*TObject::Clone(const char* newname = "") const
virtual floatColNorm() const
virtual Int_tTObject::Compare(const TObject* obj) const
virtual voidTObject::Copy(TObject& object) const
virtual voidTObject::Delete(Option_t* option = "")
virtual Double_tDeterminant() const
virtual voidDeterminant(Double_t& d1, Double_t& d2) const
virtual Int_tTObject::DistancetoPrimitive(Int_t px, Int_t py)
virtual voidDraw(Option_t* option = "")
virtual voidTObject::DrawClass() const
virtual TObject*TObject::DrawClone(Option_t* option = "") const
virtual voidTObject::Dump() const
virtual floatE2Norm() const
virtual voidTObject::Error(const char* method, const char* msgfmt) const
virtual voidTObject::Execute(const char* method, const char* params, Int_t* error = 0)
virtual voidTObject::Execute(TMethod* method, TObjArray* params, Int_t* error = 0)
virtual voidTObject::ExecuteEvent(Int_t event, Int_t px, Int_t py)
virtual voidExtractRow(Int_t row, Int_t col, float* v, Int_t n = -1) const
virtual voidTObject::Fatal(const char* method, const char* msgfmt) const
virtual TObject*TObject::FindObject(const char* name) const
virtual TObject*TObject::FindObject(const TObject* obj) const
virtual const Int_t*GetColIndexArray() const
virtual Int_t*GetColIndexArray()
Int_tGetColLwb() const
Int_tGetColUpb() const
virtual Option_t*TObject::GetDrawOption() const
static Long_tTObject::GetDtorOnly()
virtual const char*TObject::GetIconName() const
virtual voidGetMatrix2Array(float* data, Option_t* option = "") const
virtual const float*GetMatrixArray() const
virtual float*GetMatrixArray()
virtual const char*TObject::GetName() const
Int_tGetNcols() const
Int_tGetNoElements() const
Int_tGetNrows() const
virtual char*TObject::GetObjectInfo(Int_t px, Int_t py) const
static Bool_tTObject::GetObjectStat()
virtual Option_t*TObject::GetOption() const
virtual const Int_t*GetRowIndexArray() const
virtual Int_t*GetRowIndexArray()
Int_tGetRowLwb() const
Int_tGetRowUpb() const
virtual TMatrixTBase<float>&GetSub(Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb, TMatrixTBase<float>& target, Option_t* option = "S") const
virtual const char*TObject::GetTitle() const
floatGetTol() const
virtual UInt_tTObject::GetUniqueID() const
virtual Bool_tTObject::HandleTimer(TTimer* timer)
virtual ULong_tTObject::Hash() const
virtual voidTObject::Info(const char* method, const char* msgfmt) const
virtual Bool_tTObject::InheritsFrom(const char* classname) const
virtual Bool_tTObject::InheritsFrom(const TClass* cl) const
virtual TMatrixTBase<float>&InsertRow(Int_t row, Int_t col, const float* v, Int_t n = -1)
virtual voidTObject::Inspect() const
voidInvalidate()
voidTObject::InvertBit(UInt_t f)
virtual TClass*IsA() const
virtual Bool_tTObject::IsEqual(const TObject* obj) const
virtual Bool_tTObject::IsFolder() const
Bool_tTObject::IsOnHeap() const
Bool_tIsOwner() const
virtual Bool_tTObject::IsSortable() const
virtual Bool_tIsSymmetric() const
Bool_tIsValid() const
Bool_tTObject::IsZombie() const
virtual voidTObject::ls(Option_t* option = "") const
voidMakeValid()
virtual floatMax() const
voidTObject::MayNotUse(const char* method) const
virtual floatMin() const
virtual Int_tNonZeros() const
floatNorm1() const
virtual TMatrixTBase<float>&NormByDiag(const TVectorT<float>& v, Option_t* option = "D")
floatNormInf() const
virtual Bool_tTObject::Notify()
static voidTObject::operator delete(void* ptr)
static voidTObject::operator delete(void* ptr, void* vp)
static voidTObject::operator delete[](void* ptr)
static voidTObject::operator delete[](void* ptr, void* vp)
void*TObject::operator new(size_t sz)
void*TObject::operator new(size_t sz, void* vp)
void*TObject::operator new[](size_t sz)
void*TObject::operator new[](size_t sz, void* vp)
Bool_toperator!=(float val) const
virtual floatoperator()(Int_t rown, Int_t coln) const
virtual float&operator()(Int_t rown, Int_t coln)
Bool_toperator<(float val) const
Bool_toperator<=(float val) const
TMatrixTBase<float>&operator=(const TMatrixTBase<float>&)
Bool_toperator==(float val) const
Bool_toperator>(float val) const
Bool_toperator>=(float val) const
virtual voidTObject::Paint(Option_t* option = "")
virtual voidTObject::Pop()
virtual voidPrint(Option_t* name = "") const
virtual TMatrixTBase<float>&Randomize(float alpha, float beta, Double_t& seed)
virtual Int_tTObject::Read(const char* name)
virtual voidTObject::RecursiveRemove(TObject* obj)
voidTObject::ResetBit(UInt_t f)
virtual TMatrixTBase<float>&ResizeTo(Int_t nrows, Int_t ncols, Int_t nr_nonzeros = -1)
virtual TMatrixTBase<float>&ResizeTo(Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb, Int_t nr_nonzeros = -1)
virtual floatRowNorm() const
virtual voidTObject::SaveAs(const char* filename = "", Option_t* option = "") const
virtual voidTObject::SavePrimitive(basic_ostream<char,char_traits<char> >& out, Option_t* option = "")
voidTObject::SetBit(UInt_t f)
voidTObject::SetBit(UInt_t f, Bool_t set)
virtual TMatrixTBase<float>&SetColIndexArray(Int_t* data)
virtual voidTObject::SetDrawOption(Option_t* option = "")
static voidTObject::SetDtorOnly(void* obj)
virtual TMatrixTBase<float>&SetMatrixArray(const float* data, Option_t* option = "")
static voidTObject::SetObjectStat(Bool_t stat)
virtual TMatrixTBase<float>&SetRowIndexArray(Int_t* data)
virtual TMatrixTBase<float>&SetSub(Int_t row_lwb, Int_t col_lwb, const TMatrixTBase<float>& source)
floatSetTol(float newTol)
virtual voidTObject::SetUniqueID(UInt_t uid)
virtual TMatrixTBase<float>&Shift(Int_t row_shift, Int_t col_shift)
virtual voidShowMembers(TMemberInspector& insp, char* parent)
virtual TMatrixTBase<float>&Sqr()
virtual TMatrixTBase<float>&Sqrt()
virtual voidStreamer(TBuffer& b)
voidStreamerNVirtual(TBuffer& b)
virtual floatSum() const
virtual voidTObject::SysError(const char* method, const char* msgfmt) const
Bool_tTObject::TestBit(UInt_t f) const
Int_tTObject::TestBits(UInt_t f) const
virtual TMatrixTBase<float>&UnitMatrix()
virtual voidTObject::UseCurrentStyle()
virtual voidTObject::Warning(const char* method, const char* msgfmt) const
virtual Int_tTObject::Write(const char* name = 0, Int_t option = 0, Int_t bufsize = 0)
virtual Int_tTObject::Write(const char* name = 0, Int_t option = 0, Int_t bufsize = 0) const
virtual TMatrixTBase<float>&Zero()
protected:
virtual voidTObject::DoError(int level, const char* location, const char* fmt, va_list va) const
static voidDoubleLexSort(Int_t n, Int_t* first, Int_t* second, float* data)
static voidIndexedLexSort(Int_t n, Int_t* first, Int_t swapFirst, Int_t* second, Int_t swapSecond, Int_t* index)
voidTObject::MakeZombie()
private:
float*GetElements()

Data Members

public:
enum { kSizeMax
kWorkMax
};
enum EMatrixStatusBits { kStatus
};
enum TObject::EStatusBits { kCanDelete
kMustCleanup
kObjInCanvas
kIsReferenced
kHasUUID
kCannotPick
kNoContextMenu
kInvalidObject
};
enum TObject::[unnamed] { kIsOnHeap
kNotDeleted
kZombie
kBitMask
kSingleKey
kOverwrite
kWriteDelete
};
protected:
Int_tfColLwblower bound of the col index
Bool_tfIsOwner!default kTRUE, when Use array kFALSE
Int_tfNcolsnumber of columns
Int_tfNelemsnumber of elements in matrix
Int_tfNrowIndexlength of row index array (= fNrows+1) wich is only used for sparse matrices
Int_tfNrowsnumber of rows
Int_tfRowLwblower bound of the row index
floatfTolsqrt(epsilon); epsilon is smallest number number so that 1+epsilon > 1

Class Charts

Inheritance Inherited Members Includes Libraries
Class Charts

Function documentation

Element * GetElements()
void DoubleLexSort(Int_t n, Int_t* first, Int_t* second, float* data)
void IndexedLexSort(Int_t n, Int_t* first, Int_t swapFirst, Int_t* second, Int_t swapSecond, Int_t* index)
{kSizeMax = 25}
Int_t GetRowLwb()
{ return fRowLwb; }
Int_t GetRowUpb()
{ return fNrows+fRowLwb-1; }
Int_t GetNrows()
{ return fNrows; }
Int_t GetColLwb()
{ return fColLwb; }
Int_t GetColUpb()
{ return fNcols+fColLwb-1; }
Int_t GetNcols()
{ return fNcols; }
Int_t GetNoElements()
{ return fNelems; }
Element GetTol()
{ return fTol; }
const Element * GetMatrixArray()
Element * GetMatrixArray()
const Int_t * GetRowIndexArray()
Int_t * GetRowIndexArray()
const Int_t * GetColIndexArray()
Int_t * GetColIndexArray()
TMatrixTBase<Element> & SetRowIndexArray(Int_t* data)
TMatrixTBase<Element> & SetColIndexArray(Int_t* data)
TMatrixTBase<Element> & SetMatrixArray(const float* data, Option_t* option = "")
Element SetTol(float newTol)
void Clear(Option_t* option = "")
void Invalidate()
{ SetBit(kStatus); }
void MakeValid()
{ ResetBit(kStatus); }
Bool_t IsValid()
{ return !TestBit(kStatus); }
Bool_t IsOwner()
{ return fIsOwner; }
Bool_t IsSymmetric()
TMatrixTBase<Element> & GetSub(Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb, TMatrixTBase<float>& target, Option_t* option = "S") const
void GetMatrix2Array(float* data, Option_t* option = "") const
TMatrixTBase<Element> & InsertRow(Int_t row, Int_t col, const float* v, Int_t n = -1)
void ExtractRow(Int_t row, Int_t col, float* v, Int_t n = -1) const
TMatrixTBase<Element> & Shift(Int_t row_shift, Int_t col_shift)
TMatrixTBase<Element> & ResizeTo(Int_t nrows, Int_t ncols, Int_t nr_nonzeros = -1)
TMatrixTBase<Element> & ResizeTo(Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb, Int_t nr_nonzeros = -1)
Double_t Determinant()
{ AbstractMethod("Determinant()"); return 0.; }
void Determinant(Double_t& d1, Double_t& d2) const
{ AbstractMethod("Determinant()"); d1 = 0.; d2 = 0.; }
TMatrixTBase<Element> & Zero()
TMatrixTBase<Element> & Abs()
TMatrixTBase<Element> & Sqr()
TMatrixTBase<Element> & Sqrt()
TMatrixTBase<Element> & UnitMatrix()
TMatrixTBase<Element> & NormByDiag(const TVectorT<float>& v, Option_t* option = "D")
Element RowNorm()
Element ColNorm()
Element E2Norm()
Element NormInf()
{ return RowNorm(); }
Element Norm1()
{ return ColNorm(); }
Int_t NonZeros()
Element Sum()
Element Min()
Element Max()
void Draw(Option_t* option = "")
void Print(Option_t* name = "") const
Element operator()(Int_t rown,Int_t coln)
Element & operator()(Int_t rown,Int_t coln)
Bool_t operator==(float val) const
Bool_t operator!=(float val) const
Bool_t operator<(float val) const
Bool_t operator<=(float val) const
Bool_t operator>(float val) const
Bool_t operator>=(float val) const
TMatrixTBase<Element> & Apply(const TElementActionT<Element> &action)
TMatrixTBase<Element> & Apply(const TElementPosActionT<Element> &action)
TMatrixTBase<Element> & Randomize(float alpha, float beta, Double_t& seed)

Last update: root/matrix:$Id: TMatrixTBase.h 20882 2007-11-19 11:31:26Z rdm $
Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *

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