| #include "TMatrixTBase.h" |
TMatrixTBase
class description - source file - inheritance tree (.pdf)
This is an abstract class, constructors will not be documented.
Look at the header to check for available constructors.
private:
double* GetElements()
protected:
static void DoubleLexSort(Int_t n, Int_t* first, Int_t* second, double* data)
static void IndexedLexSort(Int_t n, Int_t* first, Int_t swapFirst, Int_t* second, Int_t swapSecond, Int_t* index)
public:
virtual ~TMatrixTBase<double>()
virtual TMatrixTBase<double>& Abs()
virtual TMatrixTBase<double>& Apply(const TElementActionT<double>& action)
virtual TMatrixTBase<double>& Apply(const TElementPosActionT<double>& action)
static TClass* Class()
virtual void Clear(Option_t* option = "")
virtual double ColNorm() const
virtual Double_t Determinant() const
virtual void Determinant(Double_t& d1, Double_t& d2) const
virtual void Draw(Option_t* option = "")
virtual double E2Norm() const
virtual void ExtractRow(Int_t row, Int_t col, double* v, Int_t n = -1) const
virtual const Int_t* GetColIndexArray() const
virtual Int_t* GetColIndexArray()
Int_t GetColLwb() const
Int_t GetColUpb() const
virtual void GetMatrix2Array(double* data, Option_t* option = "") const
virtual const double* GetMatrixArray() const
virtual double* GetMatrixArray()
Int_t GetNcols() const
Int_t GetNoElements() const
Int_t GetNrows() const
virtual const Int_t* GetRowIndexArray() const
virtual Int_t* GetRowIndexArray()
Int_t GetRowLwb() const
Int_t GetRowUpb() const
virtual TMatrixTBase<double>& GetSub(Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb, TMatrixTBase<double>& target, Option_t* option = "S") const
double GetTol() const
virtual TMatrixTBase<double>& InsertRow(Int_t row, Int_t col, const double* v, Int_t n = -1)
void Invalidate()
virtual TClass* IsA() const
Bool_t IsOwner() const
virtual Bool_t IsSymmetric() const
Bool_t IsValid() const
void MakeValid()
virtual double Max() const
virtual double Min() const
virtual Int_t NonZeros() const
double Norm1() const
virtual TMatrixTBase<double>& NormByDiag(const TVectorT<double>& v, Option_t* option = "D")
double NormInf() const
Bool_t operator!=(double val) const
virtual double operator()(Int_t rown, Int_t coln) const
virtual double& operator()(Int_t rown, Int_t coln)
Bool_t operator<(double val) const
Bool_t operator<=(double val) const
TMatrixTBase<double>& operator=(const TMatrixTBase<double>&)
Bool_t operator==(double val) const
Bool_t operator>(double val) const
Bool_t operator>=(double val) const
virtual void Print(Option_t* name = "") const
virtual TMatrixTBase<double>& Randomize(double alpha, double beta, Double_t& seed)
virtual TMatrixTBase<double>& ResizeTo(Int_t nrows, Int_t ncols, Int_t nr_nonzeros = -1)
virtual TMatrixTBase<double>& ResizeTo(Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb, Int_t nr_nonzeros = -1)
virtual double RowNorm() const
virtual TMatrixTBase<double>& SetColIndexArray(Int_t* data)
virtual TMatrixTBase<double>& SetMatrixArray(const double* data, Option_t* option = "")
virtual TMatrixTBase<double>& SetRowIndexArray(Int_t* data)
virtual TMatrixTBase<double>& SetSub(Int_t row_lwb, Int_t col_lwb, const TMatrixTBase<double>& source)
double SetTol(double newTol)
virtual TMatrixTBase<double>& Shift(Int_t row_shift, Int_t col_shift)
virtual void ShowMembers(TMemberInspector& insp, char* parent)
virtual TMatrixTBase<double>& Sqr()
virtual TMatrixTBase<double>& Sqrt()
virtual void Streamer(TBuffer& b)
void StreamerNVirtual(TBuffer& b)
virtual double Sum() const
virtual TMatrixTBase<double>& UnitMatrix()
virtual TMatrixTBase<double>& Zero()
protected:
Int_t fNrows number of rows
Int_t fNcols number of columns
Int_t fRowLwb lower bound of the row index
Int_t fColLwb lower bound of the col index
Int_t fNelems number of elements in matrix
Int_t fNrowIndex length of row index array (= fNrows+1) wich is only used for sparse matrices
double fTol sqrt(epsilon); epsilon is smallest number number so that 1+epsilon > 1
Bool_t fIsOwner !default kTRUE, when Use array kFALSE
public:
static const enum TMatrixTBase<double>:: kSizeMax
static const enum TMatrixTBase<double>:: kWorkMax
static const TMatrixTBase<double>::EMatrixStatusBits kStatus
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. TMatrixT 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 "TMatrixT A(TMatrixT::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:
TMatrixT foo(int n)
{
TMatrixT foom(n,n); fill_in(foom); return foom;
}
TMatrixT 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, TMatrixTLazy (see below) can construct
TMatrixT m "inplace", with only a _single_ call to the
constructor.
2. Use "two-address instructions"
"void TMatrixT::operator += (const TMatrixT &B);"
as much as possible.
That is, to add two matrices, it's much more efficient to write
A += B;
than
TMatrixT C = A + B;
(if both operand should be preserved,
TMatrixT C = A; C += B;
is still better).
3. Use glorified constructors when returning of an object seems
inevitable:
"TMatrixT A(TMatrixT::kTransposed,B);"
"TMatrixT C(A,TMatrixT::kTransposeMult,B);"
like in the following snippet (from $ROOTSYS/test/vmatrix.cxx)
that verifies that for an orthogonal matrix T, T'T = TT' = E.
TMatrixT haar = THaarMatrixT(5);
TMatrixT unit(TMatrixT::kUnit,haar);
TMatrixT haar_t(TMatrixT::kTransposed,haar);
TMatrixT hth(haar,TMatrixT::kTransposeMult,haar);
TMatrixT hht(haar,TMatrixT::kMult,haar_t);
TMatrixT 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):
TMatrixT m(n,n); TVectorT v(n); TMatrixTDiag(m) += 4;
v = TMatrixTRow(m,0);
TMatrixTColumn m1(m,1); m1(2) = 3; // the same as m(2,1)=3;
Note, constructing of, say, TMatrixTDiag 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 TMatrixT &m)
{
TMatrixT m1(TMatrixT::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 THilbertMatrixT() 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(TMatrixT &m,TMatrixT &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:
TMatrixT haar = THaarMatrixT(5);
THaarMatrixT() 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. THaarMatrixT() constructs a
TMatrixTLazy, an object of just a few bytes long. A
"TMatrixT(const TMatrixTLazy &recipe)" constructor follows the
recipe and makes the matrix haar() right in place. No matrix
element is moved whatsoever!
Inline Functions
void ~TMatrixTBase()
double* GetElements()
void DoubleLexSort(Int_t n, Int_t* first, Int_t* second, double* data)
void IndexedLexSort(Int_t n, Int_t* first, Int_t swapFirst, Int_t* second, Int_t swapSecond, Int_t* index)
Int_t GetRowLwb() const
Int_t GetRowUpb() const
Int_t GetNrows() const
Int_t GetColLwb() const
Int_t GetColUpb() const
Int_t GetNcols() const
Int_t GetNoElements() const
double GetTol() const
const double* GetMatrixArray() const
double* GetMatrixArray()
const Int_t* GetRowIndexArray() const
Int_t* GetRowIndexArray()
const Int_t* GetColIndexArray() const
Int_t* GetColIndexArray()
TMatrixTBase<double>& SetRowIndexArray(Int_t* data)
TMatrixTBase<double>& SetColIndexArray(Int_t* data)
TMatrixTBase<double>& SetMatrixArray(const double* data, Option_t* option = "")
double SetTol(double newTol)
void Clear(Option_t* option = "")
void Invalidate()
void MakeValid()
Bool_t IsValid() const
Bool_t IsOwner() const
Bool_t IsSymmetric() const
TMatrixTBase<double>& GetSub(Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb, TMatrixTBase<double>& target, Option_t* option = "S") const
TMatrixTBase<double>& SetSub(Int_t row_lwb, Int_t col_lwb, const TMatrixTBase<double>& source)
void GetMatrix2Array(double* data, Option_t* option = "") const
TMatrixTBase<double>& InsertRow(Int_t row, Int_t col, const double* v, Int_t n = -1)
void ExtractRow(Int_t row, Int_t col, double* v, Int_t n = -1) const
TMatrixTBase<double>& Shift(Int_t row_shift, Int_t col_shift)
TMatrixTBase<double>& ResizeTo(Int_t nrows, Int_t ncols, Int_t nr_nonzeros = -1)
TMatrixTBase<double>& 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() const
void Determinant(Double_t& d1, Double_t& d2) const
TMatrixTBase<double>& Zero()
TMatrixTBase<double>& Abs()
TMatrixTBase<double>& Sqr()
TMatrixTBase<double>& Sqrt()
TMatrixTBase<double>& UnitMatrix()
TMatrixTBase<double>& NormByDiag(const TVectorT<double>& v, Option_t* option = "D")
double RowNorm() const
double ColNorm() const
double E2Norm() const
double NormInf() const
double Norm1() const
Int_t NonZeros() const
double Sum() const
double Min() const
double Max() const
void Draw(Option_t* option = "")
void Print(Option_t* name = "") const
double operator()(Int_t rown, Int_t coln) const
double& operator()(Int_t rown, Int_t coln)
Bool_t operator==(double val) const
Bool_t operator!=(double val) const
Bool_t operator<(double val) const
Bool_t operator<=(double val) const
Bool_t operator>(double val) const
Bool_t operator>=(double val) const
TMatrixTBase<double>& Apply(const TElementActionT<double>& action)
TMatrixTBase<double>& Apply(const TElementPosActionT<double>& action)
TMatrixTBase<double>& Randomize(double alpha, double beta, Double_t& seed)
TClass* Class()
TClass* IsA() const
void ShowMembers(TMemberInspector& insp, char* parent)
void Streamer(TBuffer& b)
void StreamerNVirtual(TBuffer& b)
TMatrixTBase<double>& operator=(const TMatrixTBase<double>&)
Last update: root/matrix:$Name: $:$Id: TMatrixTBase.cxx,v 1.4 2006/01/26 16:31:01 brun Exp $
Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *
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