class ROOT::Math::SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >


SMatrix: a generic fixed size D1 x D2 Matrix class.
The class is template on the scalar type, on the matrix sizes:
D1 = number of rows and D2 = number of columns
amd on the representation storage type.
By default the representation is MatRepStd<T,D1,D2> (standard D1xD2 of type T),
but it can be of type MatRepSym<T,D> for symmetric matrices DxD, where the storage is only
D*(D+1)/2.

See \ref SMatrixDoc.

Original author is Thorsten Glebe
HERA-B Collaboration, MPI Heidelberg (Germany)

@ingroup SMatrixSVector

@authors T. Glebe, L. Moneta and J. Palacios


 SMatrix: column-wise storage

Function Members (Methods)

public:
~SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >()
doubleapply(unsigned int i) const
const double*Array() const
double*Array()
const double&At(unsigned int i, unsigned int j) const
double&At(unsigned int i, unsigned int j)
double*begin()
double*begin() const
ROOT::Math::SVector<double,2>Col(unsigned int thecol) const
boolDet(double& det)
boolDet2(double& det) const
ROOT::Math::SVector<double,2>Diagonal() const
double*end()
double*end() const
ROOT::Math::SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >Inverse(int& ifail) const
boolInvert()
boolIsInUse(const double* p) const
ROOT::Math::SVector<double,3>LowerBlock() const
booloperator!=(const double& rhs) const
booloperator!=(const ROOT::Math::SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >& rhs) const
const double&operator()(unsigned int i, unsigned int j) const
double&operator()(unsigned int i, unsigned int j)
ROOT::Math::SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >&operator*=(const double& rhs)
ROOT::Math::SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >&operator+=(const double& rhs)
ROOT::Math::SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >&operator-=(const double& rhs)
ROOT::Math::SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >&operator/=(const double& rhs)
booloperator<(const double& rhs) const
ROOT::Math::SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >&operator=(ROOT::Math::SMatrixIdentity)
ROOT::Math::SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >&operator=(const double& rhs)
ROOT::Math::SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >&operator=(const ROOT::Math::SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >&)
booloperator==(const double& rhs) const
booloperator>(const double& rhs) const
ostream&Print(ostream& os) const
ROOT::Math::SVector<double,2>Row(unsigned int therow) const
ROOT::Math::SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >()
ROOT::Math::SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >(ROOT::Math::SMatrixIdentity)
ROOT::Math::SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >(const ROOT::Math::SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >& rhs)
ROOT::Math::SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >(const double& rhs)
ROOT::Math::SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >SMatrix<double,2,2,ROOT::Math::MatRepSym<double,2> >(const ROOT::Math::SVector<double,3>& v, bool lower = true)
doubleTrace() const
ROOT::Math::SVector<double,3>UpperBlock() const

Data Members

public:
enum { kRows
kCols
kSize
};
public:
ROOT::Math::MatRepSym<double,2>fRep

Class Charts

Inheritance Inherited Members Includes Libraries
Class Charts

Function documentation

SMatrix<T,D1,D2,R>& operator=(const M& rhs)
Assign from another compatible matrix.
Possible Symmetirc to general but NOT vice-versa

SMatrix<T,D1,D2,R>& operator=(const Expr<A,T,D1,D2,R2>& rhs)
Assign from a matrix expression

SMatrix<T,D1,D2,R> & operator=(SMatrixIdentity )
Assign from an identity matrix

T apply(unsigned int i) const
 @name --- Access functions --- 
 access the parse tree with the index starting from zero and
following the C convention for the order in accessing
the matrix elements.
Same convention for general and symmetric matrices.

const T* Array()
 return read-only pointer to internal array
T* Array()
iterator begin()
 @name --- STL-like interface ---
The iterators access the matrix element in the order how they are
stored in memory. The C (row-major) convention is used, and in the
case of symmetric matrices the iterator spans only the lower diagonal
block. For example for a symmetric 3x3 matrices the order of the 6
elements \f${a_0,...a_5}\f$ is:
\f[
M = \left( \begin{array}{ccc}
a_0 & a_1 & a_3  \\
a_1 & a_2  & a_4  \\
a_3 & a_4 & a_5   \end{array} \right)
\f]

 STL iterator interface. 
iterator end()
 STL iterator interface. 
const_iterator begin()
 STL const_iterator interface. 
const_iterator end()
 STL const_iterator interface. 
bool operator==(const double& rhs) const
 @name --- Operators --- 
 element wise comparison
bool operator!=(const T& rhs)
 element wise comparison
bool operator!=(const SMatrix<T,D1,D2,R>& rhs)
 element wise comparison
bool operator>(const double& rhs) const
 element wise comparison
bool operator<(const double& rhs) const
 element wise comparison
const T& operator()(unsigned int i, unsigned int j)
read only access to matrix element, with indices starting from 0

T& operator()(unsigned int i, unsigned int j)
const T& At(unsigned int i, unsigned int j)
read only access to matrix element, with indices starting from 0.
Fuction will check index values and it will assert if they are wrong

T& At(unsigned int i, unsigned int j)
SMatrix<T,D1,D2,R>& operator+=(const double& rhs)
addition with a scalar

SMatrix<T,D1,D2,R>& operator-=(const double& rhs)
subtraction with a scalar

SMatrix<T,D1,D2,R>& operator*=(const double& rhs)
multiplication with a scalar

SMatrix<T,D1,D2,R>& operator/=(const double& rhs)
division with a scalar

bool Invert()
 @name --- Linear Algebra Functions --- 

Invert a square Matrix ( this method changes the current matrix).
Return true if inversion is successfull.
The method used for general square matrices is the LU factorization taken from Dinv routine
from the CERNLIB (written in C++ from CLHEP authors)
In case of symmetric matrices Bunch-Kaufman diagonal pivoting method is used
(The implementation is the one written by the CLHEP authors)

SMatrix<T,D1,D2,R> Inverse(int& ifail) const
Invert a square Matrix and  returns a new matrix. In case the inversion fails
the current matrix is returned.
\param ifail . ifail will be set to 0 when inversion is successfull.
See ROOT::Math::SMatrix::Invert for the inversion algorithm

bool Det(double& det)
determinant of square Matrix via Dfact.
Return true when the calculation is successfull.
\param det will contain the calculated determinant value
\b Note: this will destroy the contents of the Matrix!

bool Det2(double& det) const
determinant of square Matrix via Dfact.
Return true when the calculation is successfull.
\param det will contain the calculated determinant value
\b Note: this will preserve the content of the Matrix!

SVector<T,D2> Row(unsigned int therow) const
return a full Matrix row as a vector (copy the content in a new vector)

SVector<T,D1> Col(unsigned int thecol) const
return a full Matrix column as a vector (copy the content in a new vector)

SVector<T,D1> Diagonal()
return diagonal elements of a matrix as a Vector.
It works only for squared matrices D1 == D2, otherwise it will produce a compile error

T Trace()
return the trace of a matrix
Sum of the diagonal elements

SubVector UpperBlock()
SubVector LowerBlock()
bool IsInUse(const double* p) const
 @name --- Other Functions --- 

Function to check if a matrix is sharing same memory location of the passed pointer
This function is used by the expression templates to avoid the alias problem during
expression evaluation. When  the matrix is in use, for example in operations
like A = B * A, a temporary object storing the intermediate result is automatically
created when evaluating the expression.


std::ostream& Print(ostream& os) const
 submatrices
 Print: used by operator<<()

Author: T. Glebe, L. Moneta, J. Palacios 2005
Last update: root/smatrix:$Id: SMatrix.h 21553 2007-12-21 10:55:46Z moneta $

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