 ROOT   6.21/01 Reference Guide ROOT::Math::CholeskyDecomp< F, N > Class Template Reference

### template<class F, unsigned N> class ROOT::Math::CholeskyDecomp< F, N >

class to compute the Cholesky decomposition of a matrix

class to compute the Cholesky decomposition of a symmetric positive definite matrix

provides routines to check if the decomposition succeeded (i.e. if matrix is positive definite and non-singular), to solve a linear system for the given matrix and to obtain its inverse

the actual functionality is implemented in templated helper classes which have specializations for dimensions N = 1 to 6 to achieve a gain in speed for common matrix sizes

usage example:

// let m be a symmetric positive definite SMatrix (use type float
// for internal computations, matrix size is 4x4)
CholeskyDecomp<float, 4> decomp(m);
// check if the decomposition succeeded
if (!decomp) {
std::cerr << "decomposition failed!" << std::endl;
} else {
// let rhs be a vector; we seek a vector x such that m * x = rhs
decomp.Solve(rhs);
// rhs now contains the solution we are looking for
// obtain the inverse of m, put it into m itself
decomp.Invert(m);
}

Definition at line 76 of file CholeskyDecomp.h.

## Public Member Functions

template<class M >
CholeskyDecomp (const M &m)
perform a Cholesky decomposition More...

template<typename G >
CholeskyDecomp (G *m)
perform a Cholesky decomposition More...

template<class M >
bool getL (M &m) const
obtain the decomposed matrix L More...

template<typename G >
bool getL (G *m) const
obtain the decomposed matrix L More...

template<class M >
bool getLi (M &m) const
obtain the inverse of the decomposed matrix L More...

template<typename G >
bool getLi (G *m) const
obtain the inverse of the decomposed matrix L More...

template<class M >
bool Invert (M &m) const
place the inverse into m More...

template<typename G >
bool Invert (G *m) const
place the inverse into m More...

bool ok () const
returns true if decomposition was successful More...

operator bool () const
returns true if decomposition was successful More...

template<class V >
bool Solve (V &rhs) const
solves a linear system for the given right hand side More...

## Private Attributes

F fL [N *(N+1)/2]
lower triangular matrix L More...

bool fOk
flag indicating a successful decomposition More...

#include <Math/CholeskyDecomp.h>

## ◆ CholeskyDecomp() [1/2]

template<class F, unsigned N>
template<class M >
 ROOT::Math::CholeskyDecomp< F, N >::CholeskyDecomp ( const M & m )
inline

perform a Cholesky decomposition

perfrom a Cholesky decomposition of a symmetric positive definite matrix m

this is the constructor to uses with an SMatrix (and objects that behave like an SMatrix in terms of using operator()(int i, int j) for access to elements)

Definition at line 94 of file CholeskyDecomp.h.

## ◆ CholeskyDecomp() [2/2]

template<class F, unsigned N>
template<typename G >
 ROOT::Math::CholeskyDecomp< F, N >::CholeskyDecomp ( G * m )
inline

perform a Cholesky decomposition

perfrom a Cholesky decomposition of a symmetric positive definite matrix m

this is the constructor to use in special applications where plain arrays are used

NOTE: the matrix is given in packed representation, matrix element m(i,j) (j <= i) is supposed to be in array element (i * (i + 1)) / 2 + j

Definition at line 112 of file CholeskyDecomp.h.

## ◆ getL() [1/2]

template<class F, unsigned N>
template<class M >
 bool ROOT::Math::CholeskyDecomp< F, N >::getL ( M & m ) const
inline

obtain the decomposed matrix L

This is the method to use with a plain array.

Returns
if the decomposition was successful

Definition at line 183 of file CholeskyDecomp.h.

## ◆ getL() [2/2]

template<class F, unsigned N>
template<typename G >
 bool ROOT::Math::CholeskyDecomp< F, N >::getL ( G * m ) const
inline

obtain the decomposed matrix L

Returns
if the decomposition was successful

NOTE: the matrix is given in packed representation, matrix element m(i,j) (j <= i) is supposed to be in array element (i * (i + 1)) / 2 + j

Definition at line 208 of file CholeskyDecomp.h.

## ◆ getLi() [1/2]

template<class F, unsigned N>
template<class M >
 bool ROOT::Math::CholeskyDecomp< F, N >::getLi ( M & m ) const
inline

obtain the inverse of the decomposed matrix L

This is the method to use with a plain array.

Returns
if the decomposition was successful

Definition at line 227 of file CholeskyDecomp.h.

## ◆ getLi() [2/2]

template<class F, unsigned N>
template<typename G >
 bool ROOT::Math::CholeskyDecomp< F, N >::getLi ( G * m ) const
inline

obtain the inverse of the decomposed matrix L

Returns
if the decomposition was successful

NOTE: the matrix is given in packed representation, matrix element m(j,i) (j <= i) is supposed to be in array element (i * (i + 1)) / 2 + j

Definition at line 258 of file CholeskyDecomp.h.

## ◆ Invert() [1/2]

template<class F, unsigned N>
template<class M >
 bool ROOT::Math::CholeskyDecomp< F, N >::Invert ( M & m ) const
inline

place the inverse into m

This is the method to use with an SMatrix.

Returns
if the decomposition was successful

Definition at line 149 of file CholeskyDecomp.h.

## ◆ Invert() [2/2]

template<class F, unsigned N>
template<typename G >
 bool ROOT::Math::CholeskyDecomp< F, N >::Invert ( G * m ) const
inline

place the inverse into m

This is the method to use with a plain array.

Returns
if the decomposition was successful

NOTE: the matrix is given in packed representation, matrix element m(i,j) (j <= i) is supposed to be in array element (i * (i + 1)) / 2 + j

Definition at line 166 of file CholeskyDecomp.h.

## ◆ ok()

template<class F, unsigned N>
 bool ROOT::Math::CholeskyDecomp< F, N >::ok ( ) const
inline

returns true if decomposition was successful

Returns
true if decomposition was successful

Definition at line 123 of file CholeskyDecomp.h.

## ◆ operator bool()

template<class F, unsigned N>
 ROOT::Math::CholeskyDecomp< F, N >::operator bool ( ) const
inline

returns true if decomposition was successful

Returns
true if decomposition was successful

Definition at line 126 of file CholeskyDecomp.h.

## ◆ Solve()

template<class F, unsigned N>
template<class V >
 bool ROOT::Math::CholeskyDecomp< F, N >::Solve ( V & rhs ) const
inline

solves a linear system for the given right hand side

Note that you can use both SVector classes and plain arrays for rhs. (Make sure that the sizes match!). It will work with any vector implementing the operator [i]

Returns
if the decomposition was successful

Definition at line 136 of file CholeskyDecomp.h.

## ◆ fL

template<class F, unsigned N>
 F ROOT::Math::CholeskyDecomp< F, N >::fL[N *(N+1)/2]
private

lower triangular matrix L

lower triangular matrix L, packed storage, with diagonal elements pre-inverted

Definition at line 82 of file CholeskyDecomp.h.

## ◆ fOk

template<class F, unsigned N>
 bool ROOT::Math::CholeskyDecomp< F, N >::fOk
private

flag indicating a successful decomposition

Definition at line 84 of file CholeskyDecomp.h.

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