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 95 of file CholeskyDecomp.h.

Public Member Functions
template<class M >
	CholeskyDecomp (const M &m)
	perform a Cholesky decomposition
template<typename G >
	CholeskyDecomp (G *m)
	perform a Cholesky decomposition
template<typename G >
bool	getL (G *m) const
	obtain the decomposed matrix L
template<class M >
bool	getL (M &m) const
	obtain the decomposed matrix L
template<typename G >
bool	getLi (G *m) const
	obtain the inverse of the decomposed matrix L
template<class M >
bool	getLi (M &m) const
	obtain the inverse of the decomposed matrix L
template<typename G >
bool	Invert (G *m) const
	place the inverse into m
template<class M >
bool	Invert (M &m) const
	place the inverse into m
bool	ok () const
	returns true if decomposition was successful
	operator bool () const
	returns true if decomposition was successful
template<class V >
bool	Solve (V &rhs) const
	solves a linear system for the given right hand side

Private Attributes
F	fL [N *(N+1)/2]
	lower triangular matrix L
bool	fOk
	flag indicating a successful decomposition

#include <Math/CholeskyDecomp.h>

Constructor & Destructor Documentation

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

perform 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 114 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

perform 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 132 of file CholeskyDecomp.h.

Member Function Documentation

getL() [1/2]

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 234 of file CholeskyDecomp.h.

getL() [2/2]

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 207 of file CholeskyDecomp.h.

getLi() [1/2]

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 288 of file CholeskyDecomp.h.

getLi() [2/2]

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 255 of file CholeskyDecomp.h.

Invert() [1/2]

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 189 of file CholeskyDecomp.h.

Invert() [2/2]

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 170 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 141 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 144 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 155 of file CholeskyDecomp.h.

Member Data Documentation

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 100 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 102 of file CholeskyDecomp.h.