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ROOT::Math::CholeskyDecompGenDim< F > Class Template Reference
template<class F>
class ROOT::Math::CholeskyDecompGenDim< F >

class to compute the Cholesky decomposition of a matrix

class to compute the Cholesky decomposition of a symmetric positive definite matrix when the dimensionality of the problem is not known at compile time

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)
// 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);
}
class to compute the Cholesky decomposition of a matrix
TMarker m
Definition textangle.C:8

Definition at line 310 of file CholeskyDecomp.h.

## Public Member Functions

template<class M >
CholeskyDecompGenDim (unsigned N, const M &m)
perform a Cholesky decomposition

template<typename G >
CholeskyDecompGenDim (unsigned N, G *m)
perform a Cholesky decomposition

~CholeskyDecompGenDim ()
destructor

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

FfL
lower triangular matrix L

unsigned fN
dimensionality dimensionality of the problem

bool fOk
flag indicating a successful decomposition

#include <Math/CholeskyDecomp.h>

## ◆ CholeskyDecompGenDim() [1/2]

template<class F >
template<class M >
 ROOT::Math::CholeskyDecompGenDim< F >::CholeskyDecompGenDim ( unsigned N, 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 331 of file CholeskyDecomp.h.

## ◆ CholeskyDecompGenDim() [2/2]

template<class F >
template<typename G >
 ROOT::Math::CholeskyDecompGenDim< F >::CholeskyDecompGenDim ( unsigned N, 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 349 of file CholeskyDecomp.h.

## ◆ ~CholeskyDecompGenDim()

template<class F >
 ROOT::Math::CholeskyDecompGenDim< F >::~CholeskyDecompGenDim ( )
inline

destructor

Definition at line 359 of file CholeskyDecomp.h.

## ◆ getL() [1/2]

template<class F >
template<typename G >
 bool ROOT::Math::CholeskyDecompGenDim< F >::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 448 of file CholeskyDecomp.h.

## ◆ getL() [2/2]

template<class F >
template<class M >
 bool ROOT::Math::CholeskyDecompGenDim< F >::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 423 of file CholeskyDecomp.h.

## ◆ getLi() [1/2]

template<class F >
template<typename G >
 bool ROOT::Math::CholeskyDecompGenDim< F >::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 498 of file CholeskyDecomp.h.

## ◆ getLi() [2/2]

template<class F >
template<class M >
 bool ROOT::Math::CholeskyDecompGenDim< F >::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 467 of file CholeskyDecomp.h.

## ◆ Invert() [1/2]

template<class F >
template<typename G >
 bool ROOT::Math::CholeskyDecompGenDim< F >::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 406 of file CholeskyDecomp.h.

## ◆ Invert() [2/2]

template<class F >
template<class M >
 bool ROOT::Math::CholeskyDecompGenDim< F >::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 389 of file CholeskyDecomp.h.

## ◆ ok()

template<class F >
 bool ROOT::Math::CholeskyDecompGenDim< F >::ok ( ) const
inline

returns true if decomposition was successful

Returns
true if decomposition was successful

Definition at line 363 of file CholeskyDecomp.h.

## ◆ operator bool()

template<class F >
 ROOT::Math::CholeskyDecompGenDim< F >::operator bool ( ) const
inline

returns true if decomposition was successful

Returns
true if decomposition was successful

Definition at line 366 of file CholeskyDecomp.h.

## ◆ Solve()

template<class F >
template<class V >
 bool ROOT::Math::CholeskyDecompGenDim< F >::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 376 of file CholeskyDecomp.h.

## ◆ fL

template<class F >
 F* ROOT::Math::CholeskyDecompGenDim< F >::fL
private

lower triangular matrix L

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

Definition at line 319 of file CholeskyDecomp.h.

## ◆ fN

template<class F >
 unsigned ROOT::Math::CholeskyDecompGenDim< F >::fN
private

dimensionality dimensionality of the problem

Definition at line 315 of file CholeskyDecomp.h.

## ◆ fOk

template<class F >
 bool ROOT::Math::CholeskyDecompGenDim< F >::fOk
private

flag indicating a successful decomposition

Definition at line 321 of file CholeskyDecomp.h.

• math/smatrix/inc/Math/CholeskyDecomp.h