TooN::Lapack_Cholesky< Size, Precision > Class Template Reference
[Matrix decompositions]

#include <Lapack_Cholesky.h>

List of all members.

Public Member Functions
template<int Size2, int Cols2, typename P2 , typename B2 >
Matrix< Size, Cols2, Precision, ColMajor >	backsub (const Matrix< Size2, Cols2, P2, B2 > &m) const
template<int Size2, typename P2 , typename B2 >
Vector< Size, Precision >	backsub (const Vector< Size2, P2, B2 > &v) const
template<class P2 , class B2 >
void	compute (const Matrix< Size, Size, P2, B2 > &m)
Precision	determinant () const
void	do_compute ()
Matrix	get_inverse () const
Matrix< Size, Size, Precision >	get_L () const
	Lapack_Cholesky (int size)
	Constructor for Size=Dynamic.
template<class P2 , class B2 >
	Lapack_Cholesky (const Matrix< Size, Size, P2, B2 > &m)
	Lapack_Cholesky ()
template<int Size2, typename P2 , typename B2 >
Precision	mahalanobis (const Vector< Size2, P2, B2 > &v) const
int	rank () const
Private Attributes
Matrix< Size, Size, Precision >	my_cholesky
Matrix< Size, Size, Precision >	my_cholesky_lapack
int	my_rank

---

Detailed Description

template<int Size, typename Precision = DefaultPrecision>
class TooN::Lapack_Cholesky< Size, Precision >

Decomposes a positive-semidefinite symmetric matrix A (such as a covariance) into L*L^T, where L is lower-triangular. Also can compute A = S*S^T, with S lower triangular. The LDL^T form is faster to compute than the class Cholesky decomposition. The decomposition can be used to compute A^-1*x, A^-1*M, M*A^-1*M^T, and A^-1 itself, though the latter rarely needs to be explicitly represented. Also efficiently computes det(A) and rank(A). It can be used as follows:

// Declare some matrices.
Matrix<3> A = ...; // we'll pretend it is pos-def
Matrix<2,3> M;
Matrix<2> B;
Vector<3> y = make_Vector(2,3,4);
// create the Cholesky decomposition of A
Cholesky<3> chol(A);
// compute x = A^-1 * y
x = cholA.backsub(y);
//compute A^-1
Matrix<3> Ainv = cholA.get_inverse();

Cholesky decomposition of a symmetric matrix. Only the lower half of the matrix is considered This uses the non-sqrt version of the decomposition giving symmetric M = L*D*L.T() where the diagonal of L contains ones

Parameters:

	Size	the size of the matrix
	Precision	the precision of the entries in the matrix and its decomposition

Definition at line 72 of file Lapack_Cholesky.h.

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Constructor & Destructor Documentation

template<int Size, typename Precision = DefaultPrecision>

TooN::Lapack_Cholesky< Size, Precision >::Lapack_Cholesky

(

)

[inline]

Definition at line 75 of file Lapack_Cholesky.h.

template<int Size, typename Precision = DefaultPrecision>

template<class P2 , class B2 >

TooN::Lapack_Cholesky< Size, Precision >::Lapack_Cholesky

(

const Matrix< Size, Size, P2, B2 > &

m

)

[inline]

Definition at line 78 of file Lapack_Cholesky.h.

template<int Size, typename Precision = DefaultPrecision>

TooN::Lapack_Cholesky< Size, Precision >::Lapack_Cholesky

(

int

size

)

[inline]

Constructor for Size=Dynamic.

Definition at line 85 of file Lapack_Cholesky.h.

---

Member Function Documentation

template<int Size, typename Precision = DefaultPrecision>

template<int Size2, int Cols2, typename P2 , typename B2 >

Matrix<Size, Cols2, Precision, ColMajor> TooN::Lapack_Cholesky< Size, Precision >::backsub

(

const Matrix< Size2, Cols2, P2, B2 > &

m

)

const [inline]

Definition at line 133 of file Lapack_Cholesky.h.

template<int Size, typename Precision = DefaultPrecision>

template<int Size2, typename P2 , typename B2 >

Vector<Size, Precision> TooN::Lapack_Cholesky< Size, Precision >::backsub

(

const Vector< Size2, P2, B2 > &

v

)

const [inline]

Definition at line 120 of file Lapack_Cholesky.h.

template<int Size, typename Precision = DefaultPrecision>

template<class P2 , class B2 >

void TooN::Lapack_Cholesky< Size, Precision >::compute

(

const Matrix< Size, Size, P2, B2 > &

m

)

[inline]

Definition at line 87 of file Lapack_Cholesky.h.

template<int Size, typename Precision = DefaultPrecision>

Precision TooN::Lapack_Cholesky< Size, Precision >::determinant

(

)

const [inline]

Definition at line 154 of file Lapack_Cholesky.h.

template<int Size, typename Precision = DefaultPrecision>

void TooN::Lapack_Cholesky< Size, Precision >::do_compute

(

)

[inline]

Definition at line 96 of file Lapack_Cholesky.h.

template<int Size, typename Precision = DefaultPrecision>

Matrix TooN::Lapack_Cholesky< Size, Precision >::get_inverse

(

)

const [inline]

Definition at line 161 of file Lapack_Cholesky.h.

template<int Size, typename Precision = DefaultPrecision>

Matrix<Size,Size,Precision> TooN::Lapack_Cholesky< Size, Precision >::get_L

(

)

const [inline]

Definition at line 150 of file Lapack_Cholesky.h.

template<int Size, typename Precision = DefaultPrecision>

template<int Size2, typename P2 , typename B2 >

Precision TooN::Lapack_Cholesky< Size, Precision >::mahalanobis

(

const Vector< Size2, P2, B2 > &

v

)

const [inline]

Definition at line 146 of file Lapack_Cholesky.h.

template<int Size, typename Precision = DefaultPrecision>

int TooN::Lapack_Cholesky< Size, Precision >::rank

(

)

const [inline]

Definition at line 117 of file Lapack_Cholesky.h.

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Member Data Documentation

template<int Size, typename Precision = DefaultPrecision>

Matrix<Size,Size,Precision> TooN::Lapack_Cholesky< Size, Precision >::my_cholesky [private]

Definition at line 178 of file Lapack_Cholesky.h.

template<int Size, typename Precision = DefaultPrecision>

Matrix<Size,Size,Precision> TooN::Lapack_Cholesky< Size, Precision >::my_cholesky_lapack [private]

Definition at line 177 of file Lapack_Cholesky.h.

template<int Size, typename Precision = DefaultPrecision>

int TooN::Lapack_Cholesky< Size, Precision >::my_rank [private]

Definition at line 179 of file Lapack_Cholesky.h.

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

• Lapack_Cholesky.h