Decomposition of symmetric matrix. More...

#include <vnl_cholesky.h>

Public Types
enum	Operation { quiet, verbose, estimate_condition }
	Modes of computation. See constructor for details. More...

Public Member Functions
	vnl_cholesky (vnl_matrix< double > const &M, Operation mode=verbose)
	Make cholesky decomposition of M optionally computing the reciprocal condition number. More...

	~vnl_cholesky ()=default

vnl_vector< double >	solve (vnl_vector< double > const &b) const
	Solve LS problem M x = b. More...

void	solve (vnl_vector< double > const &b, vnl_vector< double > *x) const
	Solve LS problem M x = b. More...

double	determinant () const
	Compute determinant. More...

vnl_matrix< double >	inverse () const

vnl_matrix< double >	lower_triangle () const
	Return lower-triangular factor. More...

vnl_matrix< double >	upper_triangle () const
	Return upper-triangular factor. More...

vnl_matrix< double > const &	L_badly_named_method () const
	Return the decomposition matrix. More...

int	rank_deficiency () const
	A Success/failure flag. More...

double	rcond () const
	Return reciprocal condition number (smallest/largest singular values). More...

vnl_vector< double > &	nullvector ()
	Return computed nullvector. More...

vnl_vector< double > const &	nullvector () const

Protected Attributes
vnl_matrix< double >	A_

double	rcond_

long	num_dims_rank_def_

vnl_vector< double >	nullvector_

Private Member Functions
	vnl_cholesky (vnl_cholesky const &that)=delete
	Copy constructor - privatised to avoid it being used. More...

vnl_cholesky &	operator= (vnl_cholesky const &that)=delete
	Assignment operator - privatised to avoid it being used. More...

Detailed Description

Decomposition of symmetric matrix.

A class to hold the Cholesky decomposition of a symmetric matrix and use that to solve linear systems, compute determinants and inverses. The cholesky decomposition decomposes symmetric A = L*L.transpose() where L is lower triangular

To check that the decomposition can be used safely for solving a linear equation it is wise to construct with mode==estimate_condition and check that rcond()>sqrt(machine precision). If this is not the case it might be a good idea to use vnl_svd instead.

Definition at line 31 of file vnl_cholesky.h.

Member Enumeration Documentation

◆ Operation

enum vnl_cholesky::Operation

Modes of computation. See constructor for details.

Enumerator
quiet
verbose
estimate_condition

Definition at line 35 of file vnl_cholesky.h.

Constructor & Destructor Documentation

◆ vnl_cholesky() [1/2]

vnl_cholesky::vnl_cholesky	(	vnl_matrix< double > const &	M,
		Operation	mode = `verbose`
	)

Make cholesky decomposition of M optionally computing the reciprocal condition number.

Cholesky decomposition.

Make cholesky decomposition of M optionally computing the reciprocal condition number. If mode is estimate_condition, the condition number and an approximate nullspace are estimated, at a cost of a factor of (1 + 18/n). Here's a table of 1 + 18/n:

 n:              3      5     10     50    100    500   1000
 slowdown:     7.0    4.6    2.8    1.4   1.18   1.04   1.02

Definition at line 25 of file vnl_cholesky.cxx.

◆ ~vnl_cholesky()

vnl_cholesky::~vnl_cholesky ( )

default

◆ vnl_cholesky() [2/2]

vnl_cholesky::vnl_cholesky ( vnl_cholesky const & that )

privatedelete

Copy constructor - privatised to avoid it being used.

Member Function Documentation

◆ determinant()

double vnl_cholesky::determinant ( ) const

Compute determinant.

Definition at line 73 of file vnl_cholesky.cxx.

◆ inverse()

vnl_matrix< double > vnl_cholesky::inverse ( ) const

Definition at line 84 of file vnl_cholesky.cxx.

◆ L_badly_named_method()

vnl_matrix<double> const& vnl_cholesky::L_badly_named_method ( ) const

inline

Return the decomposition matrix.

Definition at line 67 of file vnl_cholesky.h.

◆ lower_triangle()

vnl_matrix< double > vnl_cholesky::lower_triangle ( ) const

Return lower-triangular factor.

Definition at line 105 of file vnl_cholesky.cxx.

◆ nullvector() [1/2]

vnl_vector<double>& vnl_cholesky::nullvector ( )

inline

Return computed nullvector.

Not calculated unless Operation mode at construction was estimate_condition.

Definition at line 80 of file vnl_cholesky.h.

◆ nullvector() [2/2]

vnl_vector<double> const& vnl_cholesky::nullvector ( ) const

inline

Definition at line 81 of file vnl_cholesky.h.

◆ operator=()

vnl_cholesky& vnl_cholesky::operator= ( vnl_cholesky const & that )

privatedelete

Assignment operator - privatised to avoid it being used.

◆ rank_deficiency()

int vnl_cholesky::rank_deficiency ( ) const

inline

A Success/failure flag.

Definition at line 70 of file vnl_cholesky.h.

◆ rcond()

double vnl_cholesky::rcond ( ) const

inline

Return reciprocal condition number (smallest/largest singular values).

As long as rcond()>sqrt(precision) the decomposition can be used for solving equations safely. Not calculated unless Operation mode at construction was estimate_condition.

Definition at line 76 of file vnl_cholesky.h.

◆ solve() [1/2]

vnl_vector< double > vnl_cholesky::solve ( vnl_vector< double > const & b ) const

Solve LS problem M x = b.

Solve least squares problem M x = b.

Definition at line 62 of file vnl_cholesky.cxx.

◆ solve() [2/2]

void vnl_cholesky::solve	(	vnl_vector< double > const &	b,
		vnl_vector< double > *	x
	)		const

Solve LS problem M x = b.

Solve least squares problem M x = b.

The right-hand-side std::vector x may be b, which will give a fractional increase in speed.

Definition at line 52 of file vnl_cholesky.cxx.

◆ upper_triangle()

vnl_matrix< double > vnl_cholesky::upper_triangle ( ) const

Return upper-triangular factor.

Definition at line 122 of file vnl_cholesky.cxx.

Member Data Documentation

◆ A_

vnl_matrix<double> vnl_cholesky::A_

protected

Definition at line 85 of file vnl_cholesky.h.

◆ nullvector_

vnl_vector<double> vnl_cholesky::nullvector_

protected

Definition at line 88 of file vnl_cholesky.h.

◆ num_dims_rank_def_

long vnl_cholesky::num_dims_rank_def_

protected

Definition at line 87 of file vnl_cholesky.h.

◆ rcond_

double vnl_cholesky::rcond_

protected

Definition at line 86 of file vnl_cholesky.h.

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

core/vnl/algo/vnl_cholesky.h
core/vnl/algo/vnl_cholesky.cxx

Public Types

Public Member Functions

Protected Attributes

Private Member Functions

Detailed Description

Member Enumeration Documentation

◆ Operation

Constructor & Destructor Documentation

◆ vnl_cholesky() [1/2]

◆ ~vnl_cholesky()

◆ vnl_cholesky() [2/2]

Member Function Documentation

◆ determinant()

◆ inverse()

◆ L_badly_named_method()

◆ lower_triangle()

◆ nullvector() [1/2]

◆ nullvector() [2/2]

◆ operator=()

◆ rank_deficiency()

◆ rcond()

◆ solve() [1/2]

◆ solve() [2/2]

◆ upper_triangle()

Member Data Documentation

◆ A_

◆ nullvector_

◆ num_dims_rank_def_

◆ rcond_