vnl_cholesky Class Reference

#include <vnl_cholesky.h>

List of all members.

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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 33 of file 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.
	~vnl_cholesky ()
vnl_vector< double >	solve (vnl_vector< double > const &b) const
	Solve LS problem M x = b.
void	solve (vnl_vector< double > const &b, vnl_vector< double > *x) const
	Solve LS problem M x = b.
double	determinant () const
	Compute determinant.
vnl_matrix< double >	inverse () const
vnl_matrix< double >	lower_triangle () const
	Return lower-triangular factor.
vnl_matrix< double >	upper_triangle () const
	Return upper-triangular factor.
vnl_matrix< double > const &	L_badly_named_method () const
	Return the decomposition matrix.
int	rank_deficiency () const
	A Success/failure flag.
double	rcond () const
	Return reciprocal condition number (smallest/largest singular values).
vnl_vector< double > &	nullvector ()
	Return computed nullvector.
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)
	Copy constructor - privatised to avoid it being used.
vnl_cholesky &	operator= (vnl_cholesky const &that)
	Assignment operator - privatised to avoid it being used.

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Member Enumeration Documentation

enum vnl_cholesky::Operation

Modes of computation. See constructor for details. Enumerator: quiet  verbose  estimate_condition  Definition at line 37 of file vnl_cholesky.h.

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Constructor & Destructor Documentation

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

Make cholesky decomposition of M optionally computing the reciprocal condition number. 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 28 of file vnl_cholesky.cxx.

vnl_cholesky::~vnl_cholesky (   )  [inline]

Definition at line 45 of file vnl_cholesky.h.

vnl_cholesky::vnl_cholesky (  vnl_cholesky const &  that  )  [private]

Copy constructor - privatised to avoid it being used.

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Member Function Documentation

double vnl_cholesky::determinant (   )  const

Compute determinant. Definition at line 75 of file vnl_cholesky.cxx.

vnl_matrix< double > vnl_cholesky::inverse (   )  const

Definition at line 86 of file vnl_cholesky.cxx.

vnl_matrix<double> const& vnl_cholesky::L_badly_named_method (   )  const [inline]

Return the decomposition matrix. Definition at line 69 of file vnl_cholesky.h.

vnl_matrix< double > vnl_cholesky::lower_triangle (   )  const

Return lower-triangular factor. Definition at line 107 of file vnl_cholesky.cxx.

vnl_vector<double> const& vnl_cholesky::nullvector (   )  const [inline]

Definition at line 83 of file vnl_cholesky.h.

vnl_vector<double>& vnl_cholesky::nullvector (   )  [inline]

Return computed nullvector. Not calculated unless Operation mode at construction was estimate_condition. Definition at line 82 of file vnl_cholesky.h.

vnl_cholesky& vnl_cholesky::operator= (  vnl_cholesky const &  that  )  [private]

Assignment operator - privatised to avoid it being used.

int vnl_cholesky::rank_deficiency (   )  const [inline]

A Success/failure flag. Definition at line 72 of file vnl_cholesky.h.

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 78 of file vnl_cholesky.h.

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

Solve LS problem M x = b. The right-hand-side vcl_vector x may be b, which will give a fractional increase in speed. Definition at line 54 of file vnl_cholesky.cxx.

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

Solve LS problem M x = b. Definition at line 64 of file vnl_cholesky.cxx.

vnl_matrix< double > vnl_cholesky::upper_triangle (   )  const

Return upper-triangular factor. Definition at line 124 of file vnl_cholesky.cxx.

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Member Data Documentation

vnl_matrix<double> vnl_cholesky::A_ [protected]

Definition at line 87 of file vnl_cholesky.h.

vnl_vector<double> vnl_cholesky::nullvector_ [protected]

Definition at line 90 of file vnl_cholesky.h.

long vnl_cholesky::num_dims_rank_def_ [protected]

Definition at line 89 of file vnl_cholesky.h.

double vnl_cholesky::rcond_ [protected]

Definition at line 88 of file vnl_cholesky.h.

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

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

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