Linear system solver for Mx = b using LU decomposition of a sparse matrix. More...

#include <vnl_sparse_lu.h>

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

Public Member Functions
	vnl_sparse_lu (vnl_sparse_matrix< double > const &M, operation mode=quiet)
	Make sparse_lu decomposition of M optionally computing the reciprocal condition number. More...

	~vnl_sparse_lu ()

void	set_pivot_thresh (double pivot_thresh)
	set the relative pivot threshold should be between 0 and 1. More...

void	set_absolute_thresh (double absolute_thresh)
	set the threshold on absolute element magnitude for pivoting. More...

void	set_diagonal_pivoting (int diag_pivoting)
	set diagonal pivoting mode, normally 1 which gives priority to diagonal elements. More...

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

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

vnl_vector< double >	solve_transpose (vnl_vector< double > const &b)
	Solve problem M^t x = b. More...

void	solve_transpose (vnl_vector< double > const &b, vnl_vector< double > *x)
	Solve problem M^t x = b. More...

double	determinant ()
	Compute determinant. More...

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

double	max_error_bound ()
	An estimate of maximum error in solution. More...

Protected Member Functions
void	decompose_matrix ()

bool	est_condition ()
	estimate the condition number. More...

Protected Attributes
vnl_sparse_matrix< double >	A_

bool	factored_

bool	condition_computed_

operation	mode_

double	norm_

double	rcond_

double	largest_

double	pivot_thresh_

double	absolute_thresh_

int	diag_pivoting_

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

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

Private Attributes
void *	pmatrix_
	The internal matrix representation. More...

Detailed Description

Linear system solver for Mx = b using LU decomposition of a sparse matrix.

Encapsulating Sparse 1.3 by Kenneth S. Kundert. The matrix is factored before solution. Any number of b vectors can be applied after the matrix is factored with out recomputation of the LU form. It is advised to construct with mode==estimate_condition and check that rcond()>sqrt(machine precision). If this is not the case the solution may be suspect. An upper bound on error is provided. The solution of M^t x = b is also available.

Definition at line 28 of file vnl_sparse_lu.h.

Member Enumeration Documentation

◆ operation

enum vnl_sparse_lu::operation

Modes of computation. See constructor for details.

Enumerator
quiet
verbose
estimate_condition
estimate_condition_verbose

Definition at line 32 of file vnl_sparse_lu.h.

Constructor & Destructor Documentation

◆ vnl_sparse_lu() [1/2]

vnl_sparse_lu::vnl_sparse_lu	(	vnl_sparse_matrix< double > const &	M,
		operation	mode = `quiet`
	)

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

constructor - controls if condition information is computed.

Definition at line 18 of file vnl_sparse_lu.cxx.

◆ ~vnl_sparse_lu()

vnl_sparse_lu::~vnl_sparse_lu ( )

Definition at line 12 of file vnl_sparse_lu.cxx.

◆ vnl_sparse_lu() [2/2]

vnl_sparse_lu::vnl_sparse_lu ( vnl_sparse_lu const & that )

private

Copy constructor - privatised to avoid it being used.

Member Function Documentation

◆ decompose_matrix()

void vnl_sparse_lu::decompose_matrix ( )

protected

◆ determinant()

double vnl_sparse_lu::determinant ( )

Compute determinant.

Definition at line 187 of file vnl_sparse_lu.cxx.

◆ est_condition()

bool vnl_sparse_lu::est_condition ( )

protected

estimate the condition number.

Definition at line 55 of file vnl_sparse_lu.cxx.

◆ max_error_bound()

double vnl_sparse_lu::max_error_bound ( )

An estimate of maximum error in solution.

Estimated upper bound of error in solution.

Not calculated unless operation mode at construction includes estimate_condition.

Definition at line 234 of file vnl_sparse_lu.cxx.

◆ operator=()

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

private

Assignment operator - privatised to avoid it being used.

◆ rcond()

double vnl_sparse_lu::rcond ( )

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

the reciprocal of the condition number.

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

Definition at line 220 of file vnl_sparse_lu.cxx.

◆ set_absolute_thresh()

void vnl_sparse_lu::set_absolute_thresh ( double absolute_thresh )

inline

set the threshold on absolute element magnitude for pivoting.

Should be either zero or significantly smaller than the absolute value of the smallest diagonal element.

Definition at line 52 of file vnl_sparse_lu.h.

◆ set_diagonal_pivoting()

void vnl_sparse_lu::set_diagonal_pivoting ( int diag_pivoting )

inline

set diagonal pivoting mode, normally 1 which gives priority to diagonal elements.

Definition at line 54 of file vnl_sparse_lu.h.

◆ set_pivot_thresh()

void vnl_sparse_lu::set_pivot_thresh ( double pivot_thresh )

inline

set the relative pivot threshold should be between 0 and 1.

If set to one then pivoting is complete and slow If near zero then roundoff error may be prohibitive but computation is fast Typical values are between 0.01 and 0.1.

Definition at line 47 of file vnl_sparse_lu.h.

◆ solve() [1/2]

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

Solve problem M x = b.

Solve least squares problem M x = b.

Definition at line 120 of file vnl_sparse_lu.cxx.

◆ solve() [2/2]

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

Solve problem M x = b.

Solve least squares problem M x = b.

Definition at line 69 of file vnl_sparse_lu.cxx.

◆ solve_transpose() [1/2]

vnl_vector< double > vnl_sparse_lu::solve_transpose ( vnl_vector< double > const & b )

Solve problem M^t x = b.

Definition at line 179 of file vnl_sparse_lu.cxx.

◆ solve_transpose() [2/2]

void vnl_sparse_lu::solve_transpose	(	vnl_vector< double > const &	b,
		vnl_vector< double > *	x
	)

Solve problem M^t x = b.

Definition at line 128 of file vnl_sparse_lu.cxx.

Member Data Documentation

◆ A_

vnl_sparse_matrix<double> vnl_sparse_lu::A_

protected

Definition at line 86 of file vnl_sparse_lu.h.

◆ absolute_thresh_

double vnl_sparse_lu::absolute_thresh_

protected

Definition at line 94 of file vnl_sparse_lu.h.

◆ condition_computed_

bool vnl_sparse_lu::condition_computed_

protected

Definition at line 88 of file vnl_sparse_lu.h.

◆ diag_pivoting_

int vnl_sparse_lu::diag_pivoting_

protected

Definition at line 95 of file vnl_sparse_lu.h.

◆ factored_

bool vnl_sparse_lu::factored_

protected

Definition at line 87 of file vnl_sparse_lu.h.

◆ largest_

double vnl_sparse_lu::largest_

protected

Definition at line 92 of file vnl_sparse_lu.h.

◆ mode_

operation vnl_sparse_lu::mode_

protected

Definition at line 89 of file vnl_sparse_lu.h.

◆ norm_

double vnl_sparse_lu::norm_

protected

Definition at line 90 of file vnl_sparse_lu.h.

◆ pivot_thresh_

double vnl_sparse_lu::pivot_thresh_

protected

Definition at line 93 of file vnl_sparse_lu.h.

◆ pmatrix_

void* vnl_sparse_lu::pmatrix_

private

The internal matrix representation.

We don't use the typedef spMatrix directly here to avoid exposing the implementation detail (sparse/spMatrix.h) to the user.

Definition at line 105 of file vnl_sparse_lu.h.

◆ rcond_

double vnl_sparse_lu::rcond_

protected

Definition at line 91 of file vnl_sparse_lu.h.

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

core/vnl/algo/vnl_sparse_lu.h
core/vnl/algo/vnl_sparse_lu.cxx

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

Member Enumeration Documentation

◆ operation

Constructor & Destructor Documentation

◆ vnl_sparse_lu() [1/2]

◆ ~vnl_sparse_lu()

◆ vnl_sparse_lu() [2/2]

Member Function Documentation

◆ decompose_matrix()

◆ determinant()

◆ est_condition()

◆ max_error_bound()

◆ operator=()

◆ rcond()

◆ set_absolute_thresh()

◆ set_diagonal_pivoting()

◆ set_pivot_thresh()

◆ solve() [1/2]

◆ solve() [2/2]

◆ solve_transpose() [1/2]

◆ solve_transpose() [2/2]

Member Data Documentation

◆ A_

◆ absolute_thresh_

◆ condition_computed_

◆ diag_pivoting_

◆ factored_

◆ largest_

◆ mode_

◆ norm_

◆ pivot_thresh_

◆ pmatrix_

◆ rcond_