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.
	~vnl_sparse_lu ()
void	set_pivot_thresh (double pivot_thresh)
	set the relative pivot threshold should be between 0 and 1.
void	set_absolute_thresh (double absolute_thresh)
	set the threshold on absolute element magnitude for pivoting.
void	set_diagonal_pivoting (int diag_pivoting)
	set diagonal pivoting mode, normally 1 which gives priority to diagonal elements.
vnl_vector< double >	solve (vnl_vector< double > const &b)
	Solve problem M x = b.
void	solve (vnl_vector< double > const &b, vnl_vector< double > *x)
	Solve problem M x = b.
vnl_vector< double >	solve_transpose (vnl_vector< double > const &b)
	Solve problem M^t x = b.
void	solve_transpose (vnl_vector< double > const &b, vnl_vector< double > *x)
	Solve problem M^t x = b.
double	determinant ()
	Compute determinant.
double	rcond ()
	Return reciprocal condition number (smallest/largest singular values).
double	max_error_bound ()
	An estimate of maximum error in solution.
Protected Member Functions
void	decompose_matrix ()
bool	est_condition ()
	estimate the condition number.
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.
vnl_sparse_lu &	operator= (vnl_sparse_lu const &that)
	Assignment operator - privatised to avoid it being used.
Private Attributes
void *	pmatrix_
	The internal matrix representation.

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 30 of file vnl_sparse_lu.h.

Member Enumeration Documentation

enum vnl_sparse_lu::operation

Modes of computation. See constructor for details.

Enumerator:

quiet
verbose
estimate_condition
estimate_condition_verbose

Definition at line 34 of file vnl_sparse_lu.h.

Constructor & Destructor Documentation

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 21 of file vnl_sparse_lu.cxx.

vnl_sparse_lu::~vnl_sparse_lu ( )

Definition at line 15 of file vnl_sparse_lu.cxx.

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

Copy constructor - privatised to avoid it being used.

Member Function Documentation

void vnl_sparse_lu::decompose_matrix ( ) [protected]

double vnl_sparse_lu::determinant ( )

Compute determinant.

Definition at line 245 of file vnl_sparse_lu.cxx.

bool vnl_sparse_lu::est_condition ( ) [protected]

estimate the condition number.

Definition at line 58 of file vnl_sparse_lu.cxx.

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 292 of file vnl_sparse_lu.cxx.

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

Assignment operator - privatised to avoid it being used.

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 278 of file vnl_sparse_lu.cxx.

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 54 of file vnl_sparse_lu.h.

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 56 of file vnl_sparse_lu.h.

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 49 of file vnl_sparse_lu.h.

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 123 of file vnl_sparse_lu.cxx.