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. | |
| ~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. | |
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.
Modes of computation. See constructor for details.
Definition at line 37 of file vnl_cholesky.h.
| 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 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.
| double vnl_cholesky::determinant | ( | ) | const |
Compute determinant.
Definition at line 76 of file vnl_cholesky.cxx.
| vnl_matrix< double > vnl_cholesky::inverse | ( | ) | const |
Definition at line 87 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 108 of file vnl_cholesky.cxx.
| 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_vector<double> const& vnl_cholesky::nullvector | ( | ) | const [inline] |
Definition at line 83 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.
| 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 65 of file vnl_cholesky.cxx.
| 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 vcl_vector x may be b, which will give a fractional increase in speed.
Definition at line 55 of file vnl_cholesky.cxx.
| vnl_matrix< double > vnl_cholesky::upper_triangle | ( | ) | const |
Return upper-triangular factor.
Definition at line 125 of file vnl_cholesky.cxx.
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.
1.7.5.1