Calculates inverse of a matrix (wrapper around vnl_svd<double>). More...
#include <vnl_matrix_inverse.h>
Public Types | |
| typedef vnl_numeric_traits< T > ::abs_t | singval_t |
| The singular values of a matrix of complex<T> are of type T, not complex<T>. | |
Public Member Functions | |
| vnl_matrix_inverse (vnl_matrix< T > const &M) | |
| ~vnl_matrix_inverse () | |
| operator vnl_matrix< T > () const | |
| void | zero_out_absolute (double tol=1e-8) |
| find weights below threshold tol, zero them out, and update W_ and Winverse_. | |
| void | zero_out_relative (double tol=1e-8) |
| find weights below tol*max(w) and zero them out. | |
| int | singularities () const |
| unsigned int | rank () const |
| singval_t | well_condition () const |
| singval_t | determinant_magnitude () const |
| Calculate determinant as product of diagonals in W. | |
| singval_t | norm () const |
| vnl_matrix< T > & | U () |
| Return the matrix U. | |
| vnl_matrix< T > const & | U () const |
| Return the matrix U. | |
| T | U (int i, int j) const |
| Return the matrix U's (i,j)th entry (to avoid svd.U()(i,j); ). | |
| vnl_diag_matrix< singval_t > & | W () |
| Get at DiagMatrix (q.v.) of singular values, sorted from largest to smallest. | |
| vnl_diag_matrix< singval_t > const & | W () const |
| Get at DiagMatrix (q.v.) of singular values, sorted from largest to smallest. | |
| singval_t & | W (int i, int j) |
| singval_t & | W (int i) |
| vnl_diag_matrix< singval_t > & | Winverse () |
| vnl_diag_matrix< singval_t > const & | Winverse () const |
| singval_t | sigma_max () const |
| singval_t | sigma_min () const |
| vnl_matrix< T > & | V () |
| Return the matrix V. | |
| vnl_matrix< T > const & | V () const |
| Return the matrix V. | |
| T | V (int i, int j) const |
| Return the matrix V's (i,j)th entry (to avoid svd.V()(i,j); ). | |
| vnl_matrix< T > | inverse () const |
| vnl_matrix< T > | pinverse (unsigned int rank=~0u) const |
| pseudo-inverse (for non-square matrix) of desired rank. | |
| vnl_matrix< T > | tinverse (unsigned int rank=~0u) const |
| Calculate inverse of transpose, using desired rank. | |
| vnl_matrix< T > | recompose (unsigned int rank=~0u) const |
| Recompose SVD to U*W*V', using desired rank. | |
| vnl_matrix< T > | solve (vnl_matrix< T > const &B) const |
| Solve the matrix equation M X = B, returning X. | |
| vnl_vector< T > | solve (vnl_vector< T > const &y) const |
| Solve the matrix-vector system M x = y, returning x. | |
| void | solve (T const *rhs, T *lhs) const |
| void | solve_preinverted (vnl_vector< T > const &rhs, vnl_vector< T > *out) const |
| Solve the matrix-vector system M x = y. | |
| vnl_matrix< T > | nullspace () const |
| Return N such that M * N = 0. | |
| vnl_matrix< T > | nullspace (int required_nullspace_dimension) const |
| Return N such that M * N = 0. | |
| vnl_matrix< T > | left_nullspace () const |
| Return N such that M' * N = 0. | |
| vnl_matrix< T > | left_nullspace (int required_nullspace_dimension) const |
| Implementation to be done yet; currently returns left_nullspace(). - PVR. | |
| vnl_vector< T > | nullvector () const |
| Return the rightmost column of V. | |
| vnl_vector< T > | left_nullvector () const |
| Return the rightmost column of U. | |
| bool | valid () const |
Detailed Description
template<class T>
struct vnl_matrix_inverse< T >
Calculates inverse of a matrix (wrapper around vnl_svd<double>).
vnl_matrix_inverse is a wrapper around vnl_svd<double> that allows you to write
x = vnl_matrix_inverse<double>(A) * b;
This is exactly equivalent to
x = vnl_svd<double>(A).solve(b);
but is arguably clearer, and also allows for the vnl_matrix_inverse class to be changed to use vnl_qr, say.
Definition at line 34 of file vnl_matrix_inverse.h.
Member Typedef Documentation
Constructor & Destructor Documentation
| vnl_matrix_inverse< T >::vnl_matrix_inverse | ( | vnl_matrix< T > const & | M | ) | [inline] |
Definition at line 36 of file vnl_matrix_inverse.h.
| vnl_matrix_inverse< T >::~vnl_matrix_inverse | ( | ) | [inline] |
Definition at line 37 of file vnl_matrix_inverse.h.
Member Function Documentation
| vnl_svd< T >::singval_t vnl_svd< T >::determinant_magnitude | ( | ) | const [inherited] |
Calculate determinant as product of diagonals in W.
Definition at line 210 of file vnl_svd.txx.
| vnl_matrix<T> vnl_svd< T >::inverse | ( | ) | const [inline, inherited] |
| vnl_matrix< T > vnl_svd< T >::left_nullspace | ( | ) | const [inherited] |
Return N such that M' * N = 0.
Return N s.t. M' * N = 0.
Definition at line 381 of file vnl_svd.txx.
| vnl_matrix< T > vnl_svd< T >::left_nullspace | ( | int | required_nullspace_dimension | ) | const [inherited] |
Implementation to be done yet; currently returns left_nullspace(). - PVR.
- Todo:
- Implementation to be done yet; currently returns left_nullspace().
- PVr.
Definition at line 392 of file vnl_svd.txx.
| vnl_vector< T > vnl_svd< T >::left_nullvector | ( | ) | const [inherited] |
Return the rightmost column of U.
Does not check to see whether or not the matrix actually was rank-deficient.
Definition at line 415 of file vnl_svd.txx.
Definition at line 223 of file vnl_svd.txx.
| vnl_matrix< T > vnl_svd< T >::nullspace | ( | ) | const [inherited] |
| vnl_matrix< T > vnl_svd< T >::nullspace | ( | int | required_nullspace_dimension | ) | const [inherited] |
| vnl_vector< T > vnl_svd< T >::nullvector | ( | ) | const [inherited] |
Return the rightmost column of V.
Does not check to see whether or not the matrix actually was rank-deficient - the caller is assumed to have examined W and decided that to his or her satisfaction.
Definition at line 403 of file vnl_svd.txx.
| vnl_matrix_inverse< T >::operator vnl_matrix< T > | ( | ) | const [inline] |
Definition at line 39 of file vnl_matrix_inverse.h.
| vnl_matrix< T > vnl_svd< T >::pinverse | ( | unsigned int | rank = ~0u | ) | const [inherited] |
pseudo-inverse (for non-square matrix) of desired rank.
Calculate pseudo-inverse.
Definition at line 244 of file vnl_svd.txx.
| unsigned int vnl_svd< T >::rank | ( | ) | const [inline, inherited] |
| vnl_matrix< T > vnl_svd< T >::recompose | ( | unsigned int | rank = ~0u | ) | const [inherited] |
Recompose SVD to U*W*V', using desired rank.
Recompose SVD to U*W*V'.
Definition at line 230 of file vnl_svd.txx.
| int vnl_svd< T >::singularities | ( | ) | const [inline, inherited] |
| vnl_matrix< T > vnl_svd< T >::solve | ( | vnl_matrix< T > const & | B | ) | const [inherited] |
Solve the matrix equation M X = B, returning X.
Definition at line 272 of file vnl_svd.txx.
| vnl_vector< T > vnl_svd< T >::solve | ( | vnl_vector< T > const & | y | ) | const [inherited] |
Solve the matrix-vector system M x = y, returning x.
Definition at line 295 of file vnl_svd.txx.
| void vnl_svd< T >::solve | ( | T const * | rhs, |
| T * | lhs | ||
| ) | const [inherited] |
Definition at line 334 of file vnl_svd.txx.
| void vnl_svd< T >::solve_preinverted | ( | vnl_vector< T > const & | y, |
| vnl_vector< T > * | x_out | ||
| ) | const [inherited] |
Solve the matrix-vector system M x = y.
Assuming that the singular values W have been preinverted by the caller.
Assume that the singular values W have been preinverted by the caller.
Definition at line 342 of file vnl_svd.txx.
| vnl_matrix< T > vnl_svd< T >::tinverse | ( | unsigned int | rank = ~0u | ) | const [inherited] |
Calculate inverse of transpose, using desired rank.
Calculate (pseudo-)inverse of transpose.
Definition at line 258 of file vnl_svd.txx.
| vnl_matrix<T>& vnl_svd< T >::U | ( | ) | [inline, inherited] |
| vnl_matrix<T> const& vnl_svd< T >::U | ( | ) | const [inline, inherited] |
| T vnl_svd< T >::U | ( | int | i, |
| int | j | ||
| ) | const [inline, inherited] |
| vnl_matrix<T>& vnl_svd< T >::V | ( | ) | [inline, inherited] |
| vnl_matrix<T> const& vnl_svd< T >::V | ( | ) | const [inline, inherited] |
| T vnl_svd< T >::V | ( | int | i, |
| int | j | ||
| ) | const [inline, inherited] |
| bool vnl_svd< T >::valid | ( | ) | const [inline, inherited] |
| vnl_diag_matrix<singval_t>& vnl_svd< T >::W | ( | ) | [inline, inherited] |
| vnl_diag_matrix<singval_t> const& vnl_svd< T >::W | ( | ) | const [inline, inherited] |
| vnl_diag_matrix<singval_t>& vnl_svd< T >::Winverse | ( | ) | [inline, inherited] |
| vnl_diag_matrix<singval_t> const& vnl_svd< T >::Winverse | ( | ) | const [inline, inherited] |
| void vnl_svd< T >::zero_out_absolute | ( | double | tol = 1e-8 | ) | [inherited] |
find weights below threshold tol, zero them out, and update W_ and Winverse_.
Definition at line 179 of file vnl_svd.txx.
| void vnl_svd< T >::zero_out_relative | ( | double | tol = 1e-8 | ) | [inherited] |
find weights below tol*max(w) and zero them out.
Definition at line 200 of file vnl_svd.txx.
The documentation for this struct was generated from the following file:
- core/vnl/algo/vnl_matrix_inverse.h
