#include <Cholesky.h>
Public Member Functions | |
| template<int Size2, int C2, class P2 , class B2 > | |
| Matrix< Size, C2, Precision > | backsub (const Matrix< Size2, C2, P2, B2 > &m) const |
| template<int Size2, class P2 , class B2 > | |
| Vector< Size, Precision > | backsub (const Vector< Size2, P2, B2 > &v) const |
| Run time is O(N^2). | |
| Cholesky (int size) | |
| Constructor for Size=Dynamic. | |
| template<class P2 , class B2 > | |
| Cholesky (const Matrix< Size, Size, P2, B2 > &m) | |
| Cholesky () | |
| template<class P2 , class B2 > | |
| void | compute (const Matrix< Size, Size, P2, B2 > &m) |
| Precision | determinant () |
| Compute the determinant. | |
| Matrix< Size, Size, Precision > | get_D () const |
| Matrix< Size, Size, Precision > | get_inverse () |
| Matrix< Size, Size, Precision > | get_L () const |
| Matrix< Size, Size, Precision > | get_unscaled_L () const |
| template<int Size2, typename P2 , typename B2 > | |
| Precision | mahalanobis (const Vector< Size2, P2, B2 > &v) const |
Private Member Functions | |
| void | do_compute () |
Private Attributes | |
| Matrix< Size, Size, Precision > | my_cholesky |
Decomposes a positive-semidefinite symmetric matrix A (such as a covariance) into L*D*L^T, where L is lower-triangular and D is diagonal. Also can compute the classic A = L*L^T, with L lower triangular. The LDL^T form is faster to compute than the classical Cholesky decomposition. Use get_unscaled_L() and get_D() to access the individual matrices of L*D*L^T decomposition. Use get_L() to access the lower triangular matrix of the classic Cholesky decomposition L*L^T. The decomposition can be used to compute A^-1*x, A^-1*M, M*A^-1*M^T, and A^-1 itself, though the latter rarely needs to be explicitly represented. Also efficiently computes det(A) and rank(A). It can be used as follows:
// Declare some matrices. Matrix<3> A = ...; // we'll pretend it is pos-def Matrix<2,3> M; Matrix<2> B; Vector<3> y = make_Vector(2,3,4); // create the Cholesky decomposition of A Cholesky<3> chol(A); // compute x = A^-1 * y x = cholA.backsub(y); //compute A^-1 Matrix<3> Ainv = cholA.get_inverse();
Cholesky decomposition of a symmetric matrix. Only the lower half of the matrix is considered This uses the non-sqrt version of the decomposition giving symmetric M = L*D*L.T() where the diagonal of L contains ones
| Size | the size of the matrix | |
| Precision | the precision of the entries in the matrix and its decomposition |
Definition at line 69 of file Cholesky.h.
| TooN::Cholesky< Size, Precision >::Cholesky | ( | ) | [inline] |
Definition at line 71 of file Cholesky.h.
| TooN::Cholesky< Size, Precision >::Cholesky | ( | const Matrix< Size, Size, P2, B2 > & | m | ) | [inline] |
Construct the Cholesky decomposition of a matrix. This initialises the class, and performs the decomposition immediately. Run time is O(N^3)
Definition at line 77 of file Cholesky.h.
| TooN::Cholesky< Size, Precision >::Cholesky | ( | int | size | ) | [inline] |
Constructor for Size=Dynamic.
Definition at line 84 of file Cholesky.h.
| Matrix<Size, C2, Precision> TooN::Cholesky< Size, Precision >::backsub | ( | const Matrix< Size2, C2, P2, B2 > & | m | ) | const [inline] |
overload
Definition at line 161 of file Cholesky.h.
| Vector<Size, Precision> TooN::Cholesky< Size, Precision >::backsub | ( | const Vector< Size2, P2, B2 > & | v | ) | const [inline] |
| void TooN::Cholesky< Size, Precision >::compute | ( | const Matrix< Size, Size, P2, B2 > & | m | ) | [inline] |
Compute the LDL^T decomposition of another matrix. Run time is O(N^3)
Definition at line 89 of file Cholesky.h.
| Precision TooN::Cholesky< Size, Precision >::determinant | ( | ) | [inline] |
Compute the determinant.
Definition at line 202 of file Cholesky.h.
| void TooN::Cholesky< Size, Precision >::do_compute | ( | ) | [inline, private] |
Definition at line 97 of file Cholesky.h.
| Matrix<Size,Size,Precision> TooN::Cholesky< Size, Precision >::get_D | ( | ) | const [inline] |
Definition at line 227 of file Cholesky.h.
| Matrix<Size,Size,Precision> TooN::Cholesky< Size, Precision >::get_inverse | ( | ) | [inline] |
Compute A^-1 and store in M Run time is O(N^3)
Definition at line 196 of file Cholesky.h.
| Matrix<Size,Size,Precision> TooN::Cholesky< Size, Precision >::get_L | ( | ) | const [inline] |
Definition at line 237 of file Cholesky.h.
| Matrix<Size,Size,Precision> TooN::Cholesky< Size, Precision >::get_unscaled_L | ( | ) | const [inline] |
Definition at line 215 of file Cholesky.h.
| Precision TooN::Cholesky< Size, Precision >::mahalanobis | ( | const Vector< Size2, P2, B2 > & | v | ) | const [inline] |
Definition at line 211 of file Cholesky.h.
Matrix<Size,Size,Precision> TooN::Cholesky< Size, Precision >::my_cholesky [private] |
Definition at line 252 of file Cholesky.h.
