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| | Cholesky () |
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| template<class P2 , class B2 > |
| | Cholesky (const Matrix< Size, Size, P2, B2 > &m) |
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| | Cholesky (int size) |
| | Constructor for Size=Dynamic. More...
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| template<class P2 , class B2 > |
| void | compute (const Matrix< Size, Size, P2, B2 > &m) |
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| template<int Size2, class P2 , class B2 > |
| Vector< Size, Precision > | backsub (const Vector< Size2, P2, B2 > &v) const |
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| template<int Size2, int C2, class P2 , class B2 > |
| Matrix< Size, C2, Precision > | backsub (const Matrix< Size2, C2, P2, B2 > &m) const |
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| Matrix< Size, Size, Precision > | get_inverse () |
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| Precision | determinant () |
| | Compute the determinant. More...
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| template<int Size2, typename P2 , typename B2 > |
| Precision | mahalanobis (const Vector< Size2, P2, B2 > &v) const |
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| Matrix< Size, Size, Precision > | get_unscaled_L () const |
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| Matrix< Size, Size, Precision > | get_D () const |
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| Matrix< Size, Size, Precision > | get_L () const |
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template<int Size = Dynamic, class Precision = DefaultPrecision>
class TooN::Cholesky< Size, Precision >
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:
Matrix<3> A = ...;
Matrix<2,3> M;
Matrix<2> B;
Vector<3> y = make_Vector(2,3,4);
Cholesky<3> chol(A);
x = cholA.backsub(y);
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
- Parameters
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| 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.
template<int Size = Dynamic, class Precision = DefaultPrecision>
template<class P2 , class B2 >
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.
1.8.9.1
