Detailed Description
template<typename _MatrixType, int _UpLo>
class Eigen::LLT< _MatrixType, _UpLo >
Standard Cholesky decomposition (LL^T) of a matrix and associated features.
- Parameters:
-
MatrixType | the type of the matrix of which we are computing the LL^T Cholesky decomposition |
This class performs a LL^T Cholesky decomposition of a symmetric, positive definite matrix A such that A = LL^* = U^*U, where L is lower triangular.
While the Cholesky decomposition is particularly useful to solve selfadjoint problems like D^*D x = b, for that purpose, we recommend the Cholesky decomposition without square root which is more stable and even faster. Nevertheless, this standard Cholesky decomposition remains useful in many other situations like generalised eigen problems with hermitian matrices.
Remember that Cholesky decompositions are not rank-revealing. This LLT decomposition is only stable on positive definite matrices, use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine whether a system of equations has a solution.
- See also:
- MatrixBase::llt(), class LDLT
Definition at line 59 of file Cholesky.
List of all members.
Member Typedef Documentation
template<typename _MatrixType, int _UpLo>
template<typename _MatrixType, int _UpLo>
template<typename _MatrixType, int _UpLo>
template<typename _MatrixType, int _UpLo>
template<typename _MatrixType, int _UpLo>
Member Enumeration Documentation
template<typename _MatrixType, int _UpLo>
- Enumerator:
RowsAtCompileTime |
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ColsAtCompileTime |
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Options |
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MaxColsAtCompileTime |
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Definition at line 63 of file Cholesky.
template<typename _MatrixType, int _UpLo>
- Enumerator:
PacketSize |
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AlignmentMask |
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UpLo |
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Definition at line 73 of file Cholesky.
Constructor & Destructor Documentation
template<typename _MatrixType, int _UpLo>
template<typename _MatrixType, int _UpLo>
Default Constructor with memory preallocation.
Like the default constructor but with preallocation of the internal data according to the specified problem size.
- See also:
- LLT()
Definition at line 95 of file Cholesky.
template<typename _MatrixType, int _UpLo>
Member Function Documentation
template<typename _MatrixType, int _UpLo>
template<typename MatrixType , int _UpLo>
Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of matrix.
- Returns:
- a reference to *this
Definition at line 291 of file Cholesky.
template<typename _MatrixType, int _UpLo>
Reports whether previous computation was successful.
- Returns:
Success
if computation was succesful, NumericalIssue
if the matrix.appears to be negative.
Definition at line 162 of file Cholesky.
Referenced by chol().
template<typename _MatrixType, int _UpLo>
Traits::MatrixL Eigen::LLT< _MatrixType, _UpLo >::matrixL |
( |
) |
const [inline] |
- Returns:
- a view of the lower triangular matrix L
Definition at line 113 of file Cholesky.
template<typename _MatrixType, int _UpLo>
- Returns:
- the LLT decomposition matrix
TODO: document the storage layout
Definition at line 148 of file Cholesky.
template<typename _MatrixType, int _UpLo>
Traits::MatrixU Eigen::LLT< _MatrixType, _UpLo >::matrixU |
( |
) |
const [inline] |
- Returns:
- a view of the upper triangular matrix U
Definition at line 106 of file Cholesky.
Referenced by chol().
template<typename MatrixType , int _UpLo>
- Returns:
- the matrix represented by the decomposition, i.e., it returns the product: L L^*. This function is provided for debug purpose.
Definition at line 348 of file Cholesky.
template<typename _MatrixType, int _UpLo>
template<typename _MatrixType, int _UpLo>
template<typename Rhs >
const internal::solve_retval<LLT, Rhs> Eigen::LLT< _MatrixType, _UpLo >::solve |
( |
const MatrixBase< Rhs > & |
b ) |
const [inline] |
- Returns:
- the solution x of
using the current decomposition of A.
Since this LLT class assumes anyway that the matrix A is invertible, the solution theoretically exists and is unique regardless of b.
Example:
Output:
- See also:
- solveInPlace(), MatrixBase::llt()
Definition at line 131 of file Cholesky.
template<typename MatrixType , int _UpLo>
template<typename Derived >
Member Data Documentation
template<typename _MatrixType, int _UpLo>
template<typename _MatrixType, int _UpLo>
template<typename _MatrixType, int _UpLo>