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Eigen
5.0.1-dev
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Eigen
5.0.1-dev
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#include <Eigen/src/IterativeLinearSolvers/IncompleteCholesky.h>
Modified Incomplete Cholesky with dual threshold.
References : C-J. Lin and J. J. Moré, Incomplete Cholesky Factorizations with Limited memory, SIAM J. Sci. Comput. 21(1), pp. 24-45, 1999
| Scalar | the scalar type of the input matrices |
| UpLo_ | The triangular part that will be used for the computations. It can be Lower or Upper. Default is Lower. |
| OrderingType_ | The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<int>. |
This class follows the sparse solver concept .
It performs the following incomplete factorization: \( S P A P' S + \sigma I \approx L L' \) where L is a lower triangular factor, S is a diagonal scaling matrix, P is a fill-in reducing permutation as computed by the ordering method, and \( \sigma \) is a shift for ensuring the decomposed matrix is positive definite.
Shifting strategy: Let \( B = S P A P' S \) be the scaled matrix on which the factorization is carried out, and \( \beta \) be the minimum value of the diagonal. If \( \beta > 0 \) then, the factorization is directly performed on the matrix B, and \( \sigma = 0 \). Otherwise, the factorization is performed on the shifted matrix \( B + \sigma I \) for a shifting factor \( \sigma \). We start with \( \sigma = \sigma_0 - \beta \), where \( \sigma_0 \) is the initial shift value as returned and set by setInitialShift() method. The default value is \(\sigma_0 = 10^{-3} \). If the factorization fails, then the shift in doubled until it succeed or a maximum of ten attempts. If it still fails, as returned by the info() method, then you can either increase the initial shift, or better use another preconditioning technique.
Public Member Functions | |
| template<typename MatrixType> | |
| void | analyzePattern (const MatrixType &mat) |
| Computes the fill reducing permutation vector using the sparsity pattern of mat. | |
| constexpr Index | cols () const noexcept |
| template<typename MatrixType> | |
| void | compute (const MatrixType &mat) |
| template<typename MatrixType> | |
| void | factorize (const MatrixType &mat) |
| Performs the numerical factorization of the input matrix mat. | |
| IncompleteCholesky () | |
| template<typename MatrixType> | |
| IncompleteCholesky (const MatrixType &matrix) | |
| ComputationInfo | info () const |
| Reports whether previous computation was successful. | |
| const FactorType & | matrixL () const |
| const PermutationType & | permutationP () const |
| constexpr Index | rows () const noexcept |
| const VectorRx & | scalingS () const |
| void | setInitialShift (RealScalar shift) |
| Set the initial shift parameter \( \sigma \). | |
| RealScalar | shift () const |
| Public Member Functions inherited from Eigen::SparseSolverBase< Derived > | |
| template<typename Rhs> | |
| const Solve< Derived, Rhs > | solve (const MatrixBase< Rhs > &b) const |
| template<typename Rhs> | |
| const Solve< Derived, Rhs > | solve (const SparseMatrixBase< Rhs > &b) const |
| SparseSolverBase () | |
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Default constructor leaving the object in a partly non-initialized stage.
You must call compute() or the pair analyzePattern()/factorize() to make it valid.
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Constructor computing the incomplete factorization for the given matrix matrix.
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Computes or re-computes the incomplete Cholesky factorization of the input matrix mat
It is a shortcut for a sequential call to the analyzePattern() and factorize() methods.
| void Eigen::IncompleteCholesky< Scalar, UpLo_, OrderingType_ >::factorize | ( | const MatrixType & | mat | ) |
Performs the numerical factorization of the input matrix mat.
The method analyzePattern() or compute() must have been called beforehand with a matrix having the same pattern.
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Reports whether previous computation was successful.
It triggers an assertion if *this has not been initialized through the respective constructor, or a call to compute() or analyzePattern().
Success if computation was successful, NumericalIssue if the matrix appears to be negative.
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1.15.0