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| enum | { RowsAtCompileTime = MatrixType::RowsAtCompileTime,
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
} |
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typedef _MatrixType | MatrixType |
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typedef MatrixType::Scalar | Scalar |
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typedef MatrixType::RealScalar | RealScalar |
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typedef MatrixType::StorageIndex | StorageIndex |
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typedef internal::plain_diag_type< MatrixType >::type | HCoeffsType |
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typedef PermutationMatrix< ColsAtCompileTime, MaxColsAtCompileTime > | PermutationType |
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typedef internal::plain_row_type< MatrixType, Index >::type | IntRowVectorType |
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typedef internal::plain_row_type< MatrixType >::type | RowVectorType |
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typedef internal::plain_row_type< MatrixType, RealScalar >::type | RealRowVectorType |
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typedef HouseholderSequence< MatrixType, typename internal::remove_all< typename HCoeffsType::ConjugateReturnType >::type > | HouseholderSequenceType |
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typedef MatrixType::PlainObject | PlainObject |
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| | CompleteOrthogonalDecomposition () |
| | Default Constructor. More...
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| | CompleteOrthogonalDecomposition (Index rows, Index cols) |
| | Default Constructor with memory preallocation. More...
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| template<typename InputType > |
| | CompleteOrthogonalDecomposition (const EigenBase< InputType > &matrix) |
| | Constructs a complete orthogonal decomposition from a given matrix. More...
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| template<typename InputType > |
| | CompleteOrthogonalDecomposition (EigenBase< InputType > &matrix) |
| | Constructs a complete orthogonal decomposition from a given matrix. More...
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| template<typename Rhs > |
| const Solve< CompleteOrthogonalDecomposition, Rhs > | solve (const MatrixBase< Rhs > &b) const |
| | This method computes the minimum-norm solution X to a least squares problem
\[\mathrm{minimize} \|A X - B\|, \]
where A is the matrix of which *this is the complete orthogonal decomposition. More...
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| HouseholderSequenceType | householderQ (void) const |
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HouseholderSequenceType | matrixQ (void) const |
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| MatrixType | matrixZ () const |
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| const MatrixType & | matrixQTZ () const |
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| const MatrixType & | matrixT () const |
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template<typename InputType > |
| CompleteOrthogonalDecomposition & | compute (const EigenBase< InputType > &matrix) |
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| const PermutationType & | colsPermutation () const |
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| MatrixType::RealScalar | absDeterminant () const |
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| MatrixType::RealScalar | logAbsDeterminant () const |
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| Index | rank () const |
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| Index | dimensionOfKernel () const |
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| bool | isInjective () const |
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| bool | isSurjective () const |
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| bool | isInvertible () const |
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| const Inverse< CompleteOrthogonalDecomposition > | pseudoInverse () const |
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Index | rows () const |
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Index | cols () const |
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| const HCoeffsType & | hCoeffs () const |
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| const HCoeffsType & | zCoeffs () const |
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| CompleteOrthogonalDecomposition & | setThreshold (const RealScalar &threshold) |
| | Allows to prescribe a threshold to be used by certain methods, such as rank(), who need to determine when pivots are to be considered nonzero. More...
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| CompleteOrthogonalDecomposition & | setThreshold (Default_t) |
| | Allows to come back to the default behavior, letting Eigen use its default formula for determining the threshold. More...
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| RealScalar | threshold () const |
| | Returns the threshold that will be used by certain methods such as rank(). More...
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| Index | nonzeroPivots () const |
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| RealScalar | maxPivot () const |
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| ComputationInfo | info () const |
| | Reports whether the complete orthogonal decomposition was succesful. More...
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template<typename RhsType , typename DstType > |
| EIGEN_DEVICE_FUNC void | _solve_impl (const RhsType &rhs, DstType &dst) const |
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template<typename RhsType , typename DstType > |
| void | _solve_impl (const RhsType &rhs, DstType &dst) const |
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template<typename _MatrixType>
class Eigen::CompleteOrthogonalDecomposition< _MatrixType >
Complete orthogonal decomposition (COD) of a matrix.
- Parameters
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| MatrixType | the type of the matrix of which we are computing the COD. |
This class performs a rank-revealing complete orthogonal decomposition of a matrix A into matrices P, Q, T, and Z such that
\[ \mathbf{A} \, \mathbf{P} = \mathbf{Q} \, \begin{bmatrix} \mathbf{T} & \mathbf{0} \\ \mathbf{0} & \mathbf{0} \end{bmatrix} \, \mathbf{Z} \]
by using Householder transformations. Here, P is a permutation matrix, Q and Z are unitary matrices and T an upper triangular matrix of size rank-by-rank. A may be rank deficient.
This class supports the inplace decomposition mechanism.
- See also
- MatrixBase::completeOrthogonalDecomposition()
template<typename _MatrixType>
Allows to prescribe a threshold to be used by certain methods, such as rank(), who need to determine when pivots are to be considered nonzero.
Most be called before calling compute().
When it needs to get the threshold value, Eigen calls threshold(). By default, this uses a formula to automatically determine a reasonable threshold. Once you have called the present method setThreshold(const RealScalar&), your value is used instead.
- Parameters
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| threshold | The new value to use as the threshold. |
A pivot will be considered nonzero if its absolute value is strictly greater than \( \vert pivot \vert \leqslant threshold \times \vert maxpivot \vert \) where maxpivot is the biggest pivot.
If you want to come back to the default behavior, call setThreshold(Default_t)
