Mother class of SVD classes algorithms. More...
#include <SVDBase.h>
Public Types | |
| enum | { RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime), MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime, MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime,MaxColsAtCompileTime), MatrixOptions = MatrixType::Options } |
| typedef internal::plain_col_type < MatrixType >::type | ColType |
| typedef MatrixType::Index | Index |
| typedef _MatrixType | MatrixType |
| typedef Matrix< Scalar, RowsAtCompileTime, RowsAtCompileTime, MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime > | MatrixUType |
| typedef Matrix< Scalar, ColsAtCompileTime, ColsAtCompileTime, MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime > | MatrixVType |
| typedef NumTraits< typename MatrixType::Scalar >::Real | RealScalar |
| typedef internal::plain_row_type < MatrixType >::type | RowType |
| typedef MatrixType::Scalar | Scalar |
| typedef internal::plain_diag_type < MatrixType, RealScalar > ::type | SingularValuesType |
| typedef Matrix< Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime, MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime > | WorkMatrixType |
Public Member Functions | |
| Index | cols () const |
| SVDBase & | compute (const MatrixType &matrix, unsigned int computationOptions) |
| Method performing the decomposition of given matrix using custom options. | |
| SVDBase & | compute (const MatrixType &matrix) |
| Method performing the decomposition of given matrix using current options. | |
| bool | computeU () const |
| bool | computeV () const |
| const MatrixUType & | matrixU () const |
| const MatrixVType & | matrixV () const |
| Index | nonzeroSingularValues () const |
| Index | rows () const |
| const SingularValuesType & | singularValues () const |
Protected Member Functions | |
| bool | allocate (Index rows, Index cols, unsigned int computationOptions) |
| SVDBase () | |
| Default Constructor. | |
Protected Attributes | |
| Index | m_cols |
| unsigned int | m_computationOptions |
| bool | m_computeFullU |
| bool | m_computeFullV |
| bool | m_computeThinU |
| bool | m_computeThinV |
| Index | m_diagSize |
| bool | m_isAllocated |
| bool | m_isInitialized |
| MatrixUType | m_matrixU |
| MatrixVType | m_matrixV |
| Index | m_nonzeroSingularValues |
| Index | m_rows |
| SingularValuesType | m_singularValues |
Detailed Description
template<typename _MatrixType>
class Eigen::SVDBase< _MatrixType >
Mother class of SVD classes algorithms.
- Parameters:
-
MatrixType the type of the matrix of which we are computing the SVD decomposition SVD decomposition consists in decomposing any n-by-p matrix A as a product
where U is a n-by-n unitary, V is a p-by-p unitary, and S is a n-by-p real positive matrix which is zero outside of its main diagonal; the diagonal entries of S are known as the singular values of A and the columns of U and V are known as the left and right singular vectors of A respectively.![\[ A = U S V^* \]](form_186.png)
Singular values are always sorted in decreasing order.
You can ask for only thin U or V to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting m be the smaller value among n and p, there are only m singular vectors; the remaining columns of U and V do not correspond to actual singular vectors. Asking for thin U or V means asking for only their m first columns to be formed. So U is then a n-by-m matrix, and V is then a p-by-m matrix. Notice that thin U and V are all you need for (least squares) solving.
If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to terminate in finite (and reasonable) time.
- See also:
- MatrixBase::genericSvd()
Member Typedef Documentation
| typedef internal::plain_col_type<MatrixType>::type Eigen::SVDBase< _MatrixType >::ColType |
| typedef MatrixType::Index Eigen::SVDBase< _MatrixType >::Index |
| typedef _MatrixType Eigen::SVDBase< _MatrixType >::MatrixType |
| typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime> Eigen::SVDBase< _MatrixType >::MatrixUType |
| typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime, MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime> Eigen::SVDBase< _MatrixType >::MatrixVType |
| typedef NumTraits<typename MatrixType::Scalar>::Real Eigen::SVDBase< _MatrixType >::RealScalar |
| typedef internal::plain_row_type<MatrixType>::type Eigen::SVDBase< _MatrixType >::RowType |
| typedef MatrixType::Scalar Eigen::SVDBase< _MatrixType >::Scalar |
| typedef internal::plain_diag_type<MatrixType, RealScalar>::type Eigen::SVDBase< _MatrixType >::SingularValuesType |
| typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime, MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime> Eigen::SVDBase< _MatrixType >::WorkMatrixType |
Member Enumeration Documentation
| anonymous enum |
Constructor & Destructor Documentation
| Eigen::SVDBase< _MatrixType >::SVDBase | ( | ) | [inline, protected] |
Member Function Documentation
| bool Eigen::SVDBase< MatrixType >::allocate | ( | Index | rows, |
| Index | cols, | ||
| unsigned int | computationOptions | ||
| ) | [protected] |
| Index Eigen::SVDBase< _MatrixType >::cols | ( | void | ) | const [inline] |
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
| SVDBase& Eigen::SVDBase< _MatrixType >::compute | ( | const MatrixType & | matrix, |
| unsigned int | computationOptions | ||
| ) |
Method performing the decomposition of given matrix using custom options.
- Parameters:
-
matrix the matrix to decompose computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed. By default, none is computed. This is a bit-field, the possible bits are ComputeFullU, ComputeThinU, ComputeFullV, ComputeThinV.
Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not available with the (non-default) FullPivHouseholderQR preconditioner.
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >, Eigen::JacobiSVD< _MatrixType, QRPreconditioner >, Eigen::BDCSVD< _MatrixType >, and Eigen::BDCSVD< _MatrixType >.
| SVDBase& Eigen::SVDBase< _MatrixType >::compute | ( | const MatrixType & | matrix | ) |
Method performing the decomposition of given matrix using current options.
- Parameters:
-
matrix the matrix to decompose
This method uses the current computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int).
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >, Eigen::JacobiSVD< _MatrixType, QRPreconditioner >, and Eigen::BDCSVD< _MatrixType >.
| bool Eigen::SVDBase< _MatrixType >::computeU | ( | ) | const [inline] |
- Returns:
- true if U (full or thin) is asked for in this SVD decomposition
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
| bool Eigen::SVDBase< _MatrixType >::computeV | ( | ) | const [inline] |
- Returns:
- true if V (full or thin) is asked for in this SVD decomposition
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
| const MatrixUType& Eigen::SVDBase< _MatrixType >::matrixU | ( | ) | const [inline] |
- Returns:
- the U matrix.
For the SVDBase decomposition of a n-by-p matrix, letting m be the minimum of n and p, the U matrix is n-by-n if you asked for ComputeFullU, and is n-by-m if you asked for ComputeThinU.
The m first columns of U are the left singular vectors of the matrix being decomposed.
This method asserts that you asked for U to be computed.
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >, and Eigen::BDCSVD< _MatrixType >.
| const MatrixVType& Eigen::SVDBase< _MatrixType >::matrixV | ( | ) | const [inline] |
- Returns:
- the V matrix.
For the SVD decomposition of a n-by-p matrix, letting m be the minimum of n and p, the V matrix is p-by-p if you asked for ComputeFullV, and is p-by-m if you asked for ComputeThinV.
The m first columns of V are the right singular vectors of the matrix being decomposed.
This method asserts that you asked for V to be computed.
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >, and Eigen::BDCSVD< _MatrixType >.
| Index Eigen::SVDBase< _MatrixType >::nonzeroSingularValues | ( | ) | const [inline] |
- Returns:
- the number of singular values that are not exactly 0
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
| Index Eigen::SVDBase< _MatrixType >::rows | ( | void | ) | const [inline] |
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
| const SingularValuesType& Eigen::SVDBase< _MatrixType >::singularValues | ( | ) | const [inline] |
- Returns:
- the vector of singular values.
For the SVD decomposition of a n-by-p matrix, letting m be the minimum of n and p, the returned vector has size m. Singular values are always sorted in decreasing order.
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
Member Data Documentation
Index Eigen::SVDBase< _MatrixType >::m_cols [protected] |
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
unsigned int Eigen::SVDBase< _MatrixType >::m_computationOptions [protected] |
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
bool Eigen::SVDBase< _MatrixType >::m_computeFullU [protected] |
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
bool Eigen::SVDBase< _MatrixType >::m_computeFullV [protected] |
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
bool Eigen::SVDBase< _MatrixType >::m_computeThinU [protected] |
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
bool Eigen::SVDBase< _MatrixType >::m_computeThinV [protected] |
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
Index Eigen::SVDBase< _MatrixType >::m_diagSize [protected] |
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
bool Eigen::SVDBase< _MatrixType >::m_isAllocated [protected] |
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
bool Eigen::SVDBase< _MatrixType >::m_isInitialized [protected] |
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
MatrixUType Eigen::SVDBase< _MatrixType >::m_matrixU [protected] |
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
MatrixVType Eigen::SVDBase< _MatrixType >::m_matrixV [protected] |
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
Index Eigen::SVDBase< _MatrixType >::m_nonzeroSingularValues [protected] |
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
Index Eigen::SVDBase< _MatrixType >::m_rows [protected] |
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
SingularValuesType Eigen::SVDBase< _MatrixType >::m_singularValues [protected] |
Reimplemented in Eigen::JacobiSVD< _MatrixType, QRPreconditioner >.
The documentation for this class was generated from the following file: