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Base class of SVD algorithms. More...

#include <ForwardDeclarations.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 Eigen::Index Index
 
typedef internal::traits< Derived >::MatrixType MatrixType
 
typedef Matrix< Scalar, RowsAtCompileTime, RowsAtCompileTime, MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTimeMatrixUType
 
typedef Matrix< Scalar, ColsAtCompileTime, ColsAtCompileTime, MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTimeMatrixVType
 
typedef NumTraits< typename MatrixType::Scalar >::Real RealScalar
 
typedef MatrixType::Scalar Scalar
 
typedef internal::plain_diag_type< MatrixType, RealScalar >::type SingularValuesType
 
typedef Eigen::internal::traits< SVDBase >::StorageIndex StorageIndex
 

Public Member Functions

template<typename RhsType , typename DstType >
void _solve_impl (const RhsType &rhs, DstType &dst) const
 
template<bool Conjugate, typename RhsType , typename DstType >
void _solve_impl_transposed (const RhsType &rhs, DstType &dst) const
 
Index cols () const
 
bool computeU () const
 
bool computeV () const
 
Derived & derived ()
 
const Derived & derived () const
 
EIGEN_DEVICE_FUNC ComputationInfo info () const
 Reports whether previous computation was successful. More...
 
const MatrixUTypematrixU () const
 
const MatrixVTypematrixV () const
 
Index nonzeroSingularValues () const
 
Index rank () const
 
Index rows () const
 
Derived & setThreshold (const RealScalar &threshold)
 
Derived & setThreshold (Default_t)
 
const SingularValuesTypesingularValues () const
 
RealScalar threshold () const
 

Protected Member Functions

void _check_compute_assertions () const
 
template<bool Transpose_, typename Rhs >
void _check_solve_assertion (const Rhs &b) const
 
bool allocate (Index rows, Index cols, unsigned int computationOptions)
 
 SVDBase ()
 Default Constructor. More...
 

Static Protected Member Functions

static void check_template_parameters ()
 

Protected Attributes

Index m_cols
 
unsigned int m_computationOptions
 
bool m_computeFullU
 
bool m_computeFullV
 
bool m_computeThinU
 
bool m_computeThinV
 
Index m_diagSize
 
ComputationInfo m_info
 
bool m_isAllocated
 
bool m_isInitialized
 
MatrixUType m_matrixU
 
MatrixVType m_matrixV
 
Index m_nonzeroSingularValues
 
RealScalar m_prescribedThreshold
 
Index m_rows
 
SingularValuesType m_singularValues
 
bool m_usePrescribedThreshold
 

Friends

template<typename Derived_ >
struct internal::solve_assertion
 

Detailed Description

Base class of SVD algorithms.

Template Parameters
Derivedthe type of the actual SVD decomposition

SVD decomposition consists in decomposing any n-by-p matrix A as a product

\[ A = U S V^* \]

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.

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.

The status of the computation can be retrived using the info() method. Unless info() returns Success, the results should be not considered well defined.

If the input matrix has inf or nan coefficients, the result of the computation is undefined, and info() will return InvalidInput, but the computation is guaranteed to terminate in finite (and reasonable) time.

See also
class BDCSVD, class JacobiSVD

Definition at line 277 of file ForwardDeclarations.h.

Member Typedef Documentation

◆ Index

Deprecated:
since Eigen 3.3

Definition at line 74 of file SVDBase.h.

◆ MatrixType

Definition at line 70 of file SVDBase.h.

◆ MatrixUType

Definition at line 85 of file SVDBase.h.

◆ MatrixVType

Definition at line 86 of file SVDBase.h.

◆ RealScalar

Definition at line 72 of file SVDBase.h.

◆ Scalar

typedef MatrixType::Scalar Eigen::SVDBase::Scalar

Definition at line 71 of file SVDBase.h.

◆ SingularValuesType

Definition at line 87 of file SVDBase.h.

◆ StorageIndex

Definition at line 73 of file SVDBase.h.

Member Enumeration Documentation

◆ anonymous enum

anonymous enum
Enumerator
RowsAtCompileTime 
ColsAtCompileTime 
DiagSizeAtCompileTime 
MaxRowsAtCompileTime 
MaxColsAtCompileTime 
MaxDiagSizeAtCompileTime 
MatrixOptions 

Definition at line 75 of file SVDBase.h.

Constructor & Destructor Documentation

◆ SVDBase()

Eigen::SVDBase::SVDBase ( )
inlineprotected

Default Constructor.

Default constructor of SVDBase

Definition at line 287 of file SVDBase.h.

Member Function Documentation

◆ _check_compute_assertions()

void Eigen::SVDBase::_check_compute_assertions ( ) const
inlineprotected

Definition at line 257 of file SVDBase.h.

◆ _check_solve_assertion()

template<bool Transpose_, typename Rhs >
void Eigen::SVDBase::_check_solve_assertion ( const Rhs &  b) const
inlineprotected

Definition at line 262 of file SVDBase.h.

◆ _solve_impl()

template<typename RhsType , typename DstType >
void Eigen::SVDBase::_solve_impl ( const RhsType &  rhs,
DstType &  dst 
) const

Definition at line 308 of file SVDBase.h.

◆ _solve_impl_transposed()

template<bool Conjugate, typename RhsType , typename DstType >
void Eigen::SVDBase::_solve_impl_transposed ( const RhsType &  rhs,
DstType &  dst 
) const

Definition at line 322 of file SVDBase.h.

◆ allocate()

bool Eigen::SVDBase::allocate ( Index  rows,
Index  cols,
unsigned int  computationOptions 
)
protected

Definition at line 337 of file SVDBase.h.

◆ check_template_parameters()

static void Eigen::SVDBase::check_template_parameters ( )
inlinestaticprotected

Definition at line 252 of file SVDBase.h.

◆ cols()

Index Eigen::SVDBase::cols ( ) const
inline

Definition at line 213 of file SVDBase.h.

◆ computeU()

bool Eigen::SVDBase::computeU ( ) const
inline
Returns
true if U (full or thin) is asked for in this SVD decomposition

Definition at line 208 of file SVDBase.h.

◆ computeV()

bool Eigen::SVDBase::computeV ( ) const
inline
Returns
true if V (full or thin) is asked for in this SVD decomposition

Definition at line 210 of file SVDBase.h.

◆ derived() [1/2]

Derived& Eigen::SVDBase::derived ( )
inline

Definition at line 89 of file SVDBase.h.

◆ derived() [2/2]

const Derived& Eigen::SVDBase::derived ( ) const
inline

Definition at line 90 of file SVDBase.h.

◆ info()

EIGEN_DEVICE_FUNC ComputationInfo Eigen::SVDBase::info ( ) const
inline

Reports whether previous computation was successful.

Returns
Success if computation was successful.

Definition at line 236 of file SVDBase.h.

◆ matrixU()

const MatrixUType& Eigen::SVDBase::matrixU ( ) const
inline
Returns
the U matrix.

For the SVD 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.

Definition at line 101 of file SVDBase.h.

◆ matrixV()

const MatrixVType& Eigen::SVDBase::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.

Definition at line 117 of file SVDBase.h.

◆ nonzeroSingularValues()

Index Eigen::SVDBase::nonzeroSingularValues ( ) const
inline
Returns
the number of singular values that are not exactly 0

Definition at line 136 of file SVDBase.h.

◆ rank()

Index Eigen::SVDBase::rank ( ) const
inline
Returns
the rank of the matrix of which *this is the SVD.
Note
This method has to determine which singular values should be considered nonzero. For that, it uses the threshold value that you can control by calling setThreshold(const RealScalar&).

Definition at line 148 of file SVDBase.h.

◆ rows()

Index Eigen::SVDBase::rows ( ) const
inline

Definition at line 212 of file SVDBase.h.

◆ setThreshold() [1/2]

Derived& Eigen::SVDBase::setThreshold ( const RealScalar threshold)
inline

Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(), which need to determine when singular values are to be considered nonzero. This is not used for the SVD decomposition itself.

When it needs to get the threshold value, Eigen calls threshold(). The default is NumTraits<Scalar>::epsilon()

Parameters
thresholdThe new value to use as the threshold.

A singular value will be considered nonzero if its value is strictly greater than $ \vert singular value \vert \leqslant threshold \times \vert max singular value \vert $.

If you want to come back to the default behavior, call setThreshold(Default_t)

Definition at line 173 of file SVDBase.h.

◆ setThreshold() [2/2]

Derived& Eigen::SVDBase::setThreshold ( Default_t  )
inline

Allows to come back to the default behavior, letting Eigen use its default formula for determining the threshold.

You should pass the special object Eigen::Default as parameter here.

svd.setThreshold(Eigen::Default);

See the documentation of setThreshold(const RealScalar&).

Definition at line 188 of file SVDBase.h.

◆ singularValues()

const SingularValuesType& Eigen::SVDBase::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.

Definition at line 129 of file SVDBase.h.

◆ threshold()

RealScalar Eigen::SVDBase::threshold ( ) const
inline

Returns the threshold that will be used by certain methods such as rank().

See the documentation of setThreshold(const RealScalar&).

Definition at line 198 of file SVDBase.h.

Friends And Related Function Documentation

◆ internal::solve_assertion

template<typename Derived_ >
friend struct internal::solve_assertion
friend

Definition at line 68 of file SVDBase.h.

Member Data Documentation

◆ m_cols

Index Eigen::SVDBase::m_cols
protected

Definition at line 280 of file SVDBase.h.

◆ m_computationOptions

unsigned int Eigen::SVDBase::m_computationOptions
protected

Definition at line 279 of file SVDBase.h.

◆ m_computeFullU

bool Eigen::SVDBase::m_computeFullU
protected

Definition at line 277 of file SVDBase.h.

◆ m_computeFullV

bool Eigen::SVDBase::m_computeFullV
protected

Definition at line 278 of file SVDBase.h.

◆ m_computeThinU

bool Eigen::SVDBase::m_computeThinU
protected

Definition at line 277 of file SVDBase.h.

◆ m_computeThinV

bool Eigen::SVDBase::m_computeThinV
protected

Definition at line 278 of file SVDBase.h.

◆ m_diagSize

Index Eigen::SVDBase::m_diagSize
protected

Definition at line 280 of file SVDBase.h.

◆ m_info

ComputationInfo Eigen::SVDBase::m_info
protected

Definition at line 275 of file SVDBase.h.

◆ m_isAllocated

bool Eigen::SVDBase::m_isAllocated
protected

Definition at line 276 of file SVDBase.h.

◆ m_isInitialized

bool Eigen::SVDBase::m_isInitialized
protected

Definition at line 276 of file SVDBase.h.

◆ m_matrixU

MatrixUType Eigen::SVDBase::m_matrixU
protected

Definition at line 272 of file SVDBase.h.

◆ m_matrixV

MatrixVType Eigen::SVDBase::m_matrixV
protected

Definition at line 273 of file SVDBase.h.

◆ m_nonzeroSingularValues

Index Eigen::SVDBase::m_nonzeroSingularValues
protected

Definition at line 280 of file SVDBase.h.

◆ m_prescribedThreshold

RealScalar Eigen::SVDBase::m_prescribedThreshold
protected

Definition at line 281 of file SVDBase.h.

◆ m_rows

Index Eigen::SVDBase::m_rows
protected

Definition at line 280 of file SVDBase.h.

◆ m_singularValues

SingularValuesType Eigen::SVDBase::m_singularValues
protected

Definition at line 274 of file SVDBase.h.

◆ m_usePrescribedThreshold

bool Eigen::SVDBase::m_usePrescribedThreshold
protected

Definition at line 276 of file SVDBase.h.


The documentation for this class was generated from the following files:
svd
cout<< "Here is the matrix m:"<< endl<< m<< endl;JacobiSVD< MatrixXf > svd(m, ComputeThinU|ComputeThinV)
Eigen::Default
@ Default
Definition: Constants.h:362


gtsam
Author(s):
autogenerated on Sat Nov 16 2024 04:12:21