Please, help us to better know about our user community by answering the following short survey: https://forms.gle/wpyrxWi18ox9Z5ae9 Eigen  3.3.90 (git rev ecb7bc9514b12051d050299234b2a74ac76b5a8e) Eigen::SVDBase Class Reference

## Detailed Description

Base class of SVD algorithms.

Template Parameters
 Derived the type of the actual 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.

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.

class BDCSVD, class JacobiSVD

## Public Types

typedef Eigen::Index Index

## Public Member Functions

bool computeU () const

bool computeV () const

const MatrixUTypematrixU () const

const MatrixVTypematrixV () const

Index nonzeroSingularValues () const

Index rank () const

Derived & setThreshold (const RealScalar &threshold)

Derived & setThreshold (Default_t)

const SingularValuesType & singularValues () const

template<typename Rhs >
const Solve< Derived, Rhs > solve (const MatrixBase< Rhs > &b) const

RealScalar threshold () const

## Protected Member Functions

SVDBase ()
Default Constructor. More...

## ◆ Index

 typedef Eigen::Index Eigen::SVDBase::Index
Deprecated:
since Eigen 3.3

## ◆ SVDBase()

 Eigen::SVDBase::SVDBase ( )
inlineprotected

Default Constructor.

Default constructor of SVDBase

## ◆ computeU()

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

## ◆ computeV()

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

## ◆ 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.

## ◆ 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.

## ◆ nonzeroSingularValues()

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

## ◆ 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&).

## ◆ 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
 threshold The new value to use as the threshold.

A singular value will be considered nonzero if its value is strictly greater than .

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

## ◆ 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&).

## ◆ 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.

## ◆ solve()

template<typename Rhs >
 const Solve Eigen::SVDBase::solve ( const MatrixBase< Rhs > & b ) const
inline
Returns
a (least squares) solution of using the current SVD decomposition of A.
Parameters
 b the right-hand-side of the equation to solve.
Note
Solving requires both U and V to be computed. Thin U and V are enough, there is no need for full U or V.
SVD solving is implicitly least-squares. Thus, this method serves both purposes of exact solving and least-squares solving. In other words, the returned solution is guaranteed to minimize the Euclidean norm .

## ◆ 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&).

The documentation for this class was generated from the following files: