honey::Svd< Real > Class Template Reference

Singular Value Decomposition. Can be used to calculate the pseudo-inverse of any matrix or solve least squares problems. More...

#include <Base.h>

Public Types
enum	Mode { Mode::full, Mode::reduced }
typedef Matrix< matrix::dynamic, matrix::dynamic, Real >	Matrix
typedef Vec< matrix::dynamic, Double >	Vec_d
typedef Vec< matrix::dynamic, Real >	Vec

Public Member Functions
	Svd ()
template<class T >
	Svd (const MatrixBase< T > &a, Mode mode=Mode::reduced)
	Calculate the SVD of matrix A. More...
template<class T >
Svd &	calc (const MatrixBase< T > &a, Mode mode=Mode::reduced)
	Calculate the SVD of matrix A. More...
template<class T >
Svd &	calcValues (const MatrixBase< T > &a)
	Calculate the singular values of matrix A. This is a fast method for when the left and right singular vectors are not needed. More...
template<class B , class X >
void	solve (const MatrixBase< B > &b, MatrixBase< X > &x)
	Solve the linear system where A is the decomposed matrix. A and B row sizes must match. More...
template<class T >
void	inverse (MatrixBase< T > &res)
	Calculate the inverse of A, the decomposed matrix. More...
const Vec &	w () const
	Get the singular values of the decomposition. More...
const Matrix &	u () const
	Get the left singular column vectors of the decomposition. More...
const Matrix &	vt () const
	Get the right singular row vectors of the decomposition. More...

Detailed Description

template<class Real>
class honey::Svd< Real >

Singular Value Decomposition. Can be used to calculate the pseudo-inverse of any matrix or solve least squares problems.

The full SVD of (m x n) matrix A is: where the columns of (m x m) u and rows of (n x n) vt contain the orthogonal left and right singular vectors and (m x n) w contains the diagonal non-negative singular values.

In the reduced SVD, the singular vectors beyond the smallest dimension are not computed.
So, given w_dim = min(m,n), u is (m x w_dim), and vt is (w_dim x n).

Most linear systems do not require the full SVD to solve.

Complexity: , where n and m are the smaller and larger of the two dimensions

Member Typedef Documentation

template<class Real >

typedef Matrix<matrix::dynamic, matrix::dynamic, Real> honey::Svd< Real >::Matrix

template<class Real >

typedef Vec<matrix::dynamic, Real> honey::Svd< Real >::Vec

template<class Real >

typedef Vec<matrix::dynamic, Double> honey::Svd< Real >::Vec_d

Member Enumeration Documentation

template<class Real >

enum honey::Svd::Mode

strong

Enumerator
full	compute full SVD
reduced	compute reduced SVD

Constructor & Destructor Documentation

template<class Real >

honey::Svd< Real >::Svd ( )

inline

template<class Real >

template<class T >

honey::Svd< Real >::Svd ( const MatrixBase< T > &  a, Mode  mode = Mode::reduced  )

inline

Calculate the SVD of matrix A.

Member Function Documentation

template<class Real >

template<class T >

Svd& honey::Svd< Real >::calc ( const MatrixBase< T > &  a, Mode  mode = Mode::reduced  )

inline

Calculate the SVD of matrix A.

template<class Real >

template<class T >

Svd& honey::Svd< Real >::calcValues ( const MatrixBase< T > &  a )

inline

Calculate the singular values of matrix A. This is a fast method for when the left and right singular vectors are not needed.

template<class Real >

template<class T >

void honey::Svd< Real >::inverse ( MatrixBase< T > &  res )

inline

Calculate the inverse of A, the decomposed matrix.

template<class Real >

template<class B , class X >

void honey::Svd< Real >::solve ( const MatrixBase< B > &  b, MatrixBase< X > &  x  )

inline

Solve the linear system where A is the decomposed matrix. A and B row sizes must match.

template<class Real >

const Matrix& honey::Svd< Real >::u ( ) const

inline

Get the left singular column vectors of the decomposition.

template<class Real >

const Matrix& honey::Svd< Real >::vt ( ) const

inline

Get the right singular row vectors of the decomposition.

template<class Real >

const Vec& honey::Svd< Real >::w ( ) const

inline

Get the singular values of the decomposition.

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

• src/common/Honey/Math/Alge/Matrix/Base.h
• src/common/Honey/Math/NumAnalysis/Svd.h
• src/common/Honey/Math/NumAnalysis/Svd.cpp