Singular Value Decomposition. More...

#include <yat/utility/SVD.h>

Public Types
enum	SVDalgorithm { GolubReinsch, ModifiedGolubReinsch, Jacobi }

Public Member Functions
	SVD (const MatrixBase &Ain)
	Constructs an SVD object using the matrix Ain as only input. The input matrix is copied for further use in the object. More...

	SVD (MatrixMutable &&Ain)

	~SVD (void)
	The destructor.

void	decompose (SVDalgorithm algo=GolubReinsch)
	This function will perform SVD with the method specified by algo. More...

const Vector &	s (void) const
	Access to the s vector. More...

void	solve (const VectorBase &b, Vector &x)
	Solve the system using the decomposition of A. More...

const Matrix &	U (void) const
	Access to the U matrix. More...

const Matrix &	V (void) const
	Access to the V matrix. More...

Detailed Description

Singular Value Decomposition.

Class encapsulating GSL methods for singular value decomposition, SVD.

A = U S V' = (MxN)(NxN)(NxN) = (MxN)
A = Matrix to be decomposed, size MxN
U = Orthogonal matrix, size MxN
S = Diagonal matrix of singular values, size NxN
V = Orthogonal matrix, size NxN

Member Enumeration Documentation

◆ SVDalgorithm

enum theplu::yat::utility::SVD::SVDalgorithm

A number of SVD algorithms are implemented in GSL. They have their strengths and weaknesses.

See also: GSL's SVD documentation.

Constructor & Destructor Documentation

◆ SVD() [1/2]

theplu::yat::utility::SVD::SVD ( const MatrixBase & Ain )

explicit

Constructs an SVD object using the matrix Ain as only input. The input matrix is copied for further use in the object.

Note: Number of rows must be equal or larger than number of columns.

◆ SVD() [2/2]

theplu::yat::utility::SVD::SVD ( MatrixMutable && Ain )

explicit

Same behaviour as const& constructor, but Ain is moved rather than copied.

Since: new in yat 0.16

Member Function Documentation

◆ decompose()

void theplu::yat::utility::SVD::decompose ( SVDalgorithm algo = GolubReinsch )

This function will perform SVD with the method specified by algo.

Exceptions

GSL_error if the underlying GSL function fails.

◆ s()

const Vector& theplu::yat::utility::SVD::s ( void ) const

Access to the s vector.

Returns: A copy of the s vector.

Note: If decompose() has not been run the outcome of the call is undefined.

◆ solve()

void theplu::yat::utility::SVD::solve	(	const VectorBase &	b,
		Vector &	x
	)

Solve the system $ Ax=b $ using the decomposition of A.

Note: If decompose() has not been run the outcome of the call is undefined.

Exceptions

GSL_error if the underlying GSL function fails.

◆ U()

const Matrix& theplu::yat::utility::SVD::U ( void ) const

Access to the U matrix.

Returns: A copy of the U matrix.

Note: If decompose() has not been run the outcome of the call is undefined.

◆ V()

const Matrix& theplu::yat::utility::SVD::V ( void ) const

Access to the V matrix.

Returns: A copy of the V matrix.

Note: If decompose() has not been run the outcome of the call is undefined.

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

yat/utility/SVD.h

Public Types

Public Member Functions