Various mathematical utilities to compute SVD and the condition number of a matrix. More...

#include <svd_utils.h>

Collaboration diagram for Kratos::SVDUtils< TDataType >:

Static Public Member Functions
Operations
static std::size_t	SingularValueDecomposition (const MatrixType &InputMatrix, MatrixType &UMatrix, MatrixType &SMatrix, MatrixType &VMatrix, Parameters ThisParameters)
	This function gives the SVD of a given mxn matrix (m>=n), returns U,S; where A=USV. More...

static std::size_t	SingularValueDecomposition (const MatrixType &InputMatrix, MatrixType &UMatrix, MatrixType &SMatrix, MatrixType &VMatrix, const std::string &TypeSVD="Jacobi", const TDataType Tolerance=std::numeric_limits< double >::epsilon(), const IndexType MaxIter=200)
	This function gives the SVD of a given mxn matrix (m>=n), returns U,S; where A=USV. More...

static std::size_t	JacobiSingularValueDecomposition (const MatrixType &InputMatrix, MatrixType &UMatrix, MatrixType &SMatrix, MatrixType &VMatrix, const TDataType Tolerance=std::numeric_limits< double >::epsilon(), const IndexType MaxIter=200)
	This function gives the Jacobi SVD of a given mxn matrix (m>=n), returns U,S; where A=USV. More...

static void	SingularValueDecomposition2x2 (const MatrixType &InputMatrix, MatrixType &UMatrix, MatrixType &SMatrix, MatrixType &VMatrix)
	This function gives the Jacobi SVD of a given 2x2 matrix, returns U,S; where A=USV. More...

static void	SingularValueDecomposition2x2Symmetric (const MatrixType &InputMatrix, MatrixType &UMatrix, MatrixType &SMatrix, MatrixType &VMatrix)

static void	Jacobi (MatrixType &J1, MatrixType &J2, const MatrixType &InputMatrix, const SizeType &Size1, const SizeType &Size2, const SizeType &Index1, const SizeType &Index2)
	This method computes the Jacobi rotation operation. More...

static void	Jacobi (MatrixType &J1, const MatrixType &InputMatrix, const SizeType &Size1, const SizeType &Index1, const SizeType &Index2)
	This method computes the Jacobi rotation operation. More...

static TDataType	SVDConditionNumber (const MatrixType &InputMatrix, const std::string TypeSVD="Jacobi", const TDataType Tolerance=std::numeric_limits< double >::epsilon(), const IndexType MaxIter=200)
	This method computes the condition number using the SVD. More...

Type Definitions
typedef Matrix	MatrixType
	Definition of the matrix type. More...

typedef Vector	VectorType
	Definition of the vector type. More...

typedef std::size_t	SizeType
	Definition of the size type. More...

typedef std::size_t	IndexType
	Definition of index type. More...

typedef UblasSpace< TDataType, Matrix, Vector >	LocalSpaceType
	Definition of local space. More...

constexpr static TDataType	ZeroTolerance = std::numeric_limits<double>::epsilon()
	Definition of epsilon zero tolerance. More...

Detailed Description

template<class TDataType>
class Kratos::SVDUtils< TDataType >

Various mathematical utilities to compute SVD and the condition number of a matrix.

Defines several utility functions

Author: Vicente Mataix Ferrandiz

Member Typedef Documentation

◆ IndexType

template<class TDataType >

typedef std::size_t Kratos::SVDUtils< TDataType >::IndexType

Definition of index type.

◆ LocalSpaceType

template<class TDataType >

typedef UblasSpace<TDataType, Matrix, Vector> Kratos::SVDUtils< TDataType >::LocalSpaceType

Definition of local space.

◆ MatrixType

template<class TDataType >

typedef Matrix Kratos::SVDUtils< TDataType >::MatrixType

Definition of the matrix type.

◆ SizeType

template<class TDataType >

typedef std::size_t Kratos::SVDUtils< TDataType >::SizeType

Definition of the size type.

◆ VectorType

template<class TDataType >

typedef Vector Kratos::SVDUtils< TDataType >::VectorType

Definition of the vector type.

Member Function Documentation

◆ Jacobi() [1/2]

template<class TDataType >

static void Kratos::SVDUtils< TDataType >::Jacobi	(	MatrixType &	J1,
		const MatrixType &	InputMatrix,
		const SizeType &	Size1,
		const SizeType &	Index1,
		const SizeType &	Index2
	)

inlinestatic

This method computes the Jacobi rotation operation.

Parameters

J1	First Jacobi matrix
InputMatrix	The matrix to compute the Jacobi tolerance
Size1	The size of the matrix (number of rows)
Size2	The size of the matrix (number of columns)
Index1	The index to compute (row)
Index2	The index to compute (column)

◆ Jacobi() [2/2]

template<class TDataType >

static void Kratos::SVDUtils< TDataType >::Jacobi	(	MatrixType &	J1,
		MatrixType &	J2,
		const MatrixType &	InputMatrix,
		const SizeType &	Size1,
		const SizeType &	Size2,
		const SizeType &	Index1,
		const SizeType &	Index2
	)

inlinestatic

This method computes the Jacobi rotation operation.

Parameters

J1	First Jacobi matrix
J2	Second Jacobi matrix
InputMatrix	The matrix to compute the Jacobi tolerance
Size1	The size of the matrix (number of rows)
Size2	The size of the matrix (number of columns)
Index1	The index to compute (row)
Index2	The index to compute (column)

◆ JacobiSingularValueDecomposition()

template<class TDataType >

static std::size_t Kratos::SVDUtils< TDataType >::JacobiSingularValueDecomposition	(	const MatrixType &	InputMatrix,
		MatrixType &	UMatrix,
		MatrixType &	SMatrix,
		MatrixType &	VMatrix,
		const TDataType	Tolerance = `std::numeric_limits<double>::epsilon()`,
		const IndexType	MaxIter = `200`
	)

inlinestatic

This function gives the Jacobi SVD of a given mxn matrix (m>=n), returns U,S; where A=U*S*V.

U and V are unitary, and S is a diagonal matrix. Where s_i >= 0, and s_i >= s_i+1 (which means that the biggest number is the first one and the smallest the last one)

Todo:: This version is quite innefficient, look for a real and mathematical implementation (not the algorithm found in Wikipedia!!)

Parameters

InputMatrix	The matrix where perform the SVD
UMatrix	The unitary U matrix
SMatrix	The diagonal S matrix
VMatrix	The unitary V matrix
Tolerance	The tolerance considered
MaxIter	Maximum number of iterations

Returns: iter: The number of iterations

◆ SingularValueDecomposition() [1/2]

template<class TDataType >

static std::size_t Kratos::SVDUtils< TDataType >::SingularValueDecomposition	(	const MatrixType &	InputMatrix,
		MatrixType &	UMatrix,
		MatrixType &	SMatrix,
		MatrixType &	VMatrix,
		const std::string &	TypeSVD = `"Jacobi"`,
		const TDataType	Tolerance = `std::numeric_limits<double>::epsilon()`,
		const IndexType	MaxIter = `200`
	)

inlinestatic

This function gives the SVD of a given mxn matrix (m>=n), returns U,S; where A=U*S*V.

U and V are unitary, and S is a diagonal matrix. Where s_i >= 0, and s_i >= s_i+1 (which means that the biggest number is the first one and the smallest the last one)

Todo:: This version is quite innefficient, look for a real and mathematical implementation (not the algorithm found in Wikipedia!!)

Parameters

InputMatrix	The matrix where perform the SVD
UMatrix	The unitary U matrix
SMatrix	The diagonal S matrix
VMatrix	The unitary V matrix
TypeSVD	The type of SVD algorithm (Jacobi by default)
Tolerance	The tolerance considered
MaxIter	Maximum number of iterations

Returns: iter: The number of iterations

◆ SingularValueDecomposition() [2/2]

template<class TDataType >

static std::size_t Kratos::SVDUtils< TDataType >::SingularValueDecomposition	(	const MatrixType &	InputMatrix,
		MatrixType &	UMatrix,
		MatrixType &	SMatrix,
		MatrixType &	VMatrix,
		Parameters	ThisParameters
	)

inlinestatic

This function gives the SVD of a given mxn matrix (m>=n), returns U,S; where A=U*S*V.

U and V are unitary, and S is a diagonal matrix. Where s_i >= 0, and s_i >= s_i+1 (which means that the biggest number is the first one and the smallest the last one)

Todo:: This version is quite innefficient, look for a real and mathematical implementation (not the algorithm found in Wikipedia!!)

Parameters

InputMatrix	The matrix where perform the SVD
UMatrix	The unitary U matrix
SMatrix	The diagonal S matrix
VMatrix	The unitary V matrix
ThisParameters	The configuration parameters

Returns: iter: The number of iterations

◆ SingularValueDecomposition2x2()

template<class TDataType >

static void Kratos::SVDUtils< TDataType >::SingularValueDecomposition2x2	(	const MatrixType &	InputMatrix,
		MatrixType &	UMatrix,
		MatrixType &	SMatrix,
		MatrixType &	VMatrix
	)

inlinestatic

This function gives the Jacobi SVD of a given 2x2 matrix, returns U,S; where A=U*S*V.

U and V are unitary, and S is a diagonal matrix. Where s_i >= 0, and s_i >= s_i+1

Parameters

InputMatrix	The matrix where perform the SVD
UMatrix	The unitary U matrix
SMatrix	The diagonal S matrix
VMatrix	The unitary V matrix

◆ SingularValueDecomposition2x2Symmetric()

template<class TDataType >

static void Kratos::SVDUtils< TDataType >::SingularValueDecomposition2x2Symmetric	(	const MatrixType &	InputMatrix,
		MatrixType &	UMatrix,
		MatrixType &	SMatrix,
		MatrixType &	VMatrix
	)

inlinestatic

This function gives the Jacobi SVD of a given 2x2 matrix, returns U,S; where A=U*S*V U and V are unitary, and S is a diagonal matrix. Where s_i >= 0, and s_i >= s_i+1

Parameters

InputMatrix	The matrix where perform the SVD
UMatrix	The unitary U matrix
SMatrix	The diagonal S matrix
VMatrix	The unitary V matrix

◆ SVDConditionNumber()

template<class TDataType >

static TDataType Kratos::SVDUtils< TDataType >::SVDConditionNumber	(	const MatrixType &	InputMatrix,
		const std::string	TypeSVD = `"Jacobi"`,
		const TDataType	Tolerance = `std::numeric_limits<double>::epsilon()`,
		const IndexType	MaxIter = `200`
	)

inlinestatic

This method computes the condition number using the SVD.

The condition number can be estimated as the ratio between the largest singular value and the smallest singular value

Parameters

InputMatrix	The matrix to be evaluated
Tolerance	The tolerance considered

Returns: condition_number: The ratio between the largest SV and the smallest SV

Member Data Documentation

◆ ZeroTolerance

template<class TDataType >

constexpr static TDataType Kratos::SVDUtils< TDataType >::ZeroTolerance = std::numeric_limits<double>::epsilon()

staticconstexpr

Definition of epsilon zero tolerance.

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

/home/runner/work/Documentation/Documentation/master/kratos/utilities/svd_utils.h

Static Public Member Functions

Type Definitions

Detailed Description

template<class TDataType> class Kratos::SVDUtils< TDataType >

Member Typedef Documentation

◆ IndexType

◆ LocalSpaceType

◆ MatrixType

◆ SizeType

◆ VectorType

Member Function Documentation

◆ Jacobi() [1/2]

◆ Jacobi() [2/2]

◆ JacobiSingularValueDecomposition()

◆ SingularValueDecomposition() [1/2]

◆ SingularValueDecomposition() [2/2]

◆ SingularValueDecomposition2x2()

◆ SingularValueDecomposition2x2Symmetric()

◆ SVDConditionNumber()

Member Data Documentation

◆ ZeroTolerance

template<class TDataType>
class Kratos::SVDUtils< TDataType >