cla3p::DefaultSVD< T_Matrix > Class Template Reference

Singular Value Decomposition (SVD) implementation for dense matrices. More...

Public Member Functions
	DefaultSVD ()
	Constructs an uninitialized SVD decomposition object.
	DefaultSVD (int_t m, int_t n, svdPolicy_t leftPolicy=svdPolicy_t::Economy, svdPolicy_t rightPolicy=svdPolicy_t::Economy)
	Constructs an SVD object with pre-allocated buffers.
	~DefaultSVD ()
	Destroys the SVD decomposition object.
void	clear ()
	Clears all decomposition results and resets the object.
void	reserve (int_t m, int_t n)
	Pre-allocates buffers for decomposition.
svdPolicy_t	getLeftPolicy () const
	Retrieves the left singular vector computation policy.
svdPolicy_t	getRightPolicy () const
	Retrieves the right singular vector computation policy.
void	setLeftPolicy (svdPolicy_t leftPolicy)
	Configures the left singular vector computation policy.
void	setRightPolicy (svdPolicy_t rightPolicy)
	Configures the right singular vector computation policy.
void	decompose (const T_Matrix &mat)
	Performs Singular Value Decomposition on the input matrix.
const T_RVector &	singularValues () const
	Retrieves the computed singular values.
const T_Matrix &	leftSingularVectors () const
	Retrieves the left singular vectors matrix.
const T_Matrix &	rightSingularVectors () const
	Retrieves the right singular vectors matrix.

Detailed Description

template<typename T_Matrix>
class cla3p::DefaultSVD< T_Matrix >

Singular Value Decomposition (SVD) implementation for dense matrices.

Template Parameters

T_Matrix

The dense matrix type to decompose.

This class provides a complete Singular Value Decomposition interface, decomposing a matrix \( A \) into \( A = U \cdot \Sigma \cdot V^H \), where \( U \) and \( V \) are unitary matrices and \( \Sigma \) is diagonal.

Examples

ex08b_sv_decomposition.cpp.

Constructor & Destructor Documentation

DefaultSVD() [1/2]

template<typename T_Matrix>

cla3p::DefaultSVD< T_Matrix >::DefaultSVD

(

)

Constructs an uninitialized SVD decomposition object.

Initializes an empty SVD object with no allocated memory for decomposition results.

DefaultSVD() [2/2]

template<typename T_Matrix>

cla3p::DefaultSVD< T_Matrix >::DefaultSVD	(	int_t	m,
		int_t	n,
		svdPolicy_t	leftPolicy = svdPolicy_t::Economy,
		svdPolicy_t	rightPolicy = svdPolicy_t::Economy )

Constructs an SVD object with pre-allocated buffers.

Initializes the SVD decomposition object and allocates internal buffers to accommodate matrices up to the specified dimensions.

Parameters

[in]	m	The maximum number of matrix rows.
[in]	n	The maximum number of matrix columns.
[in]	leftPolicy	The singular vector computation policy for \( U \).
[in]	rightPolicy	The singular vector computation policy for \( V \).

~DefaultSVD()

template<typename T_Matrix>

cla3p::DefaultSVD< T_Matrix >::~DefaultSVD

(

)

Destroys the SVD decomposition object.

Releases all allocated memory and clears internal data structures.

Member Function Documentation

clear()

template<typename T_Matrix>

void cla3p::DefaultSVD< T_Matrix >::clear

(

)

Clears all decomposition results and resets the object.

Deallocates decomposition results and returns the object to its default state.

reserve()

template<typename T_Matrix>

void cla3p::DefaultSVD< T_Matrix >::reserve	(	int_t	m,
		int_t	n )

Pre-allocates buffers for decomposition.

Allocates internal buffers to accommodate matrices with up to m rows and n columns. This avoids memory reallocation during subsequent decompositions.

Parameters

[in]	m	The maximum number of matrix rows to support.
[in]	n	The maximum number of matrix columns to support.

getLeftPolicy()

template<typename T_Matrix>

svdPolicy_t cla3p::DefaultSVD< T_Matrix >::getLeftPolicy

(

)

const

Retrieves the left singular vector computation policy.

Returns the policy that determines whether the left singular vectors ( \( U \) matrix) will be computed in full, limited to \( \min(m,n) \) columns, or not at all.

Returns

The current left singular vector computation policy.

getRightPolicy()

template<typename T_Matrix>

svdPolicy_t cla3p::DefaultSVD< T_Matrix >::getRightPolicy

(

)

const

Retrieves the right singular vector computation policy.

Returns the policy that determines whether the right singular vectors ( \( V^H \) matrix) will be computed in full, limited to \( \min(m,n) \) rows, or not at all.

Returns

The current right singular vector computation policy.

setLeftPolicy()

template<typename T_Matrix>

void cla3p::DefaultSVD< T_Matrix >::setLeftPolicy

(

svdPolicy_t

leftPolicy

)

Configures the left singular vector computation policy.

Specifies whether the left singular vectors ( \( U \) matrix) should be computed in full, limited to \( \min(m,n) \) columns, or not computed at all.

Parameters

[in]

leftPolicy

The left singular vector computation policy.

setRightPolicy()

template<typename T_Matrix>

void cla3p::DefaultSVD< T_Matrix >::setRightPolicy

(

svdPolicy_t

rightPolicy

)

Configures the right singular vector computation policy.

Specifies whether the right singular vectors ( \( V^H \) matrix) should be computed in full, limited to \( \min(m,n) \) rows, or not computed at all.

Parameters

[in]

rightPolicy

The right singular vector computation policy.

decompose()

template<typename T_Matrix>

void cla3p::DefaultSVD< T_Matrix >::decompose

(

const T_Matrix &

mat

)

Performs Singular Value Decomposition on the input matrix.

Computes the decomposition \( A = U \cdot \Sigma \cdot V^H \) of the input matrix. The computation respects the singular vector policies set via setLeftPolicy() and setRightPolicy().

Parameters

[in]

mat

The matrix to decompose.

Examples

ex08b_sv_decomposition.cpp.

singularValues()

template<typename T_Matrix>

const T_RVector & cla3p::DefaultSVD< T_Matrix >::singularValues

(

)

const

Retrieves the computed singular values.

Returns the diagonal elements of \( \Sigma \) in descending order.

Returns

A constant reference to a vector of \( \min(m,n) \) singular values.

Examples

ex08b_sv_decomposition.cpp.

leftSingularVectors()

template<typename T_Matrix>

const T_Matrix & cla3p::DefaultSVD< T_Matrix >::leftSingularVectors

(

)

const

Retrieves the left singular vectors matrix.

Returns the matrix \( U \) of size \( m \times k \), where:

• \( k = m \) if left policy is Full
• \( k = \min(m,n) \) if left policy is Economy
• The matrix is empty if left policy is NoCalculation

  Returns

  A constant reference to the left singular vectors matrix.

Examples

ex08b_sv_decomposition.cpp.

rightSingularVectors()

template<typename T_Matrix>

const T_Matrix & cla3p::DefaultSVD< T_Matrix >::rightSingularVectors

(

)

const

Retrieves the right singular vectors matrix.

Returns the matrix \( V^H \) of size \( k \times n \), where:

• \( k = n \) if right policy is Full
• \( k = \min(m,n) \) if right policy is Economy
• The matrix is empty if right policy is NoCalculation

  Returns

  A constant reference to the right singular vectors matrix.

Examples

ex08b_sv_decomposition.cpp.