cla3p::PartialQR< T_Matrix > Class Template Reference

Partial Pivoted QR Decomposition for rank reduction algorithms. More...

Public Member Functions
	PartialQR ()
	Constructs an uninitialized partial QR object.
	PartialQR (int_t m, int_t n)
	Constructs a partial QR object with pre-allocated buffers.
	~PartialQR ()
	Destroys the partial QR 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.
real_t	cutTolerance () const
	Retrieves the singular value tolerance threshold.
void	setCutTolerance (real_t tol)
	Configures the singular value tolerance threshold.
void	decompose (const T_Matrix &mat)
	Initiates the partial QR decomposition.
void	resume (bool ignoreTol=false)
	Resumes the partial QR decomposition.
int_t	performDecompositionStep ()
	Performs a single decomposition step.
int_t	totalColumnsProcessed () const
	Retrieves the count of processed columns.
const T_Matrix &	R () const
	Retrieves the upper triangular matrix.
const T_Vector &	tau () const
	Retrieves the Householder reflection coefficients.
const prm::PiMatrix &	P () const
	Retrieves the column pivoting permutation matrix.
const T_Matrix &	elementaryReflectors () const
	Retrieves the elementary Householder reflector matrix.
bool	transFlag () const
	Determines if input matrix was transposed.
void	fillMatrixR (int_t numRanks=0)
	Extracts the upper triangular portion to form matrix \( R \).

Detailed Description

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

Partial Pivoted QR Decomposition for rank reduction algorithms.

Template Parameters

T_Matrix

The dense matrix type to decompose.

This class implements a partial (stopped) QR decomposition with column pivoting, useful for low-rank approximation and rank reduction processes. The algorithm processes the matrix incrementally, stopping when singular values fall below a specified tolerance threshold. The input matrix is automatically transposed as needed to ensure tall-matrix orientation ( \( m \geq n \)).

Constructor & Destructor Documentation

PartialQR() [1/2]

template<typename T_Matrix>

cla3p::PartialQR< T_Matrix >::PartialQR

(

)

Constructs an uninitialized partial QR object.

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

PartialQR() [2/2]

template<typename T_Matrix>

cla3p::PartialQR< T_Matrix >::PartialQR	(	int_t	m,
		int_t	n )

Constructs a partial QR object with pre-allocated buffers.

Initializes the partial QR 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.

~PartialQR()

template<typename T_Matrix>

cla3p::PartialQR< T_Matrix >::~PartialQR

(

)

Destroys the partial QR decomposition object.

Releases all allocated memory and clears internal data structures.

Member Function Documentation

clear()

template<typename T_Matrix>

void cla3p::PartialQR< 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::PartialQR< 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.

cutTolerance()

template<typename T_Matrix>

real_t cla3p::PartialQR< T_Matrix >::cutTolerance

(

)

const

Retrieves the singular value tolerance threshold.

Returns the relative tolerance parameter used to determine which columns are kept in the partial QR decomposition. Diagonal elements \( R_{i,i} \) are retained if \( |R_{i,i}| > |R_{0,0}| \cdot \text{cutTolerance}() \).

Returns

The current cutoff tolerance value.

setCutTolerance()

template<typename T_Matrix>

void cla3p::PartialQR< T_Matrix >::setCutTolerance

(

real_t

tol

)

Configures the singular value tolerance threshold.

Sets the relative tolerance parameter that determines stopping condition. Diagonal elements \( R_{i,i} \) are retained if \( |R_{i,i}| > |R_{0,0}| \cdot \text{tol} \).

Parameters

[in]

tol

The desired cutoff tolerance value.

decompose()

template<typename T_Matrix>

void cla3p::PartialQR< T_Matrix >::decompose

(

const T_Matrix &

mat

)

Initiates the partial QR decomposition.

Begins column-wise QR decomposition with column pivoting, stopping when the tolerance criterion \( |R_{i,i}| > |R_{0,0}| \cdot \text{cutTolerance}() \) is violated.

Parameters

[in]

mat

The matrix to decompose.

resume()

template<typename T_Matrix>

void cla3p::PartialQR< T_Matrix >::resume

(

bool

ignoreTol = false

)

Resumes the partial QR decomposition.

Continues the decomposition from where decompose() or the previous resume() stopped. The decomposition proceeds until the tolerance criterion \( |R_{i,i}| > |R_{0,0}| \cdot \text{cutTolerance}() \) is violated, or all columns are processed if ignoreTol is true.

Parameters

[in]

ignoreTol

If true, ignores the tolerance criterion and decomposes all remaining columns.

performDecompositionStep()

template<typename T_Matrix>

int_t cla3p::PartialQR< T_Matrix >::performDecompositionStep

(

)

Performs a single decomposition step.

Executes one decomposition step with an automatically determined block size.

Returns

The number of columns processed in this decomposition step.

totalColumnsProcessed()

template<typename T_Matrix>

int_t cla3p::PartialQR< T_Matrix >::totalColumnsProcessed

(

)

const

Retrieves the count of processed columns.

Returns the total number of columns processed so far throughout the partial QR decomposition.

Returns

The total number of columns processed.

R()

template<typename T_Matrix>

const T_Matrix & cla3p::PartialQR< T_Matrix >::R

(

)

const

Retrieves the upper triangular matrix.

Returns the matrix \( R \) calculated so far in the partial QR decomposition process.

Returns

A constant reference to the upper triangular matrix \( R \) in general form.

tau()

template<typename T_Matrix>

const T_Vector & cla3p::PartialQR< T_Matrix >::tau

(

)

const

Retrieves the Householder reflection coefficients.

Returns the vector \( \tau \) of size \( \min(m,n) \) containing the scalar factors for elementary Householder reflectors.

Returns

A constant reference to the Householder scalar coefficient vector.

P()

template<typename T_Matrix>

const prm::PiMatrix & cla3p::PartialQR< T_Matrix >::P

(

)

const

Retrieves the column pivoting permutation matrix.

Returns the permutation matrix \( P \) that encodes the column pivots applied during the partial QR decomposition process.

Returns

A constant reference to the column pivoting permutation matrix.

elementaryReflectors()

template<typename T_Matrix>

const T_Matrix & cla3p::PartialQR< T_Matrix >::elementaryReflectors

(

)

const

Retrieves the elementary Householder reflector matrix.

Returns a matrix containing the elementary Householder vectors used to implicitly represent the orthogonal transformation matrix from the QR decomposition.

Returns

A constant reference to the elementary reflector matrix.

transFlag()

template<typename T_Matrix>

bool cla3p::PartialQR< T_Matrix >::transFlag

(

)

const

Determines if input matrix was transposed.

Indicates whether the input matrix was automatically conjugate-transposed during initialization to achieve tall-matrix orientation.

Returns

true if the matrix was transposed, false otherwise.

fillMatrixR()

template<typename T_Matrix>

void cla3p::PartialQR< T_Matrix >::fillMatrixR

(

int_t

numRanks = 0

)

Extracts the upper triangular portion to form matrix \( R \).

Constructs matrix \( R \) from the elementary reflector matrix, optionally keeping only the first numRanks columns.

Parameters

[in]

numRanks

The number of columns to retain (0 means all columns).