cvr::qrDecomposition< T > Class Template Reference
[Linear Algebra]

This functor computes a QRDecomposition of a given rectangular m x n Matrix A of the Form:. More...

#include <cvrQrDecomposition.h>

Inheritance diagram for cvr::qrDecomposition< T >:

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Collaboration diagram for cvr::qrDecomposition< T >:

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List of all members.

Classes
class	parameters
	The parameters for the class qrDecomposition. More...
Public Member Functions
	qrDecomposition ()
	qrDecomposition (const parameters &par)
	qrDecomposition (const qrDecomposition &other)
virtual	~qrDecomposition ()
bool	apply (matrix< T > &arh, vector< T > &tau, vector< integer > &p) const
bool	apply (const matrix< T > &a, matrix< T > &rh, vector< T > &tau, vector< integer > &p) const
bool	apply (matrix< T > &arh, vector< T > &tau) const
bool	apply (const matrix< T > &a, matrix< T > &rh, vector< T > &tau) const
bool	extractR (const matrix< T > &rh, matrix< T > &r) const
bool	computeQ (const matrix< T > &rh, vector< T > &tau, matrix< T > &q) const
void	buildPermutationMatrix (const vector< integer > &pv, matrix< T > &pm) const
bool	apply (const matrix< T > &A, matrix< T > &Q, matrix< T > &R) const
qrDecomposition &	copy (const qrDecomposition &other)
qrDecomposition &	operator= (const qrDecomposition &other)
const std::string &	name () const
virtual qrDecomposition< T > *	clone () const
virtual qrDecomposition< T > *	newInstance () const
const parameters &	getParameters () const

---

Detailed Description

template<typename T>
class cvr::qrDecomposition< T >

This functor computes a QRDecomposition of a given rectangular m x n Matrix A of the Form:.

A = Q * R

Where R is an upper triangular m x m Matrix and Q is a m x n orthogonal matrix, i.e. the transposed matrix of Q multiplied with Q itself is the identity matrix.

If LAPACK is not used or not available, A must be of full rank!

 matrix<float> src(3,3);
 float data[] =  {1,2,3,4,5,6,7,8,9};
 src.fill(data);
 matrix<float> q,r;

 qrDecomposition<float> qrd;
 qrd.apply(src,q,r);

 matrix<float> result;
 result.multiply(q,r);

 std::cout << "Q:\n" << q << "\n";
 std::cout << "R:\n" << r << "\n";
 // should be identical to src
 std::cout << "A = Q * R:\n"<< result << "\n";

---

Constructor & Destructor Documentation

template<typename T>

cvr::qrDecomposition< T >::qrDecomposition

(

)

Default constructor.

template<typename T>

cvr::qrDecomposition< T >::qrDecomposition

(

const parameters &

par

)

Construct a functor using the given parameters.

template<typename T>

cvr::qrDecomposition< T >::qrDecomposition

(

const qrDecomposition< T > &

other

)

Copy constructor.

Parameters:

other

the object to be copied

template<typename T>

virtual cvr::qrDecomposition< T >::~qrDecomposition

(

)

[virtual]

Destructor.

---

Member Function Documentation

template<typename T>

bool cvr::qrDecomposition< T >::apply	(	const matrix< T > &	A,
		matrix< T > &	Q,
		matrix< T > &	R
	)			const

Computes the QR decomposition.

Warning:

You usually don't need this explicit decomposition, since most methods use the compact outputs of the other apply() to speed up the computations. However, this is provided for completeness.

Parameters:

	A	input m x n matrix.
	Q	Q is a m x n orthogonal matrix.
	R	R is an upper triangular m x m matrix.

Returns:

true if successful or false otherwise.

template<typename T>

bool cvr::qrDecomposition< T >::apply	(	const matrix< T > &	a,
		matrix< T > &	rh,
		vector< T > &	tau
	)			const

Apply QR (on copy).

Parameters:

	a	The source matrix on input
	rh	The compact representation (R + elementary reflectors) on output
	tau	The beta components on output

Returns:

true if the application was successful, false otherwise

template<typename T>

bool cvr::qrDecomposition< T >::apply	(	matrix< T > &	arh,
		vector< T > &	tau
	)			const

Apply QR (in place).

Parameters:

	arh	The source matrix on input, and on output the compact representation (R + elementary reflectors)
	tau	The beta components on output

Returns:

true if the application was successful, false otherwise

template<typename T>

bool cvr::qrDecomposition< T >::apply	(	const matrix< T > &	a,
		matrix< T > &	rh,
		vector< T > &	tau,
		vector< integer > &	p
	)			const

Apply QR using column pivoting (on copy).

Parameters:

	a	The source matrix on input
	rh	The compact representation (R + elementary reflectors) on output
	tau	The beta components on output
	p	The column permutation vector on output

Returns:

true if the application was successful, false otherwise

template<typename T>

bool cvr::qrDecomposition< T >::apply	(	matrix< T > &	arh,
		vector< T > &	tau,
		vector< integer > &	p
	)			const

Apply QR using column pivoting (in place).

Parameters:

	arh	The source matrix on input, and on output the compact representation (R + elementary reflectors)
	tau	The beta components on output
	p	The column permutation vector on output

Returns:

true if the application was successful, false otherwise

template<typename T>

void cvr::qrDecomposition< T >::buildPermutationMatrix	(	const vector< integer > &	pv,
		matrix< T > &	pm
	)			const

Builds the permutation matrix for the given permutation vector.

Parameters:

	pv	The column permutation vector on input
	pm	The column permutation matrix on output

template<typename T>

virtual qrDecomposition<T>* cvr::qrDecomposition< T >::clone

(

)

const [virtual]

Returns a pointer to a clone of this functor.

Implements cvr::functor.

template<typename T>

bool cvr::qrDecomposition< T >::computeQ	(	const matrix< T > &	rh,
		vector< T > &	tau,
		matrix< T > &	q
	)			const

Compute Q from RH and tau.

Parameters:

	rh	The compact representation (R + elementary reflectors) on input
	tau	The beta components on input
	q	Q on output

template<typename T>

qrDecomposition& cvr::qrDecomposition< T >::copy

(

const qrDecomposition< T > &

other

)

Copy data of "other" functor.

Parameters:

other

the functor to be copied

Returns:

a reference to this functor object

template<typename T>

bool cvr::qrDecomposition< T >::extractR	(	const matrix< T > &	rh,
		matrix< T > &	r
	)			const

Extract R from RH.

Parameters:

	rh	The compact representation (R + elementary reflectors) on input
	r	R on output

template<typename T>

const parameters& cvr::qrDecomposition< T >::getParameters

(

)

const

Returns used parameters.

Reimplemented from cvr::linearAlgebraFunctor.

template<typename T>

const std::string& cvr::qrDecomposition< T >::name

(

)

const [virtual]

Returns the name of this class.

Reimplemented from cvr::lapackInterface.

template<typename T>

virtual qrDecomposition<T>* cvr::qrDecomposition< T >::newInstance

(

)

const [virtual]

Returns a pointer to a clone of this functor.

Implements cvr::functor.

template<typename T>

qrDecomposition& cvr::qrDecomposition< T >::operator=

(

const qrDecomposition< T > &

other

)

Alias for copy member.

Parameters:

other

the functor to be copied

Returns:

a reference to this functor object

---

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

• cvrQrDecomposition.h