vnl_qr< T > Class Template Reference

Extract the Q*R decomposition of matrix M. More...

#include <vnl_algo_fwd.h>

Public Member Functions
	vnl_qr (vnl_matrix< T > const &M)
	~vnl_qr ()
vnl_matrix< T >	inverse () const
	return the inverse matrix of M. More...
vnl_matrix< T >	tinverse () const
	return the transpose of the inverse matrix of M. More...
vnl_matrix< T >	recompose () const
	return the original matrix M. More...
vnl_matrix< T >	solve (const vnl_matrix< T > &rhs) const
	Solve equation M x = rhs for x using the computed decomposition. More...
vnl_vector< T >	solve (const vnl_vector< T > &rhs) const
	Solve equation M x = rhs for x using the computed decomposition. More...
T	determinant () const
	Return the determinant of M. This is computed from M = Q R as follows:. More...
vnl_matrix< T > const &	Q () const
	Unpack and return unitary part Q. More...
vnl_matrix< T > const &	R () const
	Unpack and return R. More...
vnl_vector< T >	QtB (const vnl_vector< T > &b) const
	Return residual vector d of M x = b -> d = Q'b. More...
void	extract_q_and_r (vnl_matrix< T > *q, vnl_matrix< T > *r) const

Private Member Functions
	vnl_qr (const vnl_qr< T > &)
vnl_qr< T > &	operator= (const vnl_qr< T > &)

Private Attributes
vnl_matrix< T >	qrdc_out_
vnl_vector< T >	qraux_
vnl_vector< long >	jpvt_
vnl_matrix< T > *	Q_
vnl_matrix< T > *	R_

Detailed Description

template<class T>
class vnl_qr< T >

Extract the Q*R decomposition of matrix M.

The decomposition is stored in a compact and time-efficient packed form, which is most easily used via the "solve" and "determinant" methods.

Definition at line 8 of file vnl_algo_fwd.h.

Constructor & Destructor Documentation

vnl_qr() [1/2]

template<class T >

vnl_qr< T >::vnl_qr

(

vnl_matrix< T > const &

M

)

Definition at line 37 of file vnl_qr.hxx.

~vnl_qr()

template<class T >

vnl_qr< T >::~vnl_qr

(

)

Definition at line 66 of file vnl_qr.hxx.

vnl_qr() [2/2]

template<class T>

vnl_qr< T >::vnl_qr ( const vnl_qr< T > &  )

inlineprivate

Definition at line 78 of file vnl_qr.h.

Member Function Documentation

determinant()

template<class T >

T vnl_qr< T >::determinant

(

)

const

Return the determinant of M. This is computed from M = Q R as follows:.

|M| = |Q| |R|. |R| is the product of the diagonal elements. |Q| is (-1)^n as it is a product of Householder reflections. So det = -prod(-r_ii).

|M| = |Q| |R| |R| is the product of the diagonal elements. |Q| is (-1)^n as it is a product of Householder reflections. So det = -prod(-r_ii).

Definition at line 78 of file vnl_qr.hxx.

extract_q_and_r()

template<class T>

void vnl_qr< T >::extract_q_and_r ( vnl_matrix< T > *  q, vnl_matrix< T > *  r  ) const

inline

Definition at line 68 of file vnl_qr.h.

inverse()

template<class T >

vnl_matrix< T > vnl_qr< T >::inverse

(

)

const

return the inverse matrix of M.

Definition at line 251 of file vnl_qr.hxx.

operator=()

template<class T>

vnl_qr<T>& vnl_qr< T >::operator= ( const vnl_qr< T > &  )

inlineprivate

Definition at line 79 of file vnl_qr.h.

Q()

template<class T >

vnl_matrix< T > const & vnl_qr< T >::Q

(

)

const

Unpack and return unitary part Q.

Definition at line 91 of file vnl_qr.hxx.

QtB()

template<class T >

vnl_vector< T > vnl_qr< T >::QtB

(

const vnl_vector< T > &

b

)

const

Return residual vector d of M x = b -> d = Q'b.

Definition at line 220 of file vnl_qr.hxx.

R()

template<class T >

vnl_matrix< T > const & vnl_qr< T >::R

(

)

const

Unpack and return R.

Definition at line 156 of file vnl_qr.hxx.

recompose()

template<class T >

vnl_matrix< T > vnl_qr< T >::recompose

(

)

const

return the original matrix M.

Definition at line 176 of file vnl_qr.hxx.

solve() [1/2]

template<class T >

vnl_matrix< T > vnl_qr< T >::solve

(

const vnl_matrix< T > &

rhs

)

const

Solve equation M x = rhs for x using the computed decomposition.

Definition at line 289 of file vnl_qr.hxx.

solve() [2/2]

template<class T >

vnl_vector< T > vnl_qr< T >::solve

(

const vnl_vector< T > &

rhs

)

const

Solve equation M x = rhs for x using the computed decomposition.

Solve equation M x = b for x using the computed decomposition.

Definition at line 189 of file vnl_qr.hxx.

tinverse()

template<class T >

vnl_matrix< T > vnl_qr< T >::tinverse

(

)

const

return the transpose of the inverse matrix of M.

Definition at line 270 of file vnl_qr.hxx.

Member Data Documentation

jpvt_

template<class T>

vnl_vector<long> vnl_qr< T >::jpvt_

private

Definition at line 73 of file vnl_qr.h.

Q_

template<class T>

vnl_matrix<T>* vnl_qr< T >::Q_

mutableprivate

Definition at line 74 of file vnl_qr.h.

qraux_

template<class T>

vnl_vector<T> vnl_qr< T >::qraux_

private

Definition at line 72 of file vnl_qr.h.

qrdc_out_

template<class T>

vnl_matrix<T> vnl_qr< T >::qrdc_out_

private

Definition at line 71 of file vnl_qr.h.

R_

template<class T>

vnl_matrix<T>* vnl_qr< T >::R_

mutableprivate

Definition at line 75 of file vnl_qr.h.

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

• core/vnl/algo/vnl_algo_fwd.h
• core/vnl/algo/vnl_qr.h
• core/vnl/algo/vnl_qr.hxx