Householder< number > Class Template Reference
[Derived matrices]

Inheritance diagram for Householder< number >:

[legend]

List of all members.

Public Member Functions
	Householder ()
template<typename number2 >
	Householder (const FullMatrix< number2 > &)
template<typename number2 >
void	initialize (const FullMatrix< number2 > &)
template<typename number2 >
double	least_squares (Vector< number2 > &dst, const Vector< number2 > &src) const
Private Attributes
std::vector< number >	diagonal

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Detailed Description

template<typename number>
class Householder< number >

QR-decomposition of a full matrix.

Whenever an object of this class is created, it copies the matrix given and computes its QR-decomposition by Householder algorithm. Then, the function least_squares() can be used to compute the vector x minimizing ||Ax-b|| for a given vector b.

Note:

Instantiations for this template are provided for <float> and <double>; others can be generated in application programs (see the section on Template instantiations in the manual).

Author:

Guido Kanschat, 2005

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Constructor & Destructor Documentation

template<typename number>

Householder< number >::Householder

(

)

Create an empty object.

template<typename number>

template<typename number2 >

Householder< number >::Householder

(

const FullMatrix< number2 > &

)

[inline]

Create an object holding the QR-decomposition of a matrix.

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Member Function Documentation

template<typename number>

template<typename number2 >

void Householder< number >::initialize

(

const FullMatrix< number2 > &

)

[inline]

Compute the QR-decomposition of another matrix.

template<typename number>

template<typename number2 >

double Householder< number >::least_squares	(	Vector< number2 > &	dst,
		const Vector< number2 > &	src
	)			const [inline]

Solve the least-squares problem for the right hand side src. The return value is the Euclidean norm of the approximation error.

• dst contains the solution of the least squares problem on return.

• src contains the right hand side b of the least squares problem. It will be changed during the algorithm and is unusable on return.

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Member Data Documentation

template<typename number>

std::vector<number> Householder< number >::diagonal [private]

Storage for the diagonal elements of the orthogonal transformation.

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

• lac/include/lac/householder.h