Derived matrices

Collaboration diagram for Derived matrices:

Classes
class	Householder< number >
class	MatrixBlock< MatrixType >

Typedefs
using	Householder< number >::size_type = types::global_dof_index

Functions
	Householder< number >::Householder ()=default
template<typename number2 >
	Householder< number >::Householder (const FullMatrix< number2 > &A)
template<typename number2 >
void	Householder< number >::initialize (const FullMatrix< number2 > &A)
template<typename number2 >
double	Householder< number >::least_squares (Vector< number2 > &dst, const Vector< number2 > &src) const
template<typename number2 >
double	Householder< number >::least_squares (BlockVector< number2 > &dst, const BlockVector< number2 > &src) const
template<class VectorType >
void	Householder< number >::vmult (VectorType &dst, const VectorType &src) const
template<class VectorType >
void	Householder< number >::Tvmult (VectorType &dst, const VectorType &src) const

Variables
std::vector< number >	Householder< number >::diagonal
FullMatrix< double >	Householder< number >::storage

Detailed Description

These matrices are built on top of the basic matrices. They perform special operations using the interface defined by the MatrixType concept.

Typedef Documentation

size_type

template<typename number >

using Householder< number >::size_type = types::global_dof_index

Declare type of container size type.

Definition at line 85 of file householder.h.

Function Documentation

Householder() [1/2]

template<typename number >

Householder< number >::Householder ( )

default

Create an empty object.

Householder() [2/2]

template<typename number >

template<typename number2 >

Householder< number >::Householder

(

const FullMatrix< number2 > &

A

)

Create an object holding the QR-decomposition of the matrix \(A\).

initialize()

template<typename number >

template<typename number2 >

void Householder< number >::initialize

(

const FullMatrix< number2 > &

A

)

Compute the QR-decomposition of the given matrix \(A\).

This overwrites any previously computed QR decomposition.

least_squares() [1/2]

template<typename number >

template<typename number2 >

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

Solve the least-squares problem for the right hand side src. The returned scalar 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.

least_squares() [2/2]

template<typename number >

template<typename number2 >

double Householder< number >::least_squares	(	BlockVector< number2 > &	dst,
		const BlockVector< number2 > &	src
	)		const

This function does the same as the previous one, but for BlockVectors.

vmult()

template<typename number >

template<class VectorType >

void Householder< number >::vmult	(	VectorType &	dst,
		const VectorType &	src
	)		const

A wrapper to least_squares(), implementing the standard MatrixType interface.

Tvmult()

template<typename number >

template<class VectorType >

void Householder< number >::Tvmult	(	VectorType &	dst,
		const VectorType &	src
	)		const

A wrapper to least_squares() that implements multiplication with the transpose matrix.

Variable Documentation

diagonal

template<typename number >

std::vector<number> Householder< number >::diagonal

private

Storage for the diagonal elements of the orthogonal transformation. See the class documentation for more information.

Definition at line 151 of file householder.h.

storage

template<typename number >

FullMatrix<double> Householder< number >::storage

private

Storage that is internally used for the Householder transformation.

Definition at line 156 of file householder.h.