Householder< number > Class Template Reference

#include <deal.II/lac/householder.h>

Inheritance diagram for Householder< number >:

Public Types
typedef types::global_dof_index	size_type

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
template<typename number2 >
double	least_squares (BlockVector< number2 > &dst, const BlockVector< number2 > &src) const
template<class VectorType >
void	vmult (VectorType &dst, const VectorType &src) const

Private Attributes
std::vector< number >	diagonal
Private Attributes inherited from TableBase< N, T >
AlignedVector< T >	values
TableIndices< N >	table_size

Additional Inherited Members
Private Types inherited from FullMatrix< number >
typedef unsigned int	size_type
typedef number	value_type
typedef numbers::NumberTraits< number >::real_type	real_type
Private Types inherited from TableBase< N, T >
typedef AlignedVector< T >::size_type	size_type
Private Member Functions inherited from FullMatrix< number >
	FullMatrix (const size_type n=0)
	FullMatrix (const size_type rows, const size_type cols)
	FullMatrix (const size_type rows, const size_type cols, const number *entries)
	FullMatrix (const IdentityMatrix &id)
template<typename number2 >
FullMatrix< number > &	operator= (const FullMatrix< number2 > &)
FullMatrix< number > &	operator= (const number d)
FullMatrix< number > &	operator= (const IdentityMatrix &id)
template<typename number2 >
FullMatrix< number > &	operator= (const LAPACKFullMatrix< number2 > &)
template<typename MatrixType >
void	copy_from (const MatrixType &)
template<typename MatrixType >
void	copy_transposed (const MatrixType &)
template<int dim>
void	copy_from (const Tensor< 2, dim > &T, const size_type src_r_i=0, const size_type src_r_j=dim-1, const size_type src_c_i=0, const size_type src_c_j=dim-1, const size_type dst_r=0, const size_type dst_c=0)
template<int dim>
void	copy_to (Tensor< 2, dim > &T, const size_type src_r_i=0, const size_type src_r_j=dim-1, const size_type src_c_i=0, const size_type src_c_j=dim-1, const size_type dst_r=0, const size_type dst_c=0) const
template<typename MatrixType , typename index_type >
void	extract_submatrix_from (const MatrixType &matrix, const std::vector< index_type > &row_index_set, const std::vector< index_type > &column_index_set)
template<typename MatrixType , typename index_type >
void	scatter_matrix_to (const std::vector< index_type > &row_index_set, const std::vector< index_type > &column_index_set, MatrixType &matrix) const
template<typename number2 >
void	fill (const FullMatrix< number2 > &src, const size_type dst_offset_i=0, const size_type dst_offset_j=0, const size_type src_offset_i=0, const size_type src_offset_j=0)
template<typename number2 >
void	fill (const number2 *)
template<typename number2 >
void	fill_permutation (const FullMatrix< number2 > &src, const std::vector< size_type > &p_rows, const std::vector< size_type > &p_cols)
void	set (const size_type i, const size_type j, const number value)
bool	operator== (const FullMatrix< number > &) const
size_type	m () const
size_type	n () const
bool	all_zero () const
template<typename number2 >
number2	matrix_norm_square (const Vector< number2 > &v) const
template<typename number2 >
number2	matrix_scalar_product (const Vector< number2 > &u, const Vector< number2 > &v) const
real_type	l1_norm () const
real_type	linfty_norm () const
real_type	frobenius_norm () const
real_type	relative_symmetry_norm2 () const
number	determinant () const
number	trace () const
template<class StreamType >
void	print (StreamType &s, const unsigned int width=5, const unsigned int precision=2) const
void	print_formatted (std::ostream &out, const unsigned int precision=3, const bool scientific=true, const unsigned int width=0, const char *zero_string=" ", const double denominator=1., const double threshold=0.) const
std::size_t	memory_consumption () const
const_iterator	begin () const
const_iterator	end () const
const_iterator	begin (const size_type r) const
const_iterator	end (const size_type r) const
FullMatrix &	operator*= (const number factor)
FullMatrix &	operator/= (const number factor)
template<typename number2 >
void	add (const number a, const FullMatrix< number2 > &A)
template<typename number2 >
void	add (const number a, const FullMatrix< number2 > &A, const number b, const FullMatrix< number2 > &B)
template<typename number2 >
void	add (const number a, const FullMatrix< number2 > &A, const number b, const FullMatrix< number2 > &B, const number c, const FullMatrix< number2 > &C)
template<typename number2 >
void	add (const FullMatrix< number2 > &src, const number factor, const size_type dst_offset_i=0, const size_type dst_offset_j=0, const size_type src_offset_i=0, const size_type src_offset_j=0)
template<typename number2 >
void	Tadd (const number s, const FullMatrix< number2 > &B)
template<typename number2 >
void	Tadd (const FullMatrix< number2 > &src, const number factor, const size_type dst_offset_i=0, const size_type dst_offset_j=0, const size_type src_offset_i=0, const size_type src_offset_j=0)
void	add (const size_type row, const size_type column, const number value)
template<typename number2 , typename index_type >
void	add (const size_type row, const unsigned int n_cols, const index_type *col_indices, const number2 *values, const bool elide_zero_values=true, const bool col_indices_are_sorted=false)
void	add_row (const size_type i, const number s, const size_type j)
void	add_row (const size_type i, const number s, const size_type j, const number t, const size_type k)
void	add_col (const size_type i, const number s, const size_type j)
void	add_col (const size_type i, const number s, const size_type j, const number t, const size_type k)
void	swap_row (const size_type i, const size_type j)
void	swap_col (const size_type i, const size_type j)
void	diagadd (const number s)
template<typename number2 >
void	equ (const number a, const FullMatrix< number2 > &A)
template<typename number2 >
void	equ (const number a, const FullMatrix< number2 > &A, const number b, const FullMatrix< number2 > &B)
template<typename number2 >
void	equ (const number a, const FullMatrix< number2 > &A, const number b, const FullMatrix< number2 > &B, const number c, const FullMatrix< number2 > &C)
void	symmetrize ()
void	gauss_jordan ()
template<typename number2 >
void	invert (const FullMatrix< number2 > &M)
template<typename number2 >
void	cholesky (const FullMatrix< number2 > &A)
template<typename number2 >
void	outer_product (const Vector< number2 > &V, const Vector< number2 > &W)
template<typename number2 >
void	left_invert (const FullMatrix< number2 > &M)
template<typename number2 >
void	right_invert (const FullMatrix< number2 > &M)
template<typename number2 >
void	mmult (FullMatrix< number2 > &C, const FullMatrix< number2 > &B, const bool adding=false) const
template<typename number2 >
void	Tmmult (FullMatrix< number2 > &C, const FullMatrix< number2 > &B, const bool adding=false) const
template<typename number2 >
void	mTmult (FullMatrix< number2 > &C, const FullMatrix< number2 > &B, const bool adding=false) const
template<typename number2 >
void	TmTmult (FullMatrix< number2 > &C, const FullMatrix< number2 > &B, const bool adding=false) const
void	triple_product (const FullMatrix< number > &A, const FullMatrix< number > &B, const FullMatrix< number > &D, const bool transpose_B=false, const bool transpose_D=false, const number scaling=number(1.))
template<typename number2 >
void	vmult (Vector< number2 > &w, const Vector< number2 > &v, const bool adding=false) const
template<typename number2 >
void	vmult_add (Vector< number2 > &w, const Vector< number2 > &v) const
template<typename number2 >
void	Tvmult (Vector< number2 > &w, const Vector< number2 > &v, const bool adding=false) const
template<typename number2 >
void	Tvmult_add (Vector< number2 > &w, const Vector< number2 > &v) const
template<typename somenumber >
void	precondition_Jacobi (Vector< somenumber > &dst, const Vector< somenumber > &src, const number omega=1.) const
template<typename number2 , typename number3 >
number	residual (Vector< number2 > &dst, const Vector< number2 > &x, const Vector< number3 > &b) const
template<typename number2 >
void	forward (Vector< number2 > &dst, const Vector< number2 > &src) const
template<typename number2 >
void	backward (Vector< number2 > &dst, const Vector< number2 > &src) const
Private Member Functions inherited from TableBase< N, T >
	TableBase ()
	TableBase (const TableIndices< N > &sizes)
template<typename InputIterator >
	TableBase (const TableIndices< N > &sizes, InputIterator entries, const bool C_style_indexing=true)
	TableBase (const TableBase< N, T > &src)
template<typename T2 >
	TableBase (const TableBase< N, T2 > &src)
	TableBase (TableBase< N, T > &&src)
	~TableBase ()
TableBase< N, T > &	operator= (const TableBase< N, T > &src)
template<typename T2 >
TableBase< N, T > &	operator= (const TableBase< N, T2 > &src)
TableBase< N, T > &	operator= (TableBase< N, T > &&src)
bool	operator== (const TableBase< N, T > &T2) const
void	reset_values ()
void	reinit (const TableIndices< N > &new_size, const bool omit_default_initialization=false)
unsigned int	size (const unsigned int i) const
const TableIndices< N > &	size () const
size_type	n_elements () const
bool	empty () const
template<typename InputIterator >
void	fill (InputIterator entries, const bool C_style_indexing=true)
void	fill (const T &value)
AlignedVector< T >::reference	operator() (const TableIndices< N > &indices)
AlignedVector< T >::const_reference	operator() (const TableIndices< N > &indices) const
void	swap (TableBase< N, T > &v)
std::size_t	memory_consumption () const
template<class Archive >
void	serialize (Archive &ar, const unsigned int version)
size_type	position (const TableIndices< N > &indices) const
AlignedVector< T >::reference	el (const TableIndices< N > &indices)
AlignedVector< T >::const_reference	el (const TableIndices< N > &indices) const
Private Member Functions inherited from Subscriptor
	Subscriptor ()
	Subscriptor (const Subscriptor &)
	Subscriptor (Subscriptor &&)
virtual	~Subscriptor ()
Subscriptor &	operator= (const Subscriptor &)
Subscriptor &	operator= (Subscriptor &&)
void	subscribe (const char *identifier=0) const
void	unsubscribe (const char *identifier=0) const
unsigned int	n_subscriptions () const
void	list_subscribers () const
template<class Archive >
void	serialize (Archive &ar, const unsigned int version)
Static Private Member Functions inherited from FullMatrix< number >
static ::ExceptionBase &	ExcEmptyMatrix ()
static ::ExceptionBase &	ExcNotRegular (number arg1)
static ::ExceptionBase &	ExcInvalidDestination (size_type arg1, size_type arg2, size_type arg3)
static ::ExceptionBase &	ExcSourceEqualsDestination ()
static ::ExceptionBase &	ExcMatrixNotPositiveDefinite ()
Static Private Member Functions inherited from Subscriptor
static ::ExceptionBase &	ExcInUse (int arg1, char *arg2, std::string &arg3)
static ::ExceptionBase &	ExcNoSubscriber (char *arg1, char *arg2)

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

Definition at line 56 of file householder.h.

Member Typedef Documentation

size_type

template<typename number>

typedef types::global_dof_index Householder< number >::size_type

Declare type of container size.

Definition at line 62 of file householder.h.

Constructor & Destructor Documentation

Householder() [1/2]

template<typename number>

Householder< number >::Householder

(

)

Create an empty object.

Householder() [2/2]

template<typename number>

template<typename number2 >

Householder< number >::Householder

(

const FullMatrix< number2 > &

)

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

Member Function Documentation

initialize()

template<typename number>

template<typename number2 >

void Householder< number >::initialize

(

const FullMatrix< number2 > &

)

Compute the QR-decomposition of another matrix.

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 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.

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 one 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.

Member Data Documentation

diagonal

template<typename number>

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

private

Storage for the diagonal elements of the orthogonal transformation.

Definition at line 118 of file householder.h.

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

• deal.II/lac/householder.h