MathTL::InfiniteVector< C, I > Class Template Reference

#include <infinite_vector.h>

Inheritance diagram for MathTL::InfiniteVector< C, I >:

List of all members.

Classes
class	const_iterator
class	const_reverse_iterator
struct	decreasing_order
Public Member Functions
	InfiniteVector ()
	InfiniteVector (const InfiniteVector< C, I > &v)
const_iterator	begin () const
const_iterator	end () const
const_reverse_iterator	rbegin () const
const_reverse_iterator	rend () const
InfiniteVector< C, I > &	operator= (const InfiniteVector< C, I > &v)
void	swap (InfiniteVector< C, I > &v)
bool	empty () const
void	clear ()
bool	operator== (const InfiniteVector< C, I > &v) const
bool	operator!= (const InfiniteVector< C, I > &v) const
C	operator[] (const I &index) const
C	get_coefficient (const I &index) const
C &	operator[] (const I &index)
void	set_coefficient (const I &index, const C value)
size_t	size () const
void	support (std::set< I > &supp) const
void	clip (const std::set< I > &supp)
void	compress (const double eta=1e-15)
void	add_coefficient (const I &index, const C increment)
void	add (const InfiniteVector< C, I > &v)
void	add (const C s, const InfiniteVector< C, I > &v)
void	sadd (const C s, const InfiniteVector< C, I > &v)
void	scale (const C s)
void	scale (const InfiniteDiagonalMatrix< C, I > *D, const int k=1)
InfiniteVector< C, I > &	operator+= (const InfiniteVector< C, I > &v)
void	subtract (const InfiniteVector< C, I > &v)
InfiniteVector< C, I > &	operator-= (const InfiniteVector< C, I > &v)
InfiniteVector< C, I > &	operator*= (const C c)
InfiniteVector< C, I > &	operator/= (const C c)
const C	operator* (const InfiniteVector< C, I > &v) const
double	weak_norm (const double tau) const
void	COARSE (const double eps, InfiniteVector< C, I > &v) const
const double	wrmsqr_norm (const double atol, const double rtol, const InfiniteVector< C, I > &v, const InfiniteVector< C, I > &w) const

---

Detailed Description

template<class C, class I = int>
class MathTL::InfiniteVector< C, I >

A model class InfiniteVector<C,I> for inherently sparse, arbitrarily indexed vectors x = (x_i)_{i I} with entries from a (scalar) class C. InfiniteVector<C,I> may act as a realization of coefficient_type in the WaveletTL.

Although internally, we will model InfiniteVector as a map<I,C>, the access to the vector entries takes place by a nested iterator class (compare the deal.II matrix classes) which is STL-compatible.

---

Constructor & Destructor Documentation

template<class C , class I >

MathTL::InfiniteVector< C, I >::InfiniteVector

(

)

default constructor: yields empty (zero) vector

template<class C, class I>

MathTL::InfiniteVector< C, I >::InfiniteVector

(

const InfiniteVector< C, I > &

v

)

copy constructor

---

Member Function Documentation

template<class C, class I>

void MathTL::InfiniteVector< C, I >::add

(

const InfiniteVector< C, I > &

v

)

in place summation *this += v

template<class C, class I>

void MathTL::InfiniteVector< C, I >::add	(	const C	s,
		const InfiniteVector< C, I > &	v
	)

in place summation *this += s*v

template<class C, class I>

void MathTL::InfiniteVector< C, I >::add_coefficient	(	const I &	index,
		const C	increment
	)

add a value to a vector entry

template<class C , class I >

InfiniteVector< C, I >::const_iterator MathTL::InfiniteVector< C, I >::begin

(

)

const [inline]

const_iterator pointing to the first nontrivial vector entry

Reimplemented in MathTL::LaurentPolynomial< R >, and MathTL::MultivariateLaurentPolynomial< R, DIMENSION >.

template<class C , class I >

void MathTL::InfiniteVector< C, I >::clear

(

)

[inline]

set infinite vector to zero

template<class C , class I>

void MathTL::InfiniteVector< C, I >::clip

(

const std::set< I > &

supp

)

clip the infinite vector to a given support set

template<class C, class I>

void MathTL::InfiniteVector< C, I >::COARSE	(	const double	eps,
		InfiniteVector< C, I > &	v
	)		const

Computes optimal v such that \|*this-v\|_{}; "optimal" means taking the largest entries in modulus of *this. The vector v does not have to be initialized, it will be cleared at the beginning of the algorithm

template<class C , class I >

void MathTL::InfiniteVector< C, I >::compress

(

const double

eta = 1e-15

)

set all values with modulus strictly below a threshold to zero (fabs<C> should exist)

template<class C, class I = int>

bool MathTL::InfiniteVector< C, I >::empty

(

)

const [inline]

test emptyness

template<class C , class I >

InfiniteVector< C, I >::const_iterator MathTL::InfiniteVector< C, I >::end

(

)

const [inline]

const_iterator pointing to one after the last nontrivial vector entry

Reimplemented in MathTL::LaurentPolynomial< R >, and MathTL::MultivariateLaurentPolynomial< R, DIMENSION >.

template<class C , class I>

C MathTL::InfiniteVector< C, I >::get_coefficient

(

const I &

index

)

const

read-only access to the vector entries

Reimplemented in MathTL::MultivariateLaurentPolynomial< R, DIMENSION >.

template<class C, class I>

bool MathTL::InfiniteVector< C, I >::operator!=

(

const InfiniteVector< C, I > &

v

)

const [inline]

non-equality test

template<class C, class I>

const C MathTL::InfiniteVector< C, I >::operator*

(

const InfiniteVector< C, I > &

v

)

const

inner product

template<class C, class I >

InfiniteVector< C, I > & MathTL::InfiniteVector< C, I >::operator*=

(

const C

c

)

in place multiplication with a scalar

Reimplemented in MathTL::LaurentPolynomial< R >, and MathTL::MultivariateLaurentPolynomial< R, DIMENSION >.

template<class C, class I>

InfiniteVector< C, I > & MathTL::InfiniteVector< C, I >::operator+=

(

const InfiniteVector< C, I > &

v

)

[inline]

in place summation

template<class C, class I>

InfiniteVector< C, I > & MathTL::InfiniteVector< C, I >::operator-=

(

const InfiniteVector< C, I > &

v

)

[inline]

in place subtraction

template<class C, class I >

InfiniteVector< C, I > & MathTL::InfiniteVector< C, I >::operator/=

(

const C

c

)

in place division by a (nontrivial) scalar

template<class C, class I>

InfiniteVector< C, I > & MathTL::InfiniteVector< C, I >::operator=

(

const InfiniteVector< C, I > &

v

)

assignment from another vector

template<class C, class I>

bool MathTL::InfiniteVector< C, I >::operator==

(

const InfiniteVector< C, I > &

v

)

const [inline]

equality test

template<class C , class I>

C MathTL::InfiniteVector< C, I >::operator[]

(

const I &

index

)

const [inline]

read-only access to the vector entries

template<class C , class I>

C & MathTL::InfiniteVector< C, I >::operator[]

(

const I &

index

)

read-write access to the vector entries

template<class C , class I >

InfiniteVector< C, I >::const_reverse_iterator MathTL::InfiniteVector< C, I >::rbegin

(

)

const

const_reverse_iterator pointing to the last nontrivial vector entry

Reimplemented in MathTL::LaurentPolynomial< R >, and MathTL::MultivariateLaurentPolynomial< R, DIMENSION >.

template<class C , class I >

InfiniteVector< C, I >::const_reverse_iterator MathTL::InfiniteVector< C, I >::rend

(

)

const

const_reverse_iterator pointing to one before the first last nontrivial vector entry

Reimplemented in MathTL::LaurentPolynomial< R >, and MathTL::MultivariateLaurentPolynomial< R, DIMENSION >.

template<class C, class I>

void MathTL::InfiniteVector< C, I >::sadd	(	const C	s,
		const InfiniteVector< C, I > &	v
	)

in place summation *this = s*(*this) + v (AXPY level 1 BLAS routine)

template<class C, class I >

void MathTL::InfiniteVector< C, I >::scale

(

const C

s

)

in place scaling *this *= s

template<class C, class I>

void MathTL::InfiniteVector< C, I >::scale	(	const InfiniteDiagonalMatrix< C, I > *	D,
		const int	k = 1
	)

in place scaling with a diagonal matrix, *this = D^k (*this)

template<class C, class I>

void MathTL::InfiniteVector< C, I >::set_coefficient	(	const I &	index,
		const C	value
	)

set a vector entry

Reimplemented in MathTL::MultivariateLaurentPolynomial< R, DIMENSION >.

template<class C , class I >

size_t MathTL::InfiniteVector< C, I >::size

(

)

const [inline]

number of nonzero entries

template<class C, class I>

void MathTL::InfiniteVector< C, I >::subtract

(

const InfiniteVector< C, I > &

v

)

in place subtraction *this -= v

template<class C , class I>

void MathTL::InfiniteVector< C, I >::support

(

std::set< I > &

supp

)

const

return support of the current vector as a set

template<class C, class I>

void MathTL::InfiniteVector< C, I >::swap

(

InfiniteVector< C, I > &

v

)

[inline]

swap components of two vectors

template<class C , class I >

double MathTL::InfiniteVector< C, I >::weak_norm

(

const double

tau

)

const

weak l_tau norm

template<class C, class I>

const double MathTL::InfiniteVector< C, I >::wrmsqr_norm	(	const double	atol,
		const double	rtol,
		const InfiniteVector< C, I > &	v,
		const InfiniteVector< C, I > &	w
	)		const

Computes v such that \|*this-v\|_{}; In contrast to the usual coarse routine, here the This routine is a suggestion from Rob Stevenson.

weighted root mean square norm ||x||_{v,w} = (1/n * sum_i |x_i|^2 / (atol+max(|v_i|,|w_i|)*rtol)^2)^{1/2}

(this has to be modeled as a member function, since partial specialization of template functions is not allowed in C++)

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

• algebra/infinite_vector.h
• algebra/infinite_vector.cpp