VECTOR Namespace Reference

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Detailed Description

Module for generic functions on vectors.

Generic implementations for vectors are gathered in the namespace {VECTOR}. These are generic functions, that can be used to build new linear classes. The type {R} must provide the following definitions or methods: {SIGNATURE} typename index_t; typename value_type; typename iterator; typename const_iterator;

index_t this->size(); value_type this->operator[](index_t);

iterator begin(); iterator end(); const_iterator begin() const; const_iterator end() const; {SIGNATURE}

Functions
template<class OS, class R>
OS &	print (OS &os, const R &v)
	Output function for general vectors: [v1, v2, ...].
template<class OS, class R>
OS &	print (OS &os, const R &v, unsigned sz)
	Output function for general vectors: [v1, v2, ...].
template<class IS, class R>
IS &	read (IS &is, R &V)
template<class V1, class V2>
bool	equal_n (const V1 &v1, const V2 &v2, int n)
template<class V1, class V2>
bool	equal (const V1 &v1, const V2 &v2)
template<class V, class C>
void	init_n (V &a, const C &v, int n)
template<class V, class C>
void	init (V &a, const C &v)
	Set all the entries of a to the values v.
template<class V>
void	reverse_n (V &v, int a, int n)
	Reverse the entries of v, from the index a to n-1.
template<class V>
void	reverse (V &v, int n)
template<class V, class I>
void	reverse (V &v, I d)
	Reverse the entries of v, from the index 0 to d-1.
template<class V, class W>
void	neg_range (V &r, const W &w, int a, int b)
template<class V, class W>
void	neg_range (V &r, int a, int b)
template<class VI>
void	neg_i (VI a, VI eda)
template<class VI>
void	neg_i (VI a, VI eda, VI b)
template<class V>
void	neg (V &v)
template<class V>
void	neg (V &a, const V &b)
template<class V, class W>
void	copy_range (V &v, const W &w, int a, int b)
template<class V, class W>
void	add_n (V &a, const W &b, int n)
template<class VI, class WI>
void	add_i (VI a, VI ea, WI b)
template<class V, class W>
void	add (V &a, const W &b)
	Addition of two vectors.
template<class V, class W, class X>
void	add_n (V &a, const W &b, const X &c, int n)
template<class V, class W, class X>
void	add_g (V &r, const W &a, const X &b)
template<class V, class W, class X>
void	add (V &r, const W &a, const X &b)
template<class V>
void	add (V &r, const V &a, const V &b)
template<class V, class W>
void	sub_n (V &a, const W &b, int n)
template<class V, class W>
void	sub (V &a, const W &b)
	Substraction of two vectors.
template<class V, class W, class X>
void	sub_n (V &a, const W &b, const X &c, int n)
template<class V, class W, class X>
void	sub_g (V &r, const W &a, const X &b)
template<class V, class W, class X>
void	sub (V &r, const W &a, const X &b)
template<class V>
void	sub (V &r, const V &a, const V &b)
template<class V, class W>
void	mul_ext_n (V &a, const W &c, int n)
template<class V, class W, class S>
void	mul_ext_n (V &a, const W &b, const S &c, int n)
template<class VI, class W>
void	mul_ext_i (VI bga, VI eda, const W &c)
template<class VI, class VII, class W>
void	mul_ext_i (VI bga, VI eda, VII bgb, const W &c)
template<class V, class W>
void	mul_ext (V &a, const V &b, const W &c)
	Scalar multiplication.
template<class V, class SC>
void	div_ext_n (V &a, const SC &sc, int n)
template<class V1, class V2, class SC>
void	div_ext_n (V1 &a, const V2 &b, const SC &sc, int n)
template<class VI, class SC>
void	div_ext_i (VI bga, VI eda, const SC &sc)
template<class VI, class SC>
void	div_ext_i (VI a, VI eda, VI b, const SC &sc)
template<class V, class SC>
void	div_ext (V &a, const V &b, const SC &sc)
	Scalar division.
template<class V, class W>
void	div_ext (V &a, const W &c)
	Scalar division.
template<class V, class W>
void	div (V &a, const W &c)
	Inplace scalar division.
template<class R, class S, class C>
void	apply_mult (R &result, const S &a, const C &m)
template<class C, class R>
C	norm (const R &v)
	The $L_{2}$ norm for vectors.
template<class C, class R>
C	norm (const R &v, int p)
	Norm $L_{p}$ of a vector.
template<class R, class S>
R::value_type	innerprod_n (const S &v, const R &w, unsigned n)
	Innerproduct of two vectors.
template<class R, class S>
R::value_type	innerprod (const S &v, const R &w)
template<class R>
R::value_type	max_abs (const R &v)
template<class Ia, class Ib>
void	assign_i (Ia a, Ia eda, Ib b)
template<class Ra, class Rb>
void	assign (Ra &a, const Rb &b)
template<class R, class C>
void	vaddsc (R &r, const C &x)

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Function Documentation

template<class V>

void VECTOR::add	(	V &	r,
		const V &	a,
		const V &	b
	)

Specialisation of the function add when W=V. Inplace addition is used when r=a or r=b.

Definition at line 201 of file VECTOR.m.

References add(), and add_g().

template<class V, class W, class X>

void VECTOR::add	(	V &	r,
		const W &	a,
		const X &	b
	)

Addition of two vectors. r should be allocated to the correct size and with 0 entries.

Definition at line 193 of file VECTOR.m.

References add_g().

template<class V, class W>

void VECTOR::add	(	V &	a,
		const W &	b
	)

Addition of two vectors.

Definition at line 150 of file VECTOR.m.

References add_i(), and copy_range().

Referenced by add(), and add().

template<class V, class W, class X>

void VECTOR::add_g	(	V &	r,
		const W &	a,
		const X &	b
	)

Addition of two vectors. r should be allocated to the correct size and with 0 entries.

Definition at line 171 of file VECTOR.m.

References add_n(), and copy_range().

Referenced by add().

template<class V, class W>

void VECTOR::div	(	V &	a,
		const W &	c
	)

Inplace scalar division.

Definition at line 324 of file VECTOR.m.

References div_ext().

template<class V, class W>

void VECTOR::div_ext	(	V &	a,
		const W &	c
	)

Scalar division.

Definition at line 319 of file VECTOR.m.

References div_ext_i().

template<class V, class SC>

void VECTOR::div_ext	(	V &	a,
		const V &	b,
		const SC &	sc
	)

Scalar division.

Definition at line 309 of file VECTOR.m.

References div_ext_i().

Referenced by div(), div(), and quotient::ModUPol< C, R >::mul().

template<class V, class C>

void VECTOR::init	(	V &	a,
		const C &	v
	)

Set all the entries of a to the values v.

Definition at line 102 of file VECTOR.m.

References init_n().

Referenced by projection::eval_to_double(), quotient::ModUPol< C, R >::horner_to_monomial(), quotient::ModUPol< C, R >::monomial_to_horner(), UPOLDAR::mul(), UPOLDAR::mul_index(), UPOLDAR::set_monomial(), quotient::ModUPol< C, R >::square(), and UPolDse< C, R >::UPolDse().

template<class R, class S>

R::value_type VECTOR::innerprod_n	(	const S &	v,
		const R &	w,
		unsigned	n
	)

Innerproduct of two vectors.

Definition at line 361 of file VECTOR.m.

template<class V, class W>

void VECTOR::mul_ext	(	V &	a,
		const V &	b,
		const W &	c
	)

Scalar multiplication.

Definition at line 284 of file VECTOR.m.

References mul_ext_i().

Referenced by mul().

template<class C, class R>

C VECTOR::norm	(	const R &	v,
		int	p
	)

Norm $L_{p}$ of a vector.

Definition at line 352 of file VECTOR.m.

template<class C, class R>

C VECTOR::norm

(

const R &

v

)

The $L_{2}$ norm for vectors.

Definition at line 343 of file VECTOR.m.

template<class OS, class R>

OS& VECTOR::print	(	OS &	os,
		const R &	v,
		unsigned	sz
	)

Output function for general vectors: [v1, v2, ...].

Definition at line 56 of file VECTOR.m.

template<class OS, class R>

OS& VECTOR::print	(	OS &	os,
		const R &	v
	)

Output function for general vectors: [v1, v2, ...].

Definition at line 43 of file VECTOR.m.

Referenced by bezier::sbd2d< X, C, USLV >::connect_xy(), and operator<<().

template<class IS, class R>

IS& VECTOR::read	(	IS &	is,
		R &	V
	)

Input operator for standard vectors. The input format is of the form s c0 c1 ... where s is the number of elements.

Definition at line 72 of file VECTOR.m.

template<class V, class I>

void VECTOR::reverse	(	V &	v,
		I	d
	)

Reverse the entries of v, from the index 0 to d-1.

Definition at line 118 of file VECTOR.m.

template<class V>

void VECTOR::reverse_n	(	V &	v,
		int	a,
		int	n
	)

Reverse the entries of v, from the index a to n-1.

Definition at line 107 of file VECTOR.m.

Referenced by reverse().

template<class V>

void VECTOR::sub	(	V &	r,
		const V &	a,
		const V &	b
	)

Specialisation of the sub function when W=V. Inplace substraction is used when r=a or r=b.

Definition at line 262 of file VECTOR.m.

References sub(), and sub_g().

template<class V, class W, class X>

void VECTOR::sub	(	V &	r,
		const W &	a,
		const X &	b
	)

Substraction of two vectors. r should be allocated to the correct size and with 0 entries.

Definition at line 254 of file VECTOR.m.

References sub_g().

template<class V, class W>

void VECTOR::sub	(	V &	a,
		const W &	b
	)

Substraction of two vectors.

Definition at line 214 of file VECTOR.m.

References neg_range(), and sub_n().

Referenced by sub(), and sub().