Class defining operators for a multi-field with "consecutive" characteristic range. More...

#include <gudhi/Fields/Multi_field_operators.h>

Public Types
using	Element = mpz_class

using	Characteristic = Element

Public Member Functions
	Multi_field_operators ()
	Default constructor, sets the product of all characteristics to 0.

	Multi_field_operators (int minCharacteristic, int maxCharacteristic)
	Constructor setting the characteristics to all prime numbers between the two given integers. More...

	Multi_field_operators (const Multi_field_operators &toCopy)
	Copy constructor. More...

	Multi_field_operators (Multi_field_operators &&toMove) noexcept
	Move constructor. More...

void	set_characteristic (int minimum, int maximum)
	Set the characteristics of the field, which are stored in a single value as a product of all of them. The characteristics will be all prime numbers in the given interval. More...

const Characteristic &	get_characteristic () const
	Returns the current characteristics as the product of all of them. More...

Element	get_value (Element e) const
	Returns the value of an element in the field. That is the positive value of the integer modulo the current characteristic. More...

void	get_value_inplace (Element &e) const
	Stores in the given element the value of this element in the field. That is the positive value of the integer modulo the current characteristic. More...

Element	add (Element e1, const Element &e2) const
	Returns the sum of two elements in the field. More...

void	add_inplace (Element &e1, const Element &e2) const
	Stores in the first element the sum of two given elements in the field, that is `(e1 + e2) % productOfAllCharacteristics`, such that the result is positive. More...

Element	subtract (Element e1, const Element &e2) const
	Returns the subtraction in the field of the first element by the second element. More...

void	subtract_inplace_front (Element &e1, const Element &e2) const
	Stores in the first element the subtraction in the field of the first element by the second element, that is `(e1 - e2) % productOfAllCharacteristics`, such that the result is positive. More...

void	subtract_inplace_back (const Element &e1, Element &e2) const
	Stores in the second element the subtraction in the field of the first element by the second element, that is `(e1 - e2) % productOfAllCharacteristics`, such that the result is positive. More...

Element	multiply (Element e1, const Element &e2) const
	Returns the multiplication of two elements in the field. More...

void	multiply_inplace (Element &e1, const Element &e2) const
	Stores in the first element the multiplication of two given elements in the field, that is `(e1 * e2) % productOfAllCharacteristics`, such that the result is positive. More...

Element	multiply_and_add (Element e, const Element &m, const Element &a) const
	Multiplies the first element with the second one and adds the third one. Returns the result in the field. More...

void	multiply_and_add_inplace_front (Element &e, const Element &m, const Element &a) const
	Multiplies the first element with the second one and adds the third one, that is `(e * m + a) % productOfAllCharacteristics`, such that the result is positive. Stores the result in the first element. More...

void	multiply_and_add_inplace_back (const Element &e, const Element &m, Element &a) const
	Multiplies the first element with the second one and adds the third one, that is `(e * m + a) % productOfAllCharacteristics`, such that the result is positive. Stores the result in the third element. More...

Element	add_and_multiply (Element e, const Element &a, const Element &m) const
	Adds the first element to the second one and multiplies the third one with it. Returns the result in the field. More...

void	add_and_multiply_inplace_front (Element &e, const Element &a, const Element &m) const
	Adds the first element to the second one and multiplies the third one with it, that is `((e + a) * m) % productOfAllCharacteristics`, such that the result is positive. Stores the result in the first element. More...

void	add_and_multiply_inplace_back (const Element &e, const Element &a, Element &m) const
	Adds the first element to the second one and multiplies the third one with it, that is `((e + a) * m) % productOfAllCharacteristics`, such that the result is positive. Stores the result in the third element. More...

bool	are_equal (const Element &e1, const Element &e2) const
	Returns true if the two given elements are equal in the field, false otherwise. More...

Element	get_inverse (const Element &e) const
	Returns the inverse of the given element in the sense of [6] with respect to the product of all characteristics. More...

std::pair< Element, Characteristic >	get_partial_inverse (const Element &e, const Characteristic &productOfCharacteristics) const
	Returns the inverse of the given element in the multi-field corresponding to the given sub-product of the product of all characteristics in the multi-field. See [6] for more details. More...

Element	get_partial_multiplicative_identity (const Characteristic &productOfCharacteristics) const
	Returns the partial multiplicative identity of the multi-field from the given product. See [6] for more details. More...

Multi_field_operators &	operator= (Multi_field_operators other)
	Assign operator.

Static Public Member Functions
static const Element &	get_additive_identity ()
	Returns the additive identity of a field. More...

static const Element &	get_multiplicative_identity ()
	Returns the multiplicative identity of a field. More...

Friends
void	swap (Multi_field_operators &f1, Multi_field_operators &f2)
	Swap operator.

Detailed Description

Class defining operators for a multi-field with "consecutive" characteristic range.

Member Typedef Documentation

◆ Characteristic

using Gudhi::persistence_fields::Multi_field_operators::Characteristic = Element

Type for the field characteristic.

◆ Element

using Gudhi::persistence_fields::Multi_field_operators::Element = mpz_class

Type for the elements in the field.

Constructor & Destructor Documentation

◆ Multi_field_operators() [1/3]

Gudhi::persistence_fields::Multi_field_operators::Multi_field_operators	(	int	minCharacteristic,
		int	maxCharacteristic
	)

inline

Constructor setting the characteristics to all prime numbers between the two given integers.

Parameters

minCharacteristic	Smallest value of a prime.
maxCharacteristic	Highest value of a prime.

◆ Multi_field_operators() [2/3]

Gudhi::persistence_fields::Multi_field_operators::Multi_field_operators ( const Multi_field_operators & toCopy )

inline

Copy constructor.

Parameters

toCopy Operators to copy.

◆ Multi_field_operators() [3/3]

Gudhi::persistence_fields::Multi_field_operators::Multi_field_operators ( Multi_field_operators && toMove )

inlinenoexcept

Move constructor.

Parameters

toMove Operators to move.

Member Function Documentation

◆ add()

Element Gudhi::persistence_fields::Multi_field_operators::add	(	Element	e1,
		const Element &	e2
	)		const

inline

Returns the sum of two elements in the field.

Parameters

e1	First element.
e2	Second element.

Returns: (e1 + e2) % productOfAllCharacteristics, such that the result is positive.

◆ add_and_multiply()

Element Gudhi::persistence_fields::Multi_field_operators::add_and_multiply	(	Element	e,
		const Element &	a,
		const Element &	m
	)		const

inline

Adds the first element to the second one and multiplies the third one with it. Returns the result in the field.

Parameters

e	First element.
a	Second element.
m	Third element.

Returns: ((e + a) * m) % productOfAllCharacteristics, such that the result is positive.

◆ add_and_multiply_inplace_back()

void Gudhi::persistence_fields::Multi_field_operators::add_and_multiply_inplace_back	(	const Element &	e,
		const Element &	a,
		Element &	m
	)		const

inline

Adds the first element to the second one and multiplies the third one with it, that is ((e + a) * m) % productOfAllCharacteristics, such that the result is positive. Stores the result in the third element.

Parameters

e	First element.
a	Second element.
m	Third element.

◆ add_and_multiply_inplace_front()

void Gudhi::persistence_fields::Multi_field_operators::add_and_multiply_inplace_front	(	Element &	e,
		const Element &	a,
		const Element &	m
	)		const

inline

Adds the first element to the second one and multiplies the third one with it, that is ((e + a) * m) % productOfAllCharacteristics, such that the result is positive. Stores the result in the first element.

Parameters

e	First element.
a	Second element.
m	Third element.

◆ add_inplace()

void Gudhi::persistence_fields::Multi_field_operators::add_inplace	(	Element &	e1,
		const Element &	e2
	)		const

inline

Stores in the first element the sum of two given elements in the field, that is (e1 + e2) % productOfAllCharacteristics, such that the result is positive.

Parameters

e1	First element.
e2	Second element.

◆ are_equal()

bool Gudhi::persistence_fields::Multi_field_operators::are_equal	(	const Element &	e1,
		const Element &	e2
	)		const

inline

Returns true if the two given elements are equal in the field, false otherwise.

Parameters

e1	First element to compare.
e2	Second element to compare.

Returns: true If e1 % productOfAllCharacteristics == e2 % productOfAllCharacteristics.; false Otherwise.

◆ get_additive_identity()

static const Element & Gudhi::persistence_fields::Multi_field_operators::get_additive_identity ( )

inlinestatic

Returns the additive identity of a field.

Returns: The additive identity of a field.

◆ get_characteristic()

const Characteristic & Gudhi::persistence_fields::Multi_field_operators::get_characteristic ( ) const

inline

Returns the current characteristics as the product of all of them.

Returns: The value of the current characteristic.

◆ get_inverse()

Element Gudhi::persistence_fields::Multi_field_operators::get_inverse ( const Element & e ) const

inline

Returns the inverse of the given element in the sense of [6] with respect to the product of all characteristics.

Parameters

e	Element to get the inverse from.

Returns: Inverse in the current field.

◆ get_multiplicative_identity()

static const Element & Gudhi::persistence_fields::Multi_field_operators::get_multiplicative_identity ( )

inlinestatic

Returns the multiplicative identity of a field.

Returns: The multiplicative identity of a field.

◆ get_partial_inverse()

std::pair< Element, Characteristic > Gudhi::persistence_fields::Multi_field_operators::get_partial_inverse	(	const Element &	e,
		const Characteristic &	productOfCharacteristics
	)		const

inline

Returns the inverse of the given element in the multi-field corresponding to the given sub-product of the product of all characteristics in the multi-field. See [6] for more details.

Parameters

e	Element to get the inverse from.
productOfCharacteristics	Product of the different characteristics to take into account in the multi-field.

Returns: Pair of the inverse of e and the characteristic the inverse is coming from.

◆ get_partial_multiplicative_identity()

Element Gudhi::persistence_fields::Multi_field_operators::get_partial_multiplicative_identity ( const Characteristic & productOfCharacteristics ) const

inline

Returns the partial multiplicative identity of the multi-field from the given product. See [6] for more details.

Parameters

productOfCharacteristics Product of the different characteristics to take into account in the multi-field.

Returns: The partial multiplicative identity of the multi-field.

◆ get_value()

Element Gudhi::persistence_fields::Multi_field_operators::get_value ( Element e ) const

inline

Returns the value of an element in the field. That is the positive value of the integer modulo the current characteristic.

Parameters

e	Element to return the value from.

Returns: e modulo the current characteristic, such that the result is positive.

◆ get_value_inplace()

void Gudhi::persistence_fields::Multi_field_operators::get_value_inplace ( Element & e ) const

inline

Stores in the given element the value of this element in the field. That is the positive value of the integer modulo the current characteristic.

Parameters

e	Element to return the value from.

◆ multiply()

Element Gudhi::persistence_fields::Multi_field_operators::multiply	(	Element	e1,
		const Element &	e2
	)		const

inline

Returns the multiplication of two elements in the field.

Parameters

e1	First element.
e2	Second element.

Returns: (e1 * e2) % productOfAllCharacteristics, such that the result is positive.

◆ multiply_and_add()

Element Gudhi::persistence_fields::Multi_field_operators::multiply_and_add	(	Element	e,
		const Element &	m,
		const Element &	a
	)		const

inline

Multiplies the first element with the second one and adds the third one. Returns the result in the field.

Parameters

e	First element.
m	Second element.
a	Third element.

Returns: (e * m + a) % productOfAllCharacteristics, such that the result is positive.

◆ multiply_and_add_inplace_back()

void Gudhi::persistence_fields::Multi_field_operators::multiply_and_add_inplace_back	(	const Element &	e,
		const Element &	m,
		Element &	a
	)		const

inline

Multiplies the first element with the second one and adds the third one, that is (e * m + a) % productOfAllCharacteristics, such that the result is positive. Stores the result in the third element.

Parameters

e	First element.
m	Second element.
a	Third element.

◆ multiply_and_add_inplace_front()

void Gudhi::persistence_fields::Multi_field_operators::multiply_and_add_inplace_front	(	Element &	e,
		const Element &	m,
		const Element &	a
	)		const

inline

Multiplies the first element with the second one and adds the third one, that is (e * m + a) % productOfAllCharacteristics, such that the result is positive. Stores the result in the first element.

Parameters

e	First element.
m	Second element.
a	Third element.

◆ multiply_inplace()

void Gudhi::persistence_fields::Multi_field_operators::multiply_inplace	(	Element &	e1,
		const Element &	e2
	)		const

inline

Stores in the first element the multiplication of two given elements in the field, that is (e1 * e2) % productOfAllCharacteristics, such that the result is positive.

Parameters

e1	First element.
e2	Second element.

◆ set_characteristic()

void Gudhi::persistence_fields::Multi_field_operators::set_characteristic	(	int	minimum,
		int	maximum
	)

inline

Set the characteristics of the field, which are stored in a single value as a product of all of them. The characteristics will be all prime numbers in the given interval.

Parameters

minimum	Smallest value of a prime.
maximum	Highest value of a prime.

◆ subtract()

Element Gudhi::persistence_fields::Multi_field_operators::subtract	(	Element	e1,
		const Element &	e2
	)		const

inline

Returns the subtraction in the field of the first element by the second element.

Parameters

e1	First element.
e2	Second element.

Returns: (e1 - e2) % productOfAllCharacteristics, such that the result is positive.

◆ subtract_inplace_back()

void Gudhi::persistence_fields::Multi_field_operators::subtract_inplace_back	(	const Element &	e1,
		Element &	e2
	)		const

inline

Stores in the second element the subtraction in the field of the first element by the second element, that is (e1 - e2) % productOfAllCharacteristics, such that the result is positive.

Parameters

e1	First element.
e2	Second element.

◆ subtract_inplace_front()

void Gudhi::persistence_fields::Multi_field_operators::subtract_inplace_front	(	Element &	e1,
		const Element &	e2
	)		const

inline

Stores in the first element the subtraction in the field of the first element by the second element, that is (e1 - e2) % productOfAllCharacteristics, such that the result is positive.

Parameters

e1	First element.
e2	Second element.

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

include/gudhi/Fields/Multi_field_operators.h

Public Types

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Member Typedef Documentation

◆ Characteristic

◆ Element

Constructor & Destructor Documentation

◆ Multi_field_operators() [1/3]

◆ Multi_field_operators() [2/3]

◆ Multi_field_operators() [3/3]

Member Function Documentation

◆ add()

◆ add_and_multiply()

◆ add_and_multiply_inplace_back()

◆ add_and_multiply_inplace_front()

◆ add_inplace()

◆ are_equal()

◆ get_additive_identity()

◆ get_characteristic()

◆ get_inverse()

◆ get_multiplicative_identity()

◆ get_partial_inverse()

◆ get_partial_multiplicative_identity()

◆ get_value()

◆ get_value_inplace()

◆ multiply()

◆ multiply_and_add()

◆ multiply_and_add_inplace_back()

◆ multiply_and_add_inplace_front()

◆ multiply_inplace()

◆ set_characteristic()

◆ subtract()

◆ subtract_inplace_back()

◆ subtract_inplace_front()