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

Public Types
using	element_type = mpz_class

using	characteristic_type = element_type

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

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

void	add_inplace (element_type &e1, const element_type &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_type	substract (element_type e1, const element_type &e2) const
	Returns the substraction in the field of the first element by the second element. More...

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

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

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

void	multiply_inplace (element_type &e1, const element_type &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_type	multiply_and_add (element_type e, const element_type &m, const element_type &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_type &e, const element_type &m, const element_type &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_type &e, const element_type &m, element_type &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_type	add_and_multiply (element_type e, const element_type &a, const element_type &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_type &e, const element_type &a, const element_type &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_type &e, const element_type &a, element_type &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_type &e1, const element_type &e2) const
	Returns true if the two given elements are equal in the field, false otherwise. More...

element_type	get_inverse (const element_type &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_type, characteristic_type >	get_partial_inverse (const element_type &e, const characteristic_type &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_type	get_partial_multiplicative_identity (const characteristic_type &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_type &	get_additive_identity ()
	Returns the additive identity of a field. More...

static const element_type &	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" charateristic range.

Member Typedef Documentation

◆ characteristic_type

using Gudhi::persistence_fields::Multi_field_operators::characteristic_type = element_type

Type for the field characteristic.

◆ element_type

using Gudhi::persistence_fields::Multi_field_operators::element_type = 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	Heighest 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_type Gudhi::persistence_fields::Multi_field_operators::add	(	element_type	e1,
		const element_type &	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_type Gudhi::persistence_fields::Multi_field_operators::add_and_multiply	(	element_type	e,
		const element_type &	a,
		const element_type &	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_type &	e,
		const element_type &	a,
		element_type &	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_type &	e,
		const element_type &	a,
		const element_type &	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_type &	e1,
		const element_type &	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_type &	e1,
		const element_type &	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_type& 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_type& 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_type Gudhi::persistence_fields::Multi_field_operators::get_inverse ( const element_type & 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_type& 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_type, characteristic_type> Gudhi::persistence_fields::Multi_field_operators::get_partial_inverse	(	const element_type &	e,
		const characteristic_type &	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_type Gudhi::persistence_fields::Multi_field_operators::get_partial_multiplicative_identity ( const characteristic_type & 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_type Gudhi::persistence_fields::Multi_field_operators::get_value ( element_type 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_type & 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_type Gudhi::persistence_fields::Multi_field_operators::multiply	(	element_type	e1,
		const element_type &	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_type Gudhi::persistence_fields::Multi_field_operators::multiply_and_add	(	element_type	e,
		const element_type &	m,
		const element_type &	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_type &	e,
		const element_type &	m,
		element_type &	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_type &	e,
		const element_type &	m,
		const element_type &	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_type &	e1,
		const element_type &	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	Heighest value of a prime.

◆ substract()

element_type Gudhi::persistence_fields::Multi_field_operators::substract	(	element_type	e1,
		const element_type &	e2
	)		const

inline

Returns the substraction 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.

◆ substract_inplace_back()

void Gudhi::persistence_fields::Multi_field_operators::substract_inplace_back	(	const element_type &	e1,
		element_type &	e2
	)		const

inline

Stores in the second element the substraction 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.

◆ substract_inplace_front()

void Gudhi::persistence_fields::Multi_field_operators::substract_inplace_front	(	element_type &	e1,
		const element_type &	e2
	)		const

inline

Stores in the first element the substraction 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_type

◆ element_type

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()

◆ substract()

◆ substract_inplace_back()

◆ substract_inplace_front()