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Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics Class Reference

Class defining operators for a multi-field with "consecutive" characteristic range, such that productOfAllCharacteristics ^ 2 fits into an unsigned int. More...

#include <gudhi/Fields/Multi_field_small_operators.h>

Public Types

using Element = unsigned int
 
using Characteristic = Element
 

Public Member Functions

 Multi_field_operators_with_small_characteristics ()
 Default constructor, sets the product of all characteristics to 0.
 
 Multi_field_operators_with_small_characteristics (int minCharacteristic, int maxCharacteristic)
 Constructor setting the characteristics to all prime numbers between the two given integers. The product of all primes to the square has to fit into an unsigned int.
 
 Multi_field_operators_with_small_characteristics (const Multi_field_operators_with_small_characteristics &toCopy)
 Copy constructor.
 
 Multi_field_operators_with_small_characteristics (Multi_field_operators_with_small_characteristics &&toMove) noexcept
 Move constructor.
 
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. The product of all primes to the square has to fit into an unsigned int.
 
const Characteristicget_characteristic () const
 Returns the current characteristics as the product of all of them.
 
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.
 
Element add (Element e1, Element e2) const
 Returns the sum of two elements in the field.
 
void add_inplace (Element &e1, 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.
 
Element subtract (Element e1, Element e2) const
 Returns the subtraction in the field of the first element by the second element.
 
void subtract_inplace_front (Element &e1, 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.
 
void subtract_inplace_back (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.
 
Element multiply (Element e1, Element e2) const
 Returns the multiplication of two elements in the field.
 
void multiply_inplace (Element &e1, 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.
 
Element multiply_and_add (Element e, Element m, Element a) const
 Multiplies the first element with the second one and adds the third one. Returns the result in the field.
 
void multiply_and_add_inplace_front (Element &e, 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 first element.
 
void multiply_and_add_inplace_back (Element e, 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.
 
Element add_and_multiply (Element e, Element a, Element m) const
 Adds the first element to the second one and multiplies the third one with it. Returns the result in the field.
 
void add_and_multiply_inplace_front (Element &e, 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 first element.
 
void add_and_multiply_inplace_back (Element e, 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.
 
bool are_equal (Element e1, Element e2) const
 Returns true if the two given elements are equal in the field, false otherwise.
 
Element get_inverse (const Element &e) const
 Returns the inverse of the given element in the sense of [boissonnat:hal-00922572] with respect to the product of all characteristics.
 
std::pair< Element, Characteristicget_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 [boissonnat:hal-00922572] for more details.
 
Element get_partial_multiplicative_identity (const Characteristic &productOfCharacteristics) const
 Returns the partial multiplicative identity of the multi-field from the given product. See [boissonnat:hal-00922572] for more details.
 
Multi_field_operators_with_small_characteristicsoperator= (Multi_field_operators_with_small_characteristics other)
 Assign operator.
 

Static Public Member Functions

static constexpr Element get_additive_identity ()
 Returns the additive identity of a field.
 
static constexpr Element get_multiplicative_identity ()
 Returns the multiplicative identity of a field.
 

Friends

void swap (Multi_field_operators_with_small_characteristics &f1, Multi_field_operators_with_small_characteristics &f2)
 Swap operator.
 

Detailed Description

Class defining operators for a multi-field with "consecutive" characteristic range, such that productOfAllCharacteristics ^ 2 fits into an unsigned int.

Member Typedef Documentation

◆ Characteristic

◆ Element

Type for the elements in the field.

Constructor & Destructor Documentation

◆ Multi_field_operators_with_small_characteristics() [1/3]

Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::Multi_field_operators_with_small_characteristics ( int  minCharacteristic,
int  maxCharacteristic 
)
inline

Constructor setting the characteristics to all prime numbers between the two given integers. The product of all primes to the square has to fit into an unsigned int.

Parameters
minCharacteristicSmallest value of a prime.
maxCharacteristicHighest value of a prime.

◆ Multi_field_operators_with_small_characteristics() [2/3]

Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::Multi_field_operators_with_small_characteristics ( const Multi_field_operators_with_small_characteristics toCopy)
inline

Copy constructor.

Parameters
toCopyOperators to copy.

◆ Multi_field_operators_with_small_characteristics() [3/3]

Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::Multi_field_operators_with_small_characteristics ( Multi_field_operators_with_small_characteristics &&  toMove)
inlinenoexcept

Move constructor.

Parameters
toMoveOperators to move.

Member Function Documentation

◆ add()

Element Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::add ( Element  e1,
Element  e2 
) const
inline

Returns the sum of two elements in the field.

Parameters
e1First element.
e2Second element.
Returns
(e1 + e2) % productOfAllCharacteristics, such that the result is positive.

◆ add_and_multiply()

Element Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::add_and_multiply ( Element  e,
Element  a,
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.

Warning
Not overflow safe.
Parameters
eFirst element.
aSecond element.
mThird element.
Returns
((e + a) * m) % productOfAllCharacteristics, such that the result is positive.

◆ add_and_multiply_inplace_back()

void Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::add_and_multiply_inplace_back ( Element  e,
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.

Warning
Not overflow safe.
Parameters
eFirst element.
aSecond element.
mThird element.

◆ add_and_multiply_inplace_front()

void Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::add_and_multiply_inplace_front ( Element e,
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 first element.

Warning
Not overflow safe.
Parameters
eFirst element.
aSecond element.
mThird element.

◆ add_inplace()

void Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::add_inplace ( Element e1,
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
e1First element.
e2Second element.

◆ are_equal()

bool Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::are_equal ( Element  e1,
Element  e2 
) const
inline

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

Parameters
e1First element to compare.
e2Second element to compare.
Returns
true If e1 % productOfAllCharacteristics == e2 % productOfAllCharacteristics.
false Otherwise.

◆ get_additive_identity()

static constexpr Element Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::get_additive_identity ( )
inlinestaticconstexpr

Returns the additive identity of a field.

Returns
The additive identity of a field.

◆ get_characteristic()

const Characteristic & Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::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_with_small_characteristics::get_inverse ( const Element e) const
inline

Returns the inverse of the given element in the sense of [boissonnat:hal-00922572] with respect to the product of all characteristics.

Parameters
eElement to get the inverse from.
Returns
Inverse in the current field.

◆ get_multiplicative_identity()

static constexpr Element Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::get_multiplicative_identity ( )
inlinestaticconstexpr

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_with_small_characteristics::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 [boissonnat:hal-00922572] for more details.

Parameters
eElement to get the inverse from.
productOfCharacteristicsProduct 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_with_small_characteristics::get_partial_multiplicative_identity ( const Characteristic productOfCharacteristics) const
inline

Returns the partial multiplicative identity of the multi-field from the given product. See [boissonnat:hal-00922572] for more details.

Parameters
productOfCharacteristicsProduct 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_with_small_characteristics::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
eInteger to return the value from.
Returns
e modulo the current characteristic, such that the result is positive.

◆ multiply()

Element Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::multiply ( Element  e1,
Element  e2 
) const
inline

Returns the multiplication of two elements in the field.

Parameters
e1First element.
e2Second element.
Returns
(e1 * e2) % productOfAllCharacteristics, such that the result is positive.

◆ multiply_and_add()

Element Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::multiply_and_add ( Element  e,
Element  m,
Element  a 
) const
inline

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

Warning
Not overflow safe.
Parameters
eFirst element.
mSecond element.
aThird element.
Returns
(e * m + a) % productOfAllCharacteristics, such that the result is positive.

◆ multiply_and_add_inplace_back()

void Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::multiply_and_add_inplace_back ( Element  e,
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.

Warning
Not overflow safe.
Parameters
eFirst element.
mSecond element.
aThird element.

◆ multiply_and_add_inplace_front()

void Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::multiply_and_add_inplace_front ( Element e,
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 first element.

Warning
Not overflow safe.
Parameters
eFirst element.
mSecond element.
aThird element.

◆ multiply_inplace()

void Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::multiply_inplace ( Element e1,
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
e1First element.
e2Second element.

◆ set_characteristic()

void Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::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. The product of all primes to the square has to fit into an unsigned int.

Parameters
minimumSmallest value of a prime.
maximumHighest value of a prime.

◆ subtract()

Element Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::subtract ( Element  e1,
Element  e2 
) const
inline

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

Parameters
e1First element.
e2Second element.
Returns
(e1 - e2) % productOfAllCharacteristics, such that the result is positive.

◆ subtract_inplace_back()

void Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::subtract_inplace_back ( 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
e1First element.
e2Second element.

◆ subtract_inplace_front()

void Gudhi::persistence_fields::Multi_field_operators_with_small_characteristics::subtract_inplace_front ( Element e1,
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
e1First element.
e2Second element.

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