The Zipf distribution Random Number Generator (RNG) that allows stream numbers to be set deterministically. More...

#include "random-variable-stream.h"

Inheritance diagram for ns3::ZipfRandomVariable:

Collaboration diagram for ns3::ZipfRandomVariable:

Public Member Functions
	ZipfRandomVariable ()
	Creates a Zipf distribution RNG with the default values for n and alpha. More...

double	GetAlpha (void) const
	Returns the alpha value for the Zipf distribution returned by this RNG stream. More...

uint32_t	GetInteger (uint32_t n, uint32_t alpha)
	Returns a random unsigned integer from a Zipf distribution with the specified n and alpha. More...

virtual uint32_t	GetInteger (void)
	Returns a random unsigned integer from a Zipf distribution with the current n and alpha. More...

uint32_t	GetN (void) const
	Returns the n value for the Zipf distribution returned by this RNG stream. More...

double	GetValue (uint32_t n, double alpha)
	Returns a random double from a Zipf distribution with the specified n and alpha. More...

virtual double	GetValue (void)
	Returns a random double from a Zipf distribution with the current n and alpha. More...

Public Member Functions inherited from ns3::RandomVariableStream
	RandomVariableStream ()
	Default constructor. More...

virtual	~RandomVariableStream ()
	Destructor. More...

int64_t	GetStream (void) const
	Returns the stream number for the RngStream. More...

bool	IsAntithetic (void) const
	Check if antithetic values will be generated. More...

void	SetAntithetic (bool isAntithetic)
	Specify whether antithetic values should be generated. More...

void	SetStream (int64_t stream)
	Specifies the stream number for the RngStream. More...

Public Member Functions inherited from ns3::Object
	Object ()
	Constructor. More...

virtual	~Object ()
	Destructor. More...

void	AggregateObject (Ptr< Object > other)
	Aggregate two Objects together. More...

void	Dispose (void)
	Dispose of this Object. More...

AggregateIterator	GetAggregateIterator (void) const
	Get an iterator to the Objects aggregated to this one. More...

virtual TypeId	GetInstanceTypeId (void) const
	Get the most derived TypeId for this Object. More...

template<>
Ptr< Object >	GetObject () const
	Specialization of () for objects of type ns3::Object. More...

template<typename T >
Ptr< T >	GetObject (TypeId tid) const
	Get a pointer to the requested aggregated Object by TypeId. More...

template<>
Ptr< Object >	GetObject (TypeId tid) const
	Specialization of (TypeId tid) for objects of type ns3::Object. More...

template<typename T >
Ptr< T >	GetObject (void) const
	Get a pointer to the requested aggregated Object. More...

void	Initialize (void)
	Invoke DoInitialize on all Objects aggregated to this one. More...

bool	IsInitialized (void) const
	Check if the object has been initialized. More...

Public Member Functions inherited from ns3::SimpleRefCount< Object, ObjectBase, ObjectDeleter >
	SimpleRefCount ()
	Default constructor. More...

	SimpleRefCount (const SimpleRefCount &o[[maybe_unused]])
	Copy constructor. More...

uint32_t	GetReferenceCount (void) const
	Get the reference count of the object. More...

SimpleRefCount &	operator= ([[maybe_unused]] const SimpleRefCount &o)
	Assignment operator. More...

void	Ref (void) const
	Increment the reference count. More...

void	Unref (void) const
	Decrement the reference count. More...

Public Member Functions inherited from ns3::ObjectBase
virtual	~ObjectBase ()
	Virtual destructor. More...

void	GetAttribute (std::string name, AttributeValue &value) const
	Get the value of an attribute, raising fatal errors if unsuccessful. More...

bool	GetAttributeFailSafe (std::string name, AttributeValue &value) const
	Get the value of an attribute without raising erros. More...

void	SetAttribute (std::string name, const AttributeValue &value)
	Set a single attribute, raising fatal errors if unsuccessful. More...

bool	SetAttributeFailSafe (std::string name, const AttributeValue &value)
	Set a single attribute without raising errors. More...

bool	TraceConnect (std::string name, std::string context, const CallbackBase &cb)
	Connect a TraceSource to a Callback with a context. More...

bool	TraceConnectWithoutContext (std::string name, const CallbackBase &cb)
	Connect a TraceSource to a Callback without a context. More...

bool	TraceDisconnect (std::string name, std::string context, const CallbackBase &cb)
	Disconnect from a TraceSource a Callback previously connected with a context. More...

bool	TraceDisconnectWithoutContext (std::string name, const CallbackBase &cb)
	Disconnect from a TraceSource a Callback previously connected without a context. More...

Static Public Member Functions
static TypeId	GetTypeId (void)
	Register this type. More...

Static Public Member Functions inherited from ns3::RandomVariableStream
static TypeId	GetTypeId (void)
	Register this type. More...

Static Public Member Functions inherited from ns3::Object
static TypeId	GetTypeId (void)
	Register this type. More...

Static Public Member Functions inherited from ns3::ObjectBase
static TypeId	GetTypeId (void)
	Get the type ID. More...

Private Attributes
double	m_alpha
	The alpha value for the Zipf distribution returned by this RNG stream. More...

double	m_c
	The normalization constant. More...

uint32_t	m_n
	The n value for the Zipf distribution returned by this RNG stream. More...

Additional Inherited Members
Protected Member Functions inherited from ns3::RandomVariableStream
RngStream *	Peek (void) const
	Get the pointer to the underlying RngStream. More...

Protected Member Functions inherited from ns3::Object
	Object (const Object &o)
	Copy an Object. More...

virtual void	DoDispose (void)
	Destructor implementation. More...

virtual void	DoInitialize (void)
	Initialize() implementation. More...

virtual void	NotifyNewAggregate (void)
	Notify all Objects aggregated to this one of a new Object being aggregated. More...

Protected Member Functions inherited from ns3::ObjectBase
void	ConstructSelf (const AttributeConstructionList &attributes)
	Complete construction of ObjectBase; invoked by derived classes. More...

virtual void	NotifyConstructionCompleted (void)
	Notifier called once the ObjectBase is fully constructed. More...

Related Functions inherited from ns3::ObjectBase
static TypeId	GetObjectIid (void)
	Ensure the TypeId for ObjectBase gets fully configured to anchor the inheritance tree properly. More...

Detailed Description

The Zipf distribution Random Number Generator (RNG) that allows stream numbers to be set deterministically.

This class supports the creation of objects that return random numbers from a fixed Zipf distribution. It also supports the generation of single random numbers from various Zipf distributions.

The Zipf's law states that given some corpus of natural language utterances, the frequency of any word is inversely proportional to its rank in the frequency table.

Zipf's distribution has two parameters, alpha and N, where: $\alpha > 0$ (real) and $N \in \{1,2,3 \dots\}$ (integer). Probability Mass Function is $f(k; \alpha, N) = k^{-\alpha}/ H_{N,\alpha}$ where $H_{N,\alpha} = \sum_{m=1}^N m^{-\alpha}$

Here is an example of how to use this class:

uint32_t n = 1;
double alpha = 2.0;
 
Ptr<ZipfRandomVariable> x = CreateObject<ZipfRandomVariable> ();
x->SetAttribute ("N", IntegerValue (n));
x->SetAttribute ("Alpha", DoubleValue (alpha));
 
// The expected value for the mean of the values returned by a
// Zipfly distributed random variable is equal to
//
//                   H
//                    N, alpha - 1
//     E[value]  =  ---------------
//                     H
//                      N, alpha
//
// where
//
//                    N
//                   ---
//                   \     -alpha
//     H          =  /    m        .
//      N, alpha     ---
//                   m=1
//
// For this test,
//
//                      -(alpha - 1)
//                     1
//     E[value]  =  ---------------
//                      -alpha
//                     1
//
//               =  1  .
//
double value = x->GetValue ();

Config Paths

ns3::ZipfRandomVariable is accessible through the following paths with Config::Set and Config::Connect:

"/NodeList/[i]/DeviceList/[i]/$ns3::SimpleNetDevice/ReceiveErrorModel/$ns3::RateErrorModel/RanVar/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::SimpleNetDevice/ReceiveErrorModel/$ns3::BurstErrorModel/BurstStart/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::SimpleNetDevice/ReceiveErrorModel/$ns3::BurstErrorModel/BurstSize/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::PointToPointNetDevice/ReceiveErrorModel/$ns3::RateErrorModel/RanVar/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::PointToPointNetDevice/ReceiveErrorModel/$ns3::BurstErrorModel/BurstStart/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::PointToPointNetDevice/ReceiveErrorModel/$ns3::BurstErrorModel/BurstSize/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::WifiNetDevice/Channel/$ns3::SpectrumChannel/PropagationLossModel/$ns3::RandomPropagationLossModel/Variable/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::WifiNetDevice/Channel/$ns3::YansWifiChannel/PropagationLossModel/$ns3::RandomPropagationLossModel/Variable/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::WifiNetDevice/Channel/$ns3::YansWifiChannel/PropagationDelayModel/$ns3::RandomPropagationDelayModel/Variable/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::WifiNetDevice/Phy/PostReceptionErrorModel/$ns3::RateErrorModel/RanVar/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::WifiNetDevice/Phy/PostReceptionErrorModel/$ns3::BurstErrorModel/BurstStart/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::WifiNetDevice/Phy/PostReceptionErrorModel/$ns3::BurstErrorModel/BurstSize/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::WaveNetDevice/Channel/$ns3::SpectrumChannel/PropagationLossModel/$ns3::RandomPropagationLossModel/Variable/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::WaveNetDevice/Channel/$ns3::YansWifiChannel/PropagationLossModel/$ns3::RandomPropagationLossModel/Variable/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::WaveNetDevice/Channel/$ns3::YansWifiChannel/PropagationDelayModel/$ns3::RandomPropagationDelayModel/Variable/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::WaveNetDevice/PhyEntities/[i]/PostReceptionErrorModel/$ns3::RateErrorModel/RanVar/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::WaveNetDevice/PhyEntities/[i]/PostReceptionErrorModel/$ns3::BurstErrorModel/BurstStart/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::WaveNetDevice/PhyEntities/[i]/PostReceptionErrorModel/$ns3::BurstErrorModel/BurstSize/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::CsmaNetDevice/ReceiveErrorModel/$ns3::RateErrorModel/RanVar/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::CsmaNetDevice/ReceiveErrorModel/$ns3::BurstErrorModel/BurstStart/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::CsmaNetDevice/ReceiveErrorModel/$ns3::BurstErrorModel/BurstSize/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::LrWpanNetDevice/Channel/PropagationLossModel/$ns3::RandomPropagationLossModel/Variable/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::MeshPointDevice/ForwardingDelay/$ns3::ZipfRandomVariable"
"/NodeList/[i]/DeviceList/[i]/$ns3::SixLowPanNetDevice/MeshUnderJitter/$ns3::ZipfRandomVariable"
"/NodeList/[i]/ApplicationList/[i]/$ns3::OnOffApplication/OnTime/$ns3::ZipfRandomVariable"
"/NodeList/[i]/ApplicationList/[i]/$ns3::OnOffApplication/OffTime/$ns3::ZipfRandomVariable"
"/NodeList/[i]/ApplicationList/[i]/$ns3::DhcpClient/Transactions/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::GaussMarkovMobilityModel/MeanVelocity/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::GaussMarkovMobilityModel/MeanDirection/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::GaussMarkovMobilityModel/MeanPitch/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::RandomDirection2dMobilityModel/Speed/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::RandomDirection2dMobilityModel/Pause/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::RandomWalk2dMobilityModel/Direction/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::RandomWalk2dMobilityModel/Speed/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::RandomWaypointMobilityModel/Speed/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::RandomWaypointMobilityModel/Pause/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::RandomWaypointMobilityModel/PositionAllocator/$ns3::RandomRectanglePositionAllocator/X/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::RandomWaypointMobilityModel/PositionAllocator/$ns3::RandomRectanglePositionAllocator/Y/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::RandomWaypointMobilityModel/PositionAllocator/$ns3::RandomBoxPositionAllocator/X/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::RandomWaypointMobilityModel/PositionAllocator/$ns3::RandomBoxPositionAllocator/Y/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::RandomWaypointMobilityModel/PositionAllocator/$ns3::RandomBoxPositionAllocator/Z/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::RandomWaypointMobilityModel/PositionAllocator/$ns3::RandomDiscPositionAllocator/Theta/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::RandomWaypointMobilityModel/PositionAllocator/$ns3::RandomDiscPositionAllocator/Rho/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::RandomWaypointMobilityModel/PositionAllocator/$ns3::OutdoorPositionAllocator/X/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::RandomWaypointMobilityModel/PositionAllocator/$ns3::OutdoorPositionAllocator/Y/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::RandomWaypointMobilityModel/PositionAllocator/$ns3::OutdoorPositionAllocator/Z/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::RandomWalk2dOutdoorMobilityModel/Direction/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::MobilityModel/$ns3::RandomWalk2dOutdoorMobilityModel/Speed/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::ArpL3Protocol/RequestJitter/$ns3::ZipfRandomVariable"
"/NodeList/[i]/$ns3::Icmpv6L4Protocol/SolicitationJitter/$ns3::ZipfRandomVariable"
"/ChannelList/[i]/$ns3::SpectrumChannel/PropagationLossModel/$ns3::RandomPropagationLossModel/Variable/$ns3::ZipfRandomVariable"
"/ChannelList/[i]/$ns3::YansWifiChannel/PropagationLossModel/$ns3::RandomPropagationLossModel/Variable/$ns3::ZipfRandomVariable"
"/ChannelList/[i]/$ns3::YansWifiChannel/PropagationDelayModel/$ns3::RandomPropagationDelayModel/Variable/$ns3::ZipfRandomVariable"

Attributes

N: The n value for the Zipf distribution returned by this RNG stream.
- Set with class: ns3::IntegerValue
- Underlying type: uint32_t 0:4294967295
- Initial value: 1
- Flags: construct write read
Alpha: The alpha value for the Zipf distribution returned by this RNG stream.
- Set with class: ns3::DoubleValue
- Underlying type: double -1.79769e+308:1.79769e+308
- Initial value: 0
- Flags: construct write read

Attributes defined in parent class ns3::RandomVariableStream

Stream: The stream number for this RNG stream. -1 means "allocate a stream automatically". Note that if -1 is set, Get will return -1 so that it is not possible to know which value was automatically allocated.
- Set with class: ns3::IntegerValue
- Underlying type: int64_t -9223372036854775808:9223372036854775807
- Initial value: -1
- Flags: construct write read
Antithetic: Set this RNG stream to generate antithetic values
- Set with class: BooleanValue
- Underlying type: bool
- Initial value: false
- Flags: construct write read

No TraceSources are defined for this type.
Size of this type is 80 bytes (on a 64-bit architecture).

Definition at line 2094 of file random-variable-stream.h.

Constructor & Destructor Documentation

◆ ZipfRandomVariable()

ns3::ZipfRandomVariable::ZipfRandomVariable ( )

Creates a Zipf distribution RNG with the default values for n and alpha.

Definition at line 1292 of file random-variable-stream.cc.

References NS_LOG_FUNCTION.

Member Function Documentation

◆ GetAlpha()

double ns3::ZipfRandomVariable::GetAlpha ( void ) const

Returns the alpha value for the Zipf distribution returned by this RNG stream.

Returns: The alpha value for the Zipf distribution returned by this RNG stream.

Definition at line 1305 of file random-variable-stream.cc.

References m_alpha, and NS_LOG_FUNCTION.

◆ GetInteger() [1/2]

uint32_t ns3::ZipfRandomVariable::GetInteger	(	uint32_t	n,
		uint32_t	alpha
	)

Returns a random unsigned integer from a Zipf distribution with the specified n and alpha.

Parameters

[in]	n	N value for the Zipf distribution.
[in]	alpha	Alpha value for the Zipf distribution.

Returns: A random unsigned integer value.

Note that antithetic values are being generated if m_isAntithetic is equal to true. If is a uniform variable over [0,1] and is a value that would be returned normally, then ) is the distance that would be from . The value returned in the antithetic case, , uses (1-u), which is the distance is from the 1.

Definition at line 1344 of file random-variable-stream.cc.

References sample-rng-plot::alpha, GetValue(), and NS_LOG_FUNCTION.

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◆ GetInteger() [2/2]

uint32_t ns3::ZipfRandomVariable::GetInteger ( void )

virtual

Returns a random unsigned integer from a Zipf distribution with the current n and alpha.

Returns: A random unsigned integer value.

Note that antithetic values are being generated if m_isAntithetic is equal to true. If is a uniform variable over [0,1] and is a value that would be returned normally, then ) is the distance that would be from . The value returned in the antithetic case, , uses (1-u), which is the distance is from the 1.

Implements ns3::RandomVariableStream.

Definition at line 1357 of file random-variable-stream.cc.

References GetValue(), m_alpha, m_n, and NS_LOG_FUNCTION.

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◆ GetN()

uint32_t ns3::ZipfRandomVariable::GetN ( void ) const

Returns the n value for the Zipf distribution returned by this RNG stream.

Returns: The n value for the Zipf distribution returned by this RNG stream.

Definition at line 1299 of file random-variable-stream.cc.

References m_n, and NS_LOG_FUNCTION.

◆ GetTypeId()

TypeId ns3::ZipfRandomVariable::GetTypeId ( void )

static

Register this type.

Returns: The object TypeId.

Definition at line 1275 of file random-variable-stream.cc.

References m_alpha, m_n, ns3::MakeDoubleAccessor(), ns3::MakeIntegerAccessor(), and ns3::TypeId::SetParent().

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◆ GetValue() [1/2]

double ns3::ZipfRandomVariable::GetValue	(	uint32_t	n,
		double	alpha
	)

Returns a random double from a Zipf distribution with the specified n and alpha.

Parameters

[in]	n	N value for the Zipf distribution.
[in]	alpha	Alpha value for the Zipf distribution.

Returns: A floating point random value.

Note that antithetic values are being generated if m_isAntithetic is equal to true. If is a uniform variable over [0,1] and is a value that would be returned normally, then ) is the distance that would be from . The value returned in the antithetic case, , uses (1-u), which is the distance is from the 1.

Definition at line 1312 of file random-variable-stream.cc.

References sample-rng-plot::alpha, ns3::RandomVariableStream::IsAntithetic(), m_alpha, m_c, m_n, NS_LOG_FUNCTION, ns3::RandomVariableStream::Peek(), and ns3::RngStream::RandU01().

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◆ GetValue() [2/2]

double ns3::ZipfRandomVariable::GetValue ( void )

virtual

Returns a random double from a Zipf distribution with the current n and alpha.

Returns: A floating point random value.

Note that antithetic values are being generated if m_isAntithetic is equal to true. If is a uniform variable over [0,1] and is a value that would be returned normally, then ) is the distance that would be from . The value returned in the antithetic case, , uses (1-u), which is the distance is from the 1.

Note that we have to re-implement this method here because the method is overloaded above for the two-argument variant and the c++ name resolution rules don't work well with overloads split between parent and child classes.

Implements ns3::RandomVariableStream.

Definition at line 1351 of file random-variable-stream.cc.

References m_alpha, m_n, and NS_LOG_FUNCTION.

Referenced by GetInteger().

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Member Data Documentation

◆ m_alpha

double ns3::ZipfRandomVariable::m_alpha

private

The alpha value for the Zipf distribution returned by this RNG stream.

Definition at line 2187 of file random-variable-stream.h.

Referenced by GetAlpha(), GetInteger(), GetTypeId(), and GetValue().

◆ m_c

double ns3::ZipfRandomVariable::m_c

private

The normalization constant.

Definition at line 2190 of file random-variable-stream.h.

Referenced by GetValue().

◆ m_n

uint32_t ns3::ZipfRandomVariable::m_n

private

The n value for the Zipf distribution returned by this RNG stream.

Definition at line 2184 of file random-variable-stream.h.

Referenced by GetInteger(), GetN(), GetTypeId(), and GetValue().

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

src/core/model/random-variable-stream.h
src/core/model/random-variable-stream.cc

Public Member Functions

Static Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Config Paths

Attributes

Attributes defined in parent class ns3::RandomVariableStream

Constructor & Destructor Documentation

◆ ZipfRandomVariable()

Member Function Documentation

◆ GetAlpha()

◆ GetInteger() [1/2]

◆ GetInteger() [2/2]

◆ GetN()

◆ GetTypeId()

◆ GetValue() [1/2]

◆ GetValue() [2/2]

Member Data Documentation

◆ m_alpha

◆ m_c

◆ m_n