itk::CompensatedSummation< TFloat > Class Template Reference

#include <itkCompensatedSummation.h>

Detailed Description

template<typename TFloat>
class itk::CompensatedSummation< TFloat >

Perform more precise accumulation of floating point numbers.

The float and double datatypes only have finite precision. When performing a running sum of floats, the accumulated errors get progressively worse as the magnitude of the sum gets large relative to new elements.

From Wikipedia, https://en.wikipedia.org/wiki/Kahan_summation_algorithm

"In numerical analysis, the Kahan summation algorithm (also known as compensated summation) significantly reduces the numerical error in the total obtained by adding a sequence of finite precision floating point numbers, compared to the obvious approach. This is done by keeping a separate running compensation (a variable to accumulate small errors)."

For example, instead of

double sum = 0.0;
for( unsigned int i = 0; i < array.Size(); ++i )
  {
  sum += array.GetElement(i);
  }

do

using CompensatedSummationType = CompensatedSummation<double>;
CompensatedSummationType compensatedSummation;
for( unsigned int i = 0; i < array.Size(); ++i )
  {
  compensatedSummation += array.GetElement(i);
  }
double sum = compensatedSummation.GetSum();

Definition at line 66 of file itkCompensatedSummation.h.

Collaboration diagram for itk::CompensatedSummation< TFloat >:

Public Types
using	AccumulateType = typename NumericTraits< FloatType >::AccumulateType
using	FloatType = TFloat
using	Self = CompensatedSummation

Public Member Functions
	CompensatedSummation (const Self &)=default
const AccumulateType &	GetSum () const
	operator FloatType () const
Self &	operator-= (const FloatType &rhs)
Self &	operator= (const FloatType &rhs)
Self &	operator= (const Self &)=default
void	ResetToZero ()
	CompensatedSummation ()=default
	CompensatedSummation (FloatType value)
void	AddElement (const FloatType &element)
Self &	operator+= (const FloatType &rhs)
Self &	operator+= (const Self &rhs)
Self &	operator*= (const FloatType &rhs)
Self &	operator/= (const FloatType &rhs)

Private Attributes
AccumulateType	m_Compensation {}
AccumulateType	m_Sum {}

Member Typedef Documentation

AccumulateType

template<typename TFloat>

using itk::CompensatedSummation< TFloat >::AccumulateType = typename NumericTraits<FloatType>::AccumulateType

Type used for the sum and compensation.

Definition at line 73 of file itkCompensatedSummation.h.

FloatType

template<typename TFloat>

using itk::CompensatedSummation< TFloat >::FloatType = TFloat

Type of the input elements.

Definition at line 70 of file itkCompensatedSummation.h.

Self

template<typename TFloat>

using itk::CompensatedSummation< TFloat >::Self = CompensatedSummation

Standard class type aliases.

Definition at line 76 of file itkCompensatedSummation.h.

Constructor & Destructor Documentation

CompensatedSummation() [1/3]

template<typename TFloat>

itk::CompensatedSummation< TFloat >::CompensatedSummation ( )

default

Constructors.

CompensatedSummation() [2/3]

template<typename TFloat>

itk::CompensatedSummation< TFloat >::CompensatedSummation

(

FloatType

value

)

Constructors.

CompensatedSummation() [3/3]

template<typename TFloat>

itk::CompensatedSummation< TFloat >::CompensatedSummation ( const Self &  )

default

Copy constructor.

Member Function Documentation

AddElement()

template<typename TFloat>

void itk::CompensatedSummation< TFloat >::AddElement

(

const FloatType &

element

)

Add an element to the sum.

GetSum()

template<typename TFloat>

const AccumulateType& itk::CompensatedSummation< TFloat >::GetSum

(

)

const

Get the sum.

operator FloatType()

template<typename TFloat>

itk::CompensatedSummation< TFloat >::operator FloatType ( ) const

explicit

explicit conversion

operator*=()

template<typename TFloat>

Self& itk::CompensatedSummation< TFloat >::operator*=

(

const FloatType &

rhs

)

Division and multiplication. These do not provide any numerical advantages relative to vanilla division and multiplication.

operator+=() [1/2]

template<typename TFloat>

Self& itk::CompensatedSummation< TFloat >::operator+=

(

const FloatType &

rhs

)

Add an element to the sum.

operator+=() [2/2]

template<typename TFloat>

Self& itk::CompensatedSummation< TFloat >::operator+=

(

const Self &

rhs

)

Add an element to the sum.

operator-=()

template<typename TFloat>

Self& itk::CompensatedSummation< TFloat >::operator-=

(

const FloatType &

rhs

)

Subtract an element from the sum.

operator/=()

template<typename TFloat>

Self& itk::CompensatedSummation< TFloat >::operator/=

(

const FloatType &

rhs

)

Division and multiplication. These do not provide any numerical advantages relative to vanilla division and multiplication.

operator=() [1/2]

template<typename TFloat>

Self& itk::CompensatedSummation< TFloat >::operator=

(

const FloatType &

rhs

)

Reset the sum to the given value and the compensation to zero.

operator=() [2/2]

template<typename TFloat>

Self& itk::CompensatedSummation< TFloat >::operator= ( const Self &  )

default

Assignment operator.

ResetToZero()

template<typename TFloat>

void itk::CompensatedSummation< TFloat >::ResetToZero

(

)

Reset the sum and compensation to zero.

Member Data Documentation

m_Compensation

template<typename TFloat>

AccumulateType itk::CompensatedSummation< TFloat >::m_Compensation {}

private

Definition at line 129 of file itkCompensatedSummation.h.

m_Sum

template<typename TFloat>

AccumulateType itk::CompensatedSummation< TFloat >::m_Sum {}

private

Definition at line 128 of file itkCompensatedSummation.h.

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

• itkCompensatedSummation.h