ROOT::Math::KahanSum< T > Class Template Reference

Description

template<class T>
class ROOT::Math::KahanSum< T >

The Kahan compensate summation algorithm significantly reduces the numerical error in the total obtained by adding a sequence of finite precision floating point numbers. This is done by keeping a separate running compensation (a variable to accumulate small errors).
.

The intial values of the result and the correction are set to the default value of the type it hass been instantiated with.

Examples:

std::vector<double> numbers = {0.01, 0.001, 0.0001, 0.000001, 0.00000000001};
ROOT::Math::KahanSum<double> k;
k.Add(numbers);

auto result = ROOT::Math::KahanSum<double>::Accumulate(numbers);

Definition at line 85 of file Util.h.

Collaboration diagram for ROOT::Math::KahanSum< T >:

Public Member Functions
	KahanSum (const T &initialValue=T{})
	Constructor accepting a initial value for the summation as parameter. More...
template<class Iterator >
void	Add (const Iterator begin, const Iterator end)
	Iterate over a datastructure referenced by a pointer and accumulate on the exising result. More...
void	Add (const T &x)
	Single element accumulated addition. More...
T	Result ()
	Return the result. More...

Static Public Member Functions
template<class Iterator >
static T	Accumulate (const Iterator begin, const Iterator end, const T &initialValue=T{})
	Iterate over a datastructure referenced by a pointer and return the result of its accumulation. Can take an initial value as third parameter. More...

Private Attributes
T	fCorrection {}
T	fSum {}

Constructor & Destructor Documentation

KahanSum()

template<class T >

ROOT::Math::KahanSum< T >::KahanSum ( const T &  initialValue = T{} )

inline

Constructor accepting a initial value for the summation as parameter.

Definition at line 88 of file Util.h.

{}) : fSum(initialValue) {}

Member Function Documentation

Accumulate()

template<class T >

template<class Iterator >

static T ROOT::Math::KahanSum< T >::Accumulate ( const Iterator  begin, const Iterator  end, const T &  initialValue = T{}  )

inlinestatic

Iterate over a datastructure referenced by a pointer and return the result of its accumulation. Can take an initial value as third parameter.

Definition at line 111 of file Util.h.

                                                                                             {})
      {
         static_assert(!std::is_same<decltype(*begin), T>::value,
                       "Iterator points to an element of the different type than the KahanSum class");
         KahanSum init(initialValue);
         init.Add(begin, end);
         return init.fSum;
      }

Add() [1/2]

template<class T >

template<class Iterator >

void ROOT::Math::KahanSum< T >::Add ( const Iterator  begin, const Iterator  end  )

inline

Iterate over a datastructure referenced by a pointer and accumulate on the exising result.

Definition at line 101 of file Util.h.

      {
         static_assert(!std::is_same<decltype(*begin), T>::value,
                       "Iterator points to an element of the different type than the KahanSum class");
         for (auto it = begin; it != end; it++) this->Add(*it);
      }

References ROOT::Math::KahanSum< T >::Add().

Here is the call graph for this function:

Add() [2/2]

template<class T >

void ROOT::Math::KahanSum< T >::Add ( const T &  x )

inline

Single element accumulated addition.

Definition at line 91 of file Util.h.

      {
         auto y = x - fCorrection;
         auto t = fSum + y;
         fCorrection = (t - fSum) - y;
         fSum = t;
      }

References ROOT::Math::KahanSum< T >::fCorrection, and ROOT::Math::KahanSum< T >::fSum.

Referenced by ROOT::Math::KahanSum< T >::Add().

Result()

template<class T >

T ROOT::Math::KahanSum< T >::Result ( )

inline

Return the result.

Definition at line 121 of file Util.h.

{ return fSum; }

References ROOT::Math::KahanSum< T >::fSum.

Member Data Documentation

fCorrection

template<class T >

T ROOT::Math::KahanSum< T >::fCorrection {}

private

Definition at line 125 of file Util.h.

Referenced by ROOT::Math::KahanSum< T >::Add().

fSum

template<class T >

T ROOT::Math::KahanSum< T >::fSum {}

private

Definition at line 124 of file Util.h.

Referenced by ROOT::Math::KahanSum< T >::Add(), and ROOT::Math::KahanSum< T >::Result().

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

• /home/build/builds/o5h8MZZm/0/mlz/bornagain/Fit/3rdparty/RootMinimizers/mathcore/Math/Util.h