Class to calculate mean and and covariance between a number of parameters on running data without storing the actual values, also for weighted entries. More...

#include <CalcMeanCov.h>

Public Types
typedef RealType	value_type
	type of float variable to use for calculations and storage

Public Member Functions
	CalcMeanCov ()
	default constructor.

void	clear ()
	Clear all values.

template<class... T>
void	addWeighted (value_type weight, T... values)
	Update mean and covariance by adding a new, weighted entry.

template<class... T>
void	add (T... values)
	Update mean and covariance by adding a new entry.

void	add (const CalcMeanCov< N, RealType > &other)
	Merge the data set in 'other' into this one.

void	addWeightedArray (value_type weight, value_type *values)
	Update mean and covarianced by adding a new weighted entry.

void	addArray (value_type *values)
	Update mean and covariance by adding a new entry.

Getters
No range check if performed on indicies i and j
value_type	getEntries () const
	Return the number of entries.

value_type	getMean (int i) const
	Return the mean for parameter i.

value_type	getCovariance (int i, int j) const
	Return the covariance between parameters i and j.

value_type	getCorrelation (int i, int j) const
	Return the correlation coefficient between parameters i and j.

value_type	getVariance (int i) const
	Return the variance for paramter i.

value_type	getStddev (int i) const
	Return the standard deviation for parameter i.

value_type	getSum (int i) const
	Return the weighted sum values for parameter i.

Templated getters
These getters are templated and provide compile time range checking for the parameter indices
template<int i = 0>
value_type	getMean () const
	Return the mean for parameter i.

template<int i, int j>
value_type	getCovariance () const
	Return the covariance between parameters i and j.

template<int i, int j>
value_type	getCorrelation () const
	Return the correlation coefficient between parameters i and j.

template<int i = 0>
value_type	getVariance () const
	Return the variance for paramter i.

template<int i = 0>
value_type	getStddev () const
	Return the standard deviation for parameter i.

template<int i = 0>
value_type	getSum () const
	Return the weighted sum values for parameter i.

Private Member Functions
template<int i, class... T>
void	addValue (value_type weight, value_type x, T... values)
	Add a single value for parameter i and update mean and covariance.

template<int i>
void	addValue (value_type)
	Break recursion of addValue when no parameters are left.

template<int i, int j, class... T>
void	updateCov (value_type weight, value_type delta, value_type x, T... values)
	Update covariance between parameters i and j.

template<int i, int j>
void	updateCov (value_type, value_type)
	Break recursion of updateCov once all parameters are consumed.

void	addArrayValues (value_type weight, value_type *x)
	Add a new set of values and update mean and covariance.

constexpr int	getIndex (unsigned int i, unsigned int j) const
	Access element in triangular matrix including diagonal elements.

Private Attributes
value_type	m_entries
	Store the sum of weights.

value_type	m_mean [N]
	Store the mean values for all parameters.

value_type	m_covariance [N *(N+1)/2]
	Store the triangular covariance matrix for all parameters in continous memory.

Detailed Description

template<int N = 1, class RealType = double>
class Belle2::CalcMeanCov< N, RealType >

Class to calculate mean and and covariance between a number of parameters on running data without storing the actual values, also for weighted entries.

It can store more than one value per entry, e.g. x,y,z values but will not calculate correlations, only mean and standard deviation for all values. Also works with weighted entries.

See Philippe Pébay, Formulas for Robust, One-Pass Parallel Computation of Covariances and Arbitrary-Order Statistical Moments, SANDIA REPORT SAND2008-6212

Template Parameters

N	number of parameters
RealType	floating point type to be used

Definition at line 35 of file CalcMeanCov.h.

Member Typedef Documentation

◆ value_type

typedef RealType value_type

type of float variable to use for calculations and storage

Definition at line 42 of file CalcMeanCov.h.

Constructor & Destructor Documentation

◆ CalcMeanCov()

CalcMeanCov ( )

inline

default constructor.

Definition at line 39 of file CalcMeanCov.h.

39{ clear(); }

Belle2::CalcMeanCov::clear

void clear()

Clear all values.

Definition: CalcMeanCov.h:45

Member Function Documentation

◆ add() [1/2]

void add ( const CalcMeanCov< N, RealType > & other )

inline

Merge the data set in 'other' into this one.

Definition at line 77 of file CalcMeanCov.h.

    {
      const value_type n = m_entries + other.m_entries;
      if (n == 0)
        return;
      for (int i = 0; i < N; ++i) {
        const value_type delta = (other.m_mean[i] - m_mean[i]);
        //Update covariance matrix
        for (int j = i; j < N; ++j) {
          const value_type delta2 = (other.m_mean[j] - m_mean[j]);
          m_covariance[getIndex(i, j)] += other.m_covariance[getIndex(i, j)]  + m_entries * other.m_entries
                                          / n * delta * delta2;
        }
        //Update mean value
        m_mean[i] += other.m_entries * delta / n;
      }
      m_entries = n;
    }

◆ add() [2/2]

void add ( T... values )

inline

Update mean and covariance by adding a new entry.

Parameters

values values for all parameters. The number of Parameters must be equal to N

Definition at line 71 of file CalcMeanCov.h.

    {
      addWeighted(1.0, values...);
    }

◆ addArray()

void addArray ( value_type * values )

inline

Update mean and covariance by adding a new entry.

Parameters

values pointer to the first value

Definition at line 109 of file CalcMeanCov.h.

    {
      addWeightedArray(1.0, values);
    }

◆ addArrayValues()

void addArrayValues	(	value_type	weight,
		value_type *	x
	)

inlineprivate

Add a new set of values and update mean and covariance.

This function does the same as addValue and updateCov but in a non-templated way.

Parameters

weight	weight of the entry
x	pointer to the actual values

Definition at line 240 of file CalcMeanCov.h.

    {
      for (int i = 0; i < N; ++i) {
        const value_type delta = (x[i] - m_mean[i]);
        //Update covariance matrix
        for (int j = i; j < N; ++j) {
          const value_type delta2 = (x[j] - m_mean[j]);
          m_covariance[getIndex(i, j)] += (m_entries - weight) * weight
                                          / m_entries * delta * delta2;
        }
        //Update mean value
        m_mean[i] += weight * delta / m_entries;
      }
    }

◆ addValue() [1/2]

void addValue	(	value_type	weight,
		value_type	x,
		T...	values
	)

inlineprivate

Add a single value for parameter i and update mean and covariance.

See also: addArrayValues

Template Parameters

i	index of the parameter

Parameters

weight	weight of the entry
x	actual value
values	remaining values to be added recursively

Definition at line 199 of file CalcMeanCov.h.

    {
      const value_type delta = (x - m_mean[i]);
      //Update covariance elements
      updateCov<i, i>(weight, delta, x, values...);
      //Update mean value
      m_mean[i] += weight * delta / m_entries;
      //recursively call again for remaining values
      addValue < i + 1 > (weight, values...);
    }

◆ addValue() [2/2]

void addValue ( value_type )

inlineprivate

Break recursion of addValue when no parameters are left.

Definition at line 210 of file CalcMeanCov.h.

210{}

◆ addWeighted()

void addWeighted	(	value_type	weight,
		T...	values
	)

inline

Update mean and covariance by adding a new, weighted entry.

Parameters

weight	weight of the entry
values	values for all parameters. The number of parameters must be equal to N

Definition at line 59 of file CalcMeanCov.h.

    {
      static_assert(sizeof...(values) == N,
                    "Number of arguments must be equal N");
      m_entries += weight;
      addValue<0>(weight, values...);
    }

◆ addWeightedArray()

void addWeightedArray	(	value_type	weight,
		value_type *	values
	)

inline

Update mean and covarianced by adding a new weighted entry.

Parameters

weight	weight of entry
values	pointer to the first value

Definition at line 100 of file CalcMeanCov.h.

    {
      m_entries += weight;
      addArrayValues(weight, values);
    }

◆ clear()

void clear ( )

inline

Clear all values.

Definition at line 45 of file CalcMeanCov.h.

    {
      m_entries = 0;
      for (int i = 0; i < N; i++)
        m_mean[i] = 0;
      for (int i = 0; i < N * (N + 1) / 2; i++)
        m_covariance[i] = 0;
    }

◆ getCorrelation() [1/2]

value_type getCorrelation ( ) const

inline

Return the correlation coefficient between parameters i and j.

Definition at line 166 of file CalcMeanCov.h.

    {
      if (i == j) return 1.0;
      if (m_entries == 0.0) return 0.0;
      return getCovariance<i, j>() / (getStddev<i>() * getStddev<j>());
    }

◆ getCorrelation() [2/2]

value_type getCorrelation	(	int	i,
		int	j
	)		const

inline

Return the correlation coefficient between parameters i and j.

Definition at line 130 of file CalcMeanCov.h.

    {
      if (i == j) return 1.0;
      if (m_entries == 0.0) return 0.0;
      return getCovariance(i, j) / (getStddev(i) * getStddev(j));
    }

◆ getCovariance() [1/2]

value_type getCovariance ( ) const

inline

Return the covariance between parameters i and j.

Definition at line 158 of file CalcMeanCov.h.

    {
      static_assert(i >= 0 && i < N, "index i out of range");
      static_assert(j >= 0 && j < N, "index j out of range");
      if (m_entries == 0.0) return 0.0;
      return m_covariance[getIndex(i, j)] / m_entries;
    }

◆ getCovariance() [2/2]

value_type getCovariance	(	int	i,
		int	j
	)		const

inline

Return the covariance between parameters i and j.

Definition at line 124 of file CalcMeanCov.h.

    {
      if (m_entries == 0.0) return 0.0;
      return m_covariance[getIndex(i, j)] / m_entries;
    }

◆ getEntries()

value_type getEntries ( ) const

inline

Return the number of entries.

Definition at line 120 of file CalcMeanCov.h.

120{ return m_entries; }

◆ getIndex()

constexpr int getIndex	(	unsigned int	i,
		unsigned int	j
	)		const

inlineconstexprprivate

Access element in triangular matrix including diagonal elements.

This function returns the storage index of an element (i,j) in a symmetric matrix including diagonal elements if the elements are stored in a continous array of size n(n+1)/2

Definition at line 260 of file CalcMeanCov.h.

    {
      //swap indices if i >= j
      return (i < j) ? ((j + 1) * j / 2 + i) : ((i + 1) * i / 2 + j);
    }

◆ getMean() [1/2]

value_type getMean ( ) const

inline

Return the mean for parameter i.

Definition at line 152 of file CalcMeanCov.h.

    {
      static_assert(i >= 0 && i < N, "index i out of range");
      return m_mean[i];
    }

◆ getMean() [2/2]

value_type getMean ( int i ) const

inline

Return the mean for parameter i.

Definition at line 122 of file CalcMeanCov.h.

122{ return m_mean[i]; }

◆ getStddev() [1/2]

value_type getStddev ( ) const

inline

Return the standard deviation for parameter i.

Definition at line 178 of file CalcMeanCov.h.

    {
      return std::sqrt(getVariance<i>());
    }

◆ getStddev() [2/2]

value_type getStddev ( int i ) const

inline

Return the standard deviation for parameter i.

Definition at line 139 of file CalcMeanCov.h.

139{ return std::sqrt(getVariance(i)); }

Belle2::CalcMeanCov::getVariance

value_type getVariance() const

Return the variance for paramter i.

Definition: CalcMeanCov.h:173

◆ getSum() [1/2]

value_type getSum ( ) const

inline

Return the weighted sum values for parameter i.

Definition at line 183 of file CalcMeanCov.h.

    {
      return getMean<i>() * m_entries;
    }

◆ getSum() [2/2]

value_type getSum ( int i ) const

inline

Return the weighted sum values for parameter i.

Definition at line 141 of file CalcMeanCov.h.

141{ return getMean(i) * m_entries; }

Belle2::CalcMeanCov::getMean

value_type getMean() const

Return the mean for parameter i.

Definition: CalcMeanCov.h:152

◆ getVariance() [1/2]

value_type getVariance ( ) const

inline

Return the variance for paramter i.

Definition at line 173 of file CalcMeanCov.h.

    {
      return getCovariance<i, i>();
    }

◆ getVariance() [2/2]

value_type getVariance ( int i ) const

inline

Return the variance for paramter i.

Definition at line 137 of file CalcMeanCov.h.

137{ return getCovariance(i, i); }

◆ updateCov() [1/2]

void updateCov	(	value_type	weight,
		value_type	delta,
		value_type	x,
		T...	values
	)

inlineprivate

Update covariance between parameters i and j.

See also: addArrayValues

Template Parameters

i	first index
j	second index

Parameters

weight	weight of the entry
delta	difference between parameter i and mean of i
x	value of parameter j
values	remaining values with index >j

Definition at line 222 of file CalcMeanCov.h.

    {
      const value_type delta2 = (x - m_mean[j]);
      m_covariance[getIndex(i, j)] += (m_entries - weight) * weight
                                      / m_entries * delta * delta2;
      updateCov < i, j + 1 > (weight, delta, values...);
    }

◆ updateCov() [2/2]

void updateCov	(	value_type	,
		value_type
	)

inlineprivate

Break recursion of updateCov once all parameters are consumed.

Definition at line 232 of file CalcMeanCov.h.

232{}

Member Data Documentation

◆ m_covariance

value_type m_covariance[N *(N+1)/2]

private

Store the triangular covariance matrix for all parameters in continous memory.

Actual covariance is m_covariance[getIndex(i,j)]/m_entries

Definition at line 272 of file CalcMeanCov.h.

◆ m_entries

value_type m_entries

private

Store the sum of weights.

Definition at line 267 of file CalcMeanCov.h.

◆ m_mean

value_type m_mean[N]

private

Store the mean values for all parameters.

Definition at line 269 of file CalcMeanCov.h.

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

framework/utilities/include/CalcMeanCov.h

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ value_type

Constructor & Destructor Documentation

◆ CalcMeanCov()

Member Function Documentation

◆ add() [1/2]

◆ add() [2/2]

◆ addArray()

◆ addArrayValues()

◆ addValue() [1/2]

◆ addValue() [2/2]

◆ addWeighted()

◆ addWeightedArray()

◆ clear()

◆ getCorrelation() [1/2]

◆ getCorrelation() [2/2]

◆ getCovariance() [1/2]

◆ getCovariance() [2/2]

◆ getEntries()

◆ getIndex()

◆ getMean() [1/2]

◆ getMean() [2/2]

◆ getStddev() [1/2]

◆ getStddev() [2/2]

◆ getSum() [1/2]

◆ getSum() [2/2]

◆ getVariance() [1/2]

◆ getVariance() [2/2]

◆ updateCov() [1/2]

◆ updateCov() [2/2]

Member Data Documentation

◆ m_covariance

◆ m_entries

◆ m_mean