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add couple of 'mean' functions
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@VanyaBelyaev
VanyaBelyaev committed Jul 15, 2024
1 parent 84076a5 commit 012182b
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101 changes: 101 additions & 0 deletions source/include/Ostap/MoreMath.h
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#include <vector>
#include <complex>
#include <cmath>
#include <numeric>
#include <algorithm>
// ============================================================================
/** @file Ostap/MoreMath.h
* collection of various helper math functions
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( const std::complex<double>& x ,
const std::complex<double>& y ) ;
// ========================================================================
/** simple arithmetic mean for two real numbers (just for completeness)
* @param a the first number
* @param b the second number
* @return arithmetic mean
*/
inline
double
arithmetic_mean
( const double a ,
const double b ) { return 0.5 * ( a + b ) ; }
// ========================================================================
/** simple arithmetic mean for two complex numbers
* @param a the first number
* @param b the second number
* @return arithmetic mean
*/
inline
std::complex<double>
arithmetic_mean
( const std::complex<double>& a ,
const std::complex<double>& b ) { return 0.5 * ( a + b ) ; }
// ========================================================================
/** simple geometric mean for two real numbers (just for completeness)
* @param a the first number
* @param b the second number
Expand All @@ -506,6 +530,83 @@ namespace Ostap
( const std::complex<double>& a ,
const std::complex<double>& b ) ;
// ========================================================================
/** simple harmonic mean for two real numbers (just for completeness)
* @param a the first number
* @param b the second number
* @return harmonic mean
*/
double
harmonic_mean
( const double a ,
const double b ) ;
// ========================================================================
/** simple harmonic mean for two real numbers (just for completeness)
* @param a the first number
* @param b the second number
* @return harmonic mean
*/
std::complex<double>
harmonic_mean
( const std::complex<double>& a ,
const std::complex<double>& b ) ;
// ========================================================================
/** Heronian mean for two real numbers (just for completeness)
* @see https://en.wikipedia.org/wiki/Heronian_mean
* @param a the first number
* @param b the second number
* @return heronian mean
*/
double
heronian_mean
( const double a ,
const double b ) ;
// ========================================================================
/** Power mean for two real numbers (just for completeness)
* @see https://en.wikipedia.org/wiki/Power_mean
* @param x-parameter: 0<=x<=0.5
* @param a the first number
* @param b the second number
* @return power mean
*/
double
power_mean
( const double x ,
const double a ,
const double b ) ;
// ========================================================================
/** Heinz mean for two real numbers (just for completeness)
* @see https://en.wikipedia.org/wiki/Heinz_mean
* \f$ 0 \le x \l1 1/2 \f$
* @param x-parameter: 0<=x<=0.5
* @param a the first number
* @param b the second number
* @return Heinz mean
*/
double
heinz_mean
( const double x ,
const double a ,
const double b ) ;
// ========================================================================
/** Lehmer mean for two real numbers (just for completeness)
* @see https://en.wikipedia.org/wiki/Lehmer_mean
* - \f$ p \rigtharrow - \infty\f$ : minimal value
* - \f$ p = 0 \f$ : harmonic mean
* - \f$ p = 1/2 \f$ : geometric mean
* - \f$ p = 1 \f$ : arithmetic mean
* - \f$ p = 2 \f$ : contraharmonic mean
* - \f$ p \rigtharrow + \infty\f$ : maximal value
* @param p-parameter
* @param a the first number
* @param b the second number
* @return Lehmer mean
*/
double
lehmer_mean
( const double p ,
const double a ,
const double b ) ;
// ========================================================================

// ========================================================================
/** Gudermannian function
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119 changes: 119 additions & 0 deletions source/src/MoreMath.cpp
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Expand Up @@ -3699,6 +3699,125 @@ Ostap::Math::agm
}
// ============================================================================

// ============================================================================
/* simple harmonic mean for two real numbers (just for completeness)
* @param a the first number
* @param b the second number
* @return harmonic mean
*/
// ============================================================================
double
Ostap::Math::harmonic_mean
( const double a ,
const double b )
{ return
s_zero ( a ) ? 0.0 :
s_zero ( b ) ? 0.0 :
2.0 / ( 1. / a + 1. / b ) ; }
// ============================================================================
/* simple harmonic mean for two real numbers (just for completeness)
* @param a the first number
* @param b the second number
* @return harmonic mean
*/
// ============================================================================
std::complex<double>
Ostap::Math::harmonic_mean
( const std::complex<double>& a ,
const std::complex<double>& b )
{
return
s_zero ( a.real() ) && s_zero ( a.imag() ) ? 0.0 :
s_zero ( b.real() ) && s_zero ( b.imag() ) ? 0.0 :
2.0 / ( 1. / a + 1. / b ) ;
}
// ============================================================================
/* Heronian mean for two real numbers (just for completeness)
* @see https://en.wikipedia.org/wiki/Heronian_mean
* @param a the first number
* @param b the second number
* @return heronian mean
*/
// ============================================================================
double
Ostap::Math::heronian_mean
( const double a ,
const double b )
{
return ( a + std::sqrt ( a * b ) + b ) / 3 ;
}
// ============================================================================
/** Power mean for two real numbers
* @see https://en.wikipedia.org/wiki/Power_mean
* @param x-parameter: 0<=x<=0.5
* @param a the first number
* @param b the second number
* @return power mean
*/
// ============================================================================
double
Ostap::Math::power_mean
( const double p ,
const double a ,
const double b )
{
return
s_zero ( p ) ? geometric_mean ( a , b ) :
std::pow ( 0.5 * ( std::pow ( a , p ) + std::pow ( b , p ) ) , 1.0 / p ) ;
}
// ============================================================================
/* Heinz mean for two real numbers (just for completeness)
* @see https://en.wikipedia.org/wiki/Heinz_mean
* \f$ 0 \le x \l1 1/2 \f$
* @param x-parameter: 0<=x<=0.5
* @param a the first number
* @param b the second number
* @return Heinz mean
*/
// ============================================================================
double
Ostap::Math::heinz_mean
( const double x ,
const double a ,
const double b )
{
return
( x <= 0 ) || s_zero ( x ) ? 0.5 * ( a + b ) :
( 0.5 <= x ) || s_equal ( x , 0.5 ) ? std::sqrt ( a * b ) :
0.5 * ( std::pow ( a , x ) * std::pow ( b , 1 - x ) +
std::pow ( a , 1 - x ) * std::pow ( b , x ) ) ;
}
// ============================================================================
/* Lehmer mean for two real numbers (just for completeness)
* @see https://en.wikipedia.org/wiki/Lehmer_mean
* - \f$ p \rigtharrow - \infty\f$ : minimal value
* - \f$ p = 0 \f$ : harmonic mean
* - \f$ p = 1/2 \f$ : geometric mean
* - \f$ p = 1 \f$ : ariphmetic mean
* - \f$ p = 2 \f$ : contraharmonic mean
* - \f$ p \rigtharrow + \infty\f$ : maximal value
* @param p-parameter
* @param a the first number
* @param b the second number
* @return Lehmer mean
*/
// ============================================================================
double
Ostap::Math::lehmer_mean
( const double p ,
const double a ,
const double b )
{
return
s_zero ( p ) ? harmonic_mean ( a , b ) :
s_equal ( p , 0.5 ) ? geometric_mean ( a , b ) :
s_equal ( p , 1 ) ? arithmetic_mean ( a , b ) :
( std::pow ( a , p ) + std::pow ( b , p ) ) /
( std::pow ( a , p - 1 ) + std::pow ( b , p - 1 ) ) ;
}
// ============================================================================



// ============================================================================
/* Gudermannian function
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