//

// FILE: Statistic.cpp

// AUTHOR: Rob dot Tillaart at gmail dot com

// modified at 0.3 by Gil Ross at physics dot org

// VERSION: 0.3.3

// PURPOSE: Recursive statistical library for Arduino

//

// NOTE: 2011-01-07 Gill Ross

// Rob Tillaart's Statistic library uses one-pass of the data (allowing

// each value to be discarded), but expands the Sum of Squares Differences to

// difference the Sum of Squares and the Average Squared. This is susceptible

// to bit length precision errors with the float type (only 5 or 6 digits

// absolute precision) so for long runs and high ratios of

// the average value to standard deviation the estimate of the

// standard error (deviation) becomes the difference of two large

// numbers and will tend to zero.

//

// For small numbers of iterations and small Average/SE th original code is

// likely to work fine.

// It should also be recognised that for very large samples, questions

// of stability of the sample assume greater importance than the

// correctness of the asymptotic estimators.

//

// This recursive algorithm, which takes slightly more computation per

// iteration is numerically stable.

// It updates the number, mean, max, min and SumOfSquaresDiff each step to

// deliver max min average, population standard error (standard deviation) and

// unbiassed SE.

// -------------

//

// HISTORY:

// 0.1 - 2010-10-29 initial version

// 0.2 - 2010-10-29 stripped to minimal functionality

// 0.2.01 - 2010-10-30

// added minimim, maximum, unbiased stdev,

// changed counter to long -> int overflows @32K samples

// 0.3 - 2011-01-07

// branched from 0.2.01 version of Rob Tillaart's code

// 0.3.1 - minor edits

// 0.3.2 - 2012-11-10

// minor edits

// changed count -> unsigned long allows for 2^32 samples

// added variance()

// 0.3.3 - 2015-03-07

// float -> double to support ARM (compiles)

// moved count() sum() min() max() to .h; for optimizing compiler

//

// Released to the public domain

//

#include "Statistic.h"

Statistic::Statistic()

{

clear();

}

// resets all counters

void Statistic::clear()

{

_cnt = 0;

_sum = 0.0;

_min = 0.0;

_max = 0.0;

#ifdef STAT_USE_STDEV

_ssqdif = 0.0; // not _ssq but sum of square differences

// which is SUM(from i = 1 to N) of

// (f(i)-_ave_N)**2

#endif

}

// adds a new value to the data-set

void Statistic::add(double value)

{

if (_cnt == 0)

{

_min = value;

_max = value;

} else {

if (value < _min) _min = value;

else if (value > _max) _max = value;

}

_sum += value;

_cnt++;

#ifdef STAT_USE_STDEV

if (_cnt > 1)

{

_store = (_sum / _cnt - value);

_ssqdif = _ssqdif + _cnt * _store * _store / (_cnt-1);

}

#endif

}

// returns the average of the data-set added sofar

double Statistic::average()

{

if (_cnt == 0) return NAN; // original code returned 0

return _sum / _cnt;

}

// Population standard deviation = s = sqrt [ S ( Xi - µ )2 / N ]

// http://www.suite101.com/content/how-is-standard-deviation-used-a99084

#ifdef STAT_USE_STDEV

double Statistic::variance()

{

if (_cnt == 0) return NAN; // otherwise DIV0 error

return _ssqdif / _cnt;

}

double Statistic::pop_stdev()

{

if (_cnt == 0) return NAN; // otherwise DIV0 error

return sqrt( _ssqdif / _cnt);

}

double Statistic::unbiased_stdev()

{

if (_cnt < 2) return NAN; // otherwise DIV0 error

return sqrt( _ssqdif / (_cnt - 1));

}

#endif

// END OF FILE