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150 lines
4.5 KiB
C++
150 lines
4.5 KiB
C++
//
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// FILE: Statistic.cpp
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// AUTHOR: Rob dot Tillaart at gmail dot com
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// modified at 0.3 by Gil Ross at physics dot org
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// VERSION: 0.4.4
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// PURPOSE: Recursive statistical library for Arduino
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//
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// NOTE: 2011-01-07 Gill Ross
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// Rob Tillaart's Statistic library uses one-pass of the data (allowing
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// each value to be discarded), but expands the Sum of Squares Differences to
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// difference the Sum of Squares and the Average Squared. This is susceptible
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// to bit length precision errors with the float type (only 5 or 6 digits
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// absolute precision) so for long runs and high ratios of
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// the average value to standard deviation the estimate of the
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// standard error (deviation) becomes the difference of two large
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// numbers and will tend to zero.
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//
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// For small numbers of iterations and small Average/SE the original code is
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// likely to work fine.
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// It should also be recognised that for very large samples, questions
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// of stability of the sample assume greater importance than the
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// correctness of the asymptotic estimators.
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//
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// This recursive algorithm, which takes slightly more computation per
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// iteration is numerically stable.
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// It updates the number, mean, max, min and SumOfSquaresDiff each step to
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// deliver max min average, population standard error (standard deviation) and
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// unbiased SE.
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// -------------
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//
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// HISTORY:
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// 0.1 2010-10-29 initial version
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// 0.2 2010-10-29 stripped to minimal functionality
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// 0.2.01 2010-10-30
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// added minimum, maximum, unbiased stdev,
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// changed counter to long -> int overflows @32K samples
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// 0.3 2011-01-07
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// branched from 0.2.01 version of Rob Tillaart's code
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// 0.3.1 2012-11-10 minor edits
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// 0.3.2 2012-11-10 minor edits
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// changed count -> unsigned long allows for 2^32 samples
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// added variance()
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// 0.3.3 2015-03-07
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// float -> double to support ARM (compiles)
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// moved count() sum() min() max() to .h; for optimizing compiler
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// 0.3.4 2017-07-31
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// Refactored const in many places
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// [reverted] double to float on request as float is 99.99% of the cases
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// good enough and float(32 bit) is supported in HW for some processors.
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// 0.3.5 2017-09-27
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// Added #include <Arduino.h> to fix uint32_t bug
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// 0.4.0 2020-05-13
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// refactor
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// Added flag to switch on the use of stdDev runtime. [idea marc.recksiedl]
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// 0.4.1 2020-06-19 fix library.json
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// 0.4.2 2021-01-08 add Arduino-CI + unit tests
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// 0.4.3 2021-01-20 add() returns how much was actually added.
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// 0.4.4 2021-12-28 update library.json, readme, license, minor edits
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#include "Statistic.h"
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Statistic::Statistic(bool useStdDev)
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{
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clear(useStdDev);
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}
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void Statistic::clear(bool useStdDev) // useStdDev default true.
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{
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_cnt = 0;
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_sum = 0;
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_min = 0;
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_max = 0;
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_useStdDev = useStdDev;
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_ssqdif = 0.0;
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// note not _ssq but sum of square differences
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// which is SUM(from i = 1 to N) of f(i)-_ave_N)**2
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}
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// adds a new value to the data-set
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float Statistic::add(const float value)
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{
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float previousSum = _sum;
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if (_cnt == 0)
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{
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_min = value;
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_max = value;
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} else {
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if (value < _min) _min = value;
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else if (value > _max) _max = value;
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}
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_sum += value;
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_cnt++;
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if (_useStdDev && (_cnt > 1))
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{
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float _store = (_sum / _cnt - value);
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_ssqdif = _ssqdif + _cnt * _store * _store / (_cnt - 1);
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// ~10% faster but limits the amount of samples to 65K as _cnt*_cnt overflows
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// float _store = _sum - _cnt * value;
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// _ssqdif = _ssqdif + _store * _store / (_cnt*_cnt - _cnt);
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//
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// solution: TODO verify
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// _ssqdif = _ssqdif + (_store * _store / _cnt) / (_cnt - 1);
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}
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return _sum - previousSum;
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}
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// returns the average of the data-set added sofar
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float Statistic::average() const
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{
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if (_cnt == 0) return NAN; // prevent DIV0 error
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return _sum / _cnt;
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}
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// Population standard deviation = s = sqrt [ S ( Xi - <20> )2 / N ]
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// http://www.suite101.com/content/how-is-standard-deviation-used-a99084
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float Statistic::variance() const
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{
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if (!_useStdDev) return NAN;
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if (_cnt == 0) return NAN; // prevent DIV0 error
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return _ssqdif / _cnt;
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}
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float Statistic::pop_stdev() const
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{
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if (!_useStdDev) return NAN;
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if (_cnt == 0) return NAN; // prevent DIV0 error
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return sqrt( _ssqdif / _cnt);
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}
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float Statistic::unbiased_stdev() const
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{
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if (!_useStdDev) return NAN;
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if (_cnt < 2) return NAN; // prevent DIV0 error
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return sqrt( _ssqdif / (_cnt - 1));
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}
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// -- END OF FILE --
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