0.4.0 add useStdDev param of constructor and clear

LICENSE

@@ -1,6 +1,6 @@
 MIT License
 
-Copyright (c) 2020 Rob Tillaart
+Copyright (c) 2010-2020 Rob Tillaart
 
 Permission is hereby granted, free of charge, to any person obtaining a copy
 of this software and associated documentation files (the "Software"), to deal

README.md

@@ -1,2 +1,81 @@
 # Statistic
+
 Statistic library for Arduino includes sum, average, variance and std deviation
+
+# Description
+
+The statistic library is made to get basic statistical information from a 
+one dimensional set of data, e.g. a stream of values of a sensor.
+
+The stability of the formulas is improved by the help of Gil Ross (Thanks!)
+
+The functions implemented are:
+
+* **clear(useStdDev)**
+* **add(value)**
+* **count()**   returns zero if count == zero (of course)
+* **sum()**     returns zero if count == zero
+* **minimum()** returns zero if count == zero
+* **maximum()** returns zero if count == zero
+* **average()** returns NAN if count == zero
+
+These three functions only work id useStdDev == true:
+
+* **variance()**         returns NAN if count == zero
+* **pop_stdev()**        population stdev, returns NAN if count == zero
+* **unbiased_stdev()**   returnsNAN if count == zero
+
+
+# Operational
+
+See examples
+
+# FAQ
+
+### Q: Are individual samples still available?
+The values added to the library are not stored in the lib as it would use lots 
+of memory quite fast. Instead a few calculated values are kept to be able to 
+calculate the most important statistics. 
+
+
+### Q: How many samples can the lib hold?  (internal variables and overflow)
+The counter of samples is an **uint32_t**, implying a maximum of about **4 billion** samples. 
+In practice 'strange' things might happen before this number is reached. 
+There are two internal variables, **_sum** which is the sum of the values and **_ssq** 
+which is the sum of the squared values. Both can overflow especially **_ssq** 
+can and probably will grow fast. The library does not protect against it.
+
+There is a workaround for this (to some extend) if one knows the approx 
+average of the samples before. Before adding values to the lib subtract 
+the expected average. The sum of the samples would move to around zero. 
+This workaround has no influence on the standard deviation. 
+
+!! Do not forget to add the expected average to the calculated average.
+
+*(Q: should this subtraction trick be build into the lib?)*
+
+
+### Q: How about the precision of the library?
+The precision of the internal variables is restricted due to the fact 
+that they are 32 bit float (IEEE754). If the internal variable **_sum** has 
+a large value, adding relative small values to the dataset wouldn't 
+change its value any more. Same is true for **_ssq**. One might argue that 
+statistically speaking these values are less significant, but in fact it is wrong.
+
+There is a workaround for this (to some extend). If one has the samples in an 
+array or on disk, one can sort the samples in increasing order (abs value) 
+and add them from this sorted list. This will minimize the error, 
+but it works only if the samples are available and the they may be added 
+in the sorted increasing order.
+
+
+### Q: When will internal var's overflow? esp. squared sum
+IEEE754 floats have a max value of about **+-3.4028235E+38**
+
+
+### Q: Why are there two functions for stdev?
+There are two stdev functions the population stdev and the unbiased stdev. 
+See Wikipedia for an elaborate description of the difference between these two.
+
+
+

Statistic.cpp

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+//
+//    FILE: Statistic.cpp
+//  AUTHOR: Rob dot Tillaart at gmail dot com
+//          modified at 0.3 by Gil Ross at physics dot org
+// VERSION: 0.4.0
+// 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   2012-11-10 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
+// 0.3.4   2017-07-31
+//         Refactored const in many places
+//         [reverted] double to float on request as float is 99.99% of the cases
+//         good enough and float(32 bit) is supported in HW for some processors.
+// 0.3.5   2017-09-27
+//         Added #include <Arduino.h> to fix uint32_t bug
+// 0.4.0   2020-05-13
+//         refactor
+//         Added flag to switch on the use of stdDev runtime. [idea marc.recksiedl]
+
+
+#include "Statistic.h"
+
+Statistic::Statistic(bool useStdDev)
+{
+    clear(useStdDev);
+}
+
+void Statistic::clear(bool useStdDev)	// useStdDev default true.
+{
+    _cnt = 0;
+    _sum = 0;
+    _min = 0;
+    _max = 0;
+    _useStdDev = useStdDev;
+    _ssqdif = 0.0;
+    // note not _ssq but sum of square differences
+    // which is SUM(from i = 1 to N) of f(i)-_ave_N)**2
+}
+
+// adds a new value to the data-set
+void Statistic::add(const float value)
+{
+    if (_cnt == 0)
+    {
+        _min = value;
+        _max = value;
+    } else {
+        if (value < _min) _min = value;
+        else if (value > _max) _max = value;
+    }
+    _sum += value;
+    _cnt++;
+
+    if (_useStdDev && (_cnt > 1))
+    {
+        float _store = (_sum / _cnt - value);
+        _ssqdif = _ssqdif + _cnt * _store * _store / (_cnt - 1);
+
+        // ~10% faster but limits the amount of samples to 65K as _cnt*_cnt overflows
+        // float _store = _sum - _cnt * value;
+        // _ssqdif = _ssqdif + _store * _store / (_cnt*_cnt - _cnt);
+		//
+		// solution:  TODO verify
+		// _ssqdif = _ssqdif + (_store * _store / _cnt) / (_cnt - 1);
+    }
+}
+
+// returns the average of the data-set added sofar
+float Statistic::average() const
+{
+    if (_cnt == 0) return NAN; // prevent DIV0 error
+    return _sum / _cnt;
+}
+
+// Population standard deviation = s = sqrt [ S ( Xi - µ )2 / N ]
+// http://www.suite101.com/content/how-is-standard-deviation-used-a99084
+float Statistic::variance() const
+{
+    if (!_useStdDev) return NAN;
+    if (_cnt == 0) return NAN; // prevent DIV0 error
+    return _ssqdif / _cnt;
+}
+
+float Statistic::pop_stdev() const
+{
+    if (!_useStdDev) return NAN;
+    if (_cnt == 0) return NAN; // prevent DIV0 error
+    return sqrt( _ssqdif / _cnt);
+}
+
+float Statistic::unbiased_stdev() const
+{
+    if (!_useStdDev) return NAN;
+    if (_cnt < 2) return NAN; // prevent DIV0 error
+    return sqrt( _ssqdif / (_cnt - 1));
+}
+
+// -- END OF FILE --

Statistic.h

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+#pragma once
+//
+//    FILE: Statistic.h
+//  AUTHOR: Rob dot Tillaart at gmail dot com
+//          modified at 0.3 by Gil Ross at physics dot org
+// VERSION: 0.4.0
+// PURPOSE: Recursive Statistical library for Arduino
+// HISTORY: See Statistic.cpp
+//
+
+#include <Arduino.h>
+#include <math.h>
+
+#define STATISTIC_LIB_VERSION "0.4.0"
+
+class Statistic
+{
+public:
+    Statistic(bool useStdDev = true);             // "switches on/off" stdev run time
+    void clear(bool useStdDev = true);            // "switches on/off" stdev run time
+    void add(const float);
+
+    // returns the number of values added
+    uint32_t count() const { return _cnt; };      // zero if count == zero
+    float sum() const      { return _sum; };      // zero if count == zero
+    float minimum() const  { return _min; };      // zero if count == zero
+    float maximum() const  { return _max; };      // zero if count == zero
+    float average() const;                        // NAN if count == zero
+
+    // useStdDev must be true to use next three
+    float variance() const;                       // NAN if count == zero
+    float pop_stdev() const; // population stdev  // NAN if count == zero
+    float unbiased_stdev() const;                 // NAN if count == zero
+
+protected:
+    uint32_t _cnt;
+    float    _sum;
+    float    _min;
+    float    _max;
+    bool     _useStdDev;
+    float    _ssqdif;    // sum of squares difference
+
+};
+
+// -- END OF FILE -- 

examples/Average/Average.ino

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+//
+//    FILE: Average.ino
+//  AUTHOR: Rob dot Tillaart at gmail dot com
+// VERSION: 0.4
+// PURPOSE: Sample sketch for statistic library Arduino
+//
+
+#include "Statistic.h"
+
+Statistic myStats;
+
+uint32_t start;
+uint32_t stop;
+
+void setup(void)
+{
+  Serial.begin(115200);
+  Serial.println(__FILE__);
+  Serial.print("Demo Statistics lib ");
+  Serial.println(STATISTIC_LIB_VERSION);
+  myStats.clear(); //explicitly start clean
+  start = millis();
+}
+
+void loop(void)
+{
+  long rn = random(0, 9999);
+  myStats.add(rn / 100.0 + 1);
+  if (myStats.count() == 10000)
+  {
+    stop = millis();
+    Serial.print("        Count: ");
+    Serial.println(myStats.count());
+    Serial.print("          Min: ");
+    Serial.println(myStats.minimum(), 4);
+    Serial.print("          Max: ");
+    Serial.println(myStats.maximum(), 4);
+    Serial.print("      Average: ");
+    Serial.println(myStats.average(), 4);
+    Serial.print("     variance: ");
+    Serial.println(myStats.variance(), 4);
+    Serial.print("    pop stdev: ");
+    Serial.println(myStats.pop_stdev(), 4);
+    Serial.print(" unbias stdev: ");
+    Serial.println(myStats.unbiased_stdev(), 4);
+    Serial.print("     time(ms): ");
+    Serial.println(stop - start);
+    Serial.println("=====================================");
+    myStats.clear();
+    delay(1000);
+    start = millis();
+  }
+}

examples/StatisticArray/StatisticArray.ino

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+//
+//    FILE: StatisticArray.ino
+//  AUTHOR: Rob dot Tillaart at gmail dot com
+// VERSION: 0.1
+// PURPOSE: Sample sketch for statistic library Arduino
+//
+
+#include "Statistic.h"
+
+Statistic stats[4];
+
+void setup(void)
+{
+  Serial.begin(115200);
+  Serial.println(__FILE__);
+  Serial.print("Demo Statistics lib ");
+  Serial.println(STATISTIC_LIB_VERSION);
+  for (int i=0; i<4; i++)
+  {
+    stats[i].clear(); //explicitly start clean
+  }
+}
+
+void loop(void)
+{
+  long rn = random(0, 9999);
+  int idx = random(0, 4);
+  stats[idx].add(rn / 100.0 + 1);
+  
+  if (stats[idx].count() == 10000)
+  {
+    Serial.print("IDX: ");
+    Serial.println(idx);
+    Serial.print("        Count: ");
+    Serial.println(stats[idx].count());
+    Serial.print("          Min: ");
+    Serial.println(stats[idx].minimum(), 4);
+    Serial.print("          Max: ");
+    Serial.println(stats[idx].maximum(), 4);
+    Serial.print("      Average: ");
+    Serial.println(stats[idx].average(), 4);
+    Serial.println("=====================================");
+    stats[idx].clear();
+  }
+}

examples/TimingTest/TimingTest.ino

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+//
+//    FILE: TimingTest.ino
+//  AUTHOR: Rob dot Tillaart at gmail dot com
+// VERSION: 0.2.0
+// PURPOSE: measure time difference for runtime stddev toggle.
+//          add is 1024 millis faster for 10K adds ==> ~ 100uSec per add faster.
+
+#include "Statistic.h"
+
+Statistic myStats;
+
+uint32_t start;
+uint32_t stop;
+
+bool useStdDev = true;
+
+void setup(void)
+{
+  Serial.begin(115200);
+  Serial.println(__FILE__);
+  Serial.print("Demo Statistics lib ");
+  Serial.println(STATISTIC_LIB_VERSION);
+  myStats.clear(useStdDev);
+  start = millis();
+}
+
+void loop(void)
+{
+  long rn = random(0, 9999);
+  myStats.add(rn / 100.0 + 1);
+  if (myStats.count() == 10000)
+  {
+    stop = millis();
+    Serial.print("        Count: ");
+    Serial.println(myStats.count());
+    Serial.print("          Min: ");
+    Serial.println(myStats.minimum(), 4);
+    Serial.print("          Max: ");
+    Serial.println(myStats.maximum(), 4);
+    Serial.print("      Average: ");
+    Serial.println(myStats.average(), 4);
+    if (useStdDev)
+    {
+      Serial.print("     variance: ");
+      Serial.println(myStats.variance(), 4);
+      Serial.print("    pop stdev: ");
+      Serial.println(myStats.pop_stdev(), 4);
+      Serial.print(" unbias stdev: ");
+      Serial.println(myStats.unbiased_stdev(), 4);
+    }
+    Serial.print("     time(ms): ");
+    Serial.println(stop - start);
+    Serial.println("=====================================");
+    useStdDev = !useStdDev;
+    myStats.clear(useStdDev);
+    start = millis();
+  }
+}
+
+// -- END OF FILE --

keywords.txt

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+# Syntax Coloring Map For Statistic
+
+# Datatypes (KEYWORD1)
+Statistic	KEYWORD1
+
+# Methods and Functions (KEYWORD2)
+clear	KEYWORD2
+add	KEYWORD2
+count	KEYWORD2
+sum	KEYWORD2
+minimum	KEYWORD2
+maximum	KEYWORD2
+average	KEYWORD2
+variance	KEYWORD2
+pop_stdev	KEYWORD2
+unbiased_stdev	KEYWORD2
+
+# Instances (KEYWORD2)
+
+# Constants (LITERAL1)
+STATISTIC_LIB_VERSION	LITERAL1

library.json

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+{
+  "name": "Statistic",
+  "keywords": "Statistic,sum,min,max,average,variance,standard,deviation,population,unbiased",
+  "description": "Library with basic statistical functions for Arduino.",
+  "authors":
+  [
+    {
+      "name": "Rob Tillaart",
+      "email": "Rob.Tillaart@gmail.com",
+      "maintainer": true
+    },
+    {
+      "name": "Gil Ross"
+    }
+  ],
+  "repository":
+  {
+    "type": "git",
+    "url": "https://github.com/RobTillaart/Arduino.git"
+  },
+  "version":"0.4.0",
+  "frameworks": "arduino",
+  "platforms": "*",
+  "export": {
+    "include": "libraries/Statistic"
+  }
+}

library.properties

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+name=Statistic
+version=0.4.0
+author=Rob Tillaart <rob.tillaart@gmail.com>
+maintainer=Rob Tillaart <rob.tillaart@gmail.com>
+sentence=Library with basic statistical functions for Arduino. 
+paragraph=Supports 
+category=Data Processing
+url=https://github.com/RobTillaart/Statistic
+architectures=*
+includes=Statistic.h
+depends=