Calculate rolling moving average in C

Question

I know this is achievable with boost as per   Using boost  accumulators  how can I reset a rolling window size  does it keep extra history   But I really would like to avoid using boost  I have googled and not found any suitable or readable examples   Basically I want to track the moving average of an ongoing stream of a stream of floating point numbers using the most recent 1000 numbers as a data sample   What is the easiest way to achieve this     I experimented with using a circular array  exponential moving average and a more simple moving average and found that the results from the circular array suited my needs best

User · Answer

You can approximate a rolling average by applying a weighted average on your input stream.

template <unsigned N>
double approxRollingAverage (double avg, double input) {
    avg -= avg/N;
    avg += input/N;
    return avg;
}

This way, you don't need to maintain 1000 buckets. However, it is an approximation, so it's value will not match exactly with a true rolling average.

Edit: Just noticed @steveha's post. This is equivalent to the exponential moving average, with the alpha being 1/N (I was taking N to be 1000 in this case to simulate 1000 buckets).

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One way can be to circularly store the values in the buffer array  and calculate average this way    int j    int   counter   size   buffer j    mostrecentvalue  avg    avg   size - buffer j - 1    -1   size - 1   j - 1    buffer j     size   counter        buffer j - 1    -1   size - 1   j - 1  is the oldest value stored   The whole thing runs in a loop where most recent value is dynamic

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Basically I want to track the moving average of an ongoing stream of a stream of floating point numbers using the most recent 1000 numbers as a data sample    Note that the below updates the total  as elements as added replaced  avoiding costly O N  traversal to calculate the sum - needed for the average - on demand   template  lt typename T  typename Total  size t N gt  class Moving Average     public      void operator   T sample                if  num samples   lt  N                        samples  num samples       sample              total     sample                    else                       T amp  oldest   samples  num samples      N               total     sample - oldest              oldest   sample                       operator double   const   return total    std  min num samples   N        private      T samples  N       size t num samples  0       Total total  0        Total is made a different parameter from T to support e g  using a long long when totalling 1000 longs  an int for chars  or a double to total floats   Issues  This is a bit flawed in that num samples  could conceptually wrap back to 0  but it s hard to imagine anyone having 2 64 samples  if concerned  use an extra bool data member to record when the container is first filled while cycling num samples  around the array  best then renamed something innocuous like  pos     Another issue is inherent with floating point precision  and can be illustrated with a simple scenario for T double  N 2  we start with total    0  then inject samples      1E17  we execute total     1E17  so total     1E17  then inject 1  we execute total    1  but total     1E17 still  as the  1  is too insignificant to change the 64-bit double representation of a number as large as 1E17  then we inject 2  we execute total    2 - 1E17  in which 2 - 1E17 is evaluated first and yields -1E17 as the 2 is lost to imprecision insignificance  so to our total of 1E17 we add -1E17 and total  becomes 0  despite current samples of 1 and 2 for which we d want total  to be 3   Our moving average will calculate 0 instead of 1 5   As we add another sample  we ll subtract the  oldest  1 from total  despite it never having been properly incorporated therein  our total  and moving averages are likely to remain wrong    You could add code that stores the highest recent total  and if the current total  is too small a fraction of that  a template parameter could provide a multiplicative threshold   you recalculate the total  from all the samples in the samples  array  and set highest recent total  to the new total    but I ll leave that to the reader who cares sufficiently

User · Answer

I used a deque    seems to work for me   This example has a vector  but you could skip that aspect and simply add them to deque   include  lt deque gt   template  lt typename T gt  double mov avg vector lt T gt  vec  int len     deque lt T gt  dq         for auto i   0 i  lt  vec size   i         if i  lt  len         dq push back vec i              else         dq pop front          dq push back vec i                double cs   0    for auto i   dq       cs    i        return cs   len         Skip the vector portion  track the input number  or size of deque   and the value      double len   10    double val    Accept as input   double instance    Increment each time input accepted     deque lt double gt  dq    if instance  lt  len         dq push back val         else         dq pop front          dq push back val               double cs   0    for auto i   dq       cs    i        double rolling avg   cs   len     To simplify further -- add values to this  then simply average the deque   int MAX DQ   3   void add to dq deque lt double gt   amp dq  double value       if dq size    lt  MAX DQ         dq push back value        else         dq pop front          dq push back value                Another sort of hack I use occasionally is using mod to overwrite values in a vector    vector lt int gt  test mod    0 0 0 0 0     int write   0    int LEN   5       int instance   0    Filler for N -- of Nth Number added    int value   0    Filler for new number     write   instance   LEN    test mod write    value      Will write to 0  1  2  3  4  0  1  2  3          Then average it for MA       To test it      int write idx   0    int len   5    int new value    for auto i 0 i lt 100 i           cin  gt  gt  new value        write idx   i   len        test mod write idx    new value   This last  hack  has no buckets  buffers  loops  nothing  Simply a vector that s overwritten   And it s 100  accurate  for avg   values in vector   Proper order is rarely  maintained  as it starts rewriting backwards  at 0   so 5th index would be at 0 in example  5 1 2 3 4   etc

User · Answer

a simple moving average for 10 items  using a list    include  lt list gt   std  list lt float gt  listDeltaMA   float getDeltaMovingAverage float delta        listDeltaMA push back delta       if  listDeltaMA size    gt  10  listDeltaMA pop front        float sum   0      for  std  list lt float gt   iterator p   listDeltaMA begin    p    listDeltaMA end      p          sum     float  p      return sum   listDeltaMA size

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I use this quite often in hard realtime systems that have fairly insane update rates  50kilosamples sec  As a result I typically precompute the scalars   To compute a moving average of N samples  scalar1   1 N  scalar2   1 - scalar1     or  1 - 1 N  then   Average   currentSample scalar1   Average scalar2   Example  Sliding average of 10 elements  double scalar1   1 0 10 0      0 1 double scalar2   1 0 - scalar1     0 9 bool first sample   true  double average 0 0  while someCondition       double newSample   getSample       if first sample              everybody forgets the initial condition  sigh        average   newSample        first sample   false          else            average    sample scalar1     average scalar2             Note  this is just a practical implementation of the answer given by steveha above   Sometimes it s easier to understand a concrete example

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You could implement a ring buffer  Make an array of 1000 elements  and some fields to store the start and end indexes and total size  Then just store the last 1000 elements in the ring buffer  and recalculate the average as needed

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Incrementing on  Nilesh s answer  credit goes to him   you can   keep track of the sum  no need to divide and then multiply every time  generating error avoid if conditions using   operator  This is UNTESTED sample code to show the idea  it could also be wrapped into a class  const unsigned int size 10     ten elements buffer  unsigned int counterPosition 0  unsigned int counterNum 0   int buffer size   long sum 0   void reset         for int i 0 i lt size i              buffer i  0           float addValue int value        unsigned  int oldPos     counterPosition   1    size        buffer counterPosition    value      sum    sum - buffer oldPos    value         counterPosition  counterPosition 1    size      if counterNum lt size  counterNum         return   float sum   float counterNum     float removeValue         unsigned  int oldPos    counterPosition   1    size        buffer counterPosition    0      sum    sum - buffer oldPos          if counterNum gt 1       leave one last item at the end  forever         counterPosition  counterPosition 1    size          counterNum--     here the two counters are different           return   float sum   float counterNum     It should be noted that  if the buffer is reset to all zeroes  this method works fine while receiving the first values in as - buffer oldPos  is zero and counter grows  First output is the first number received  Second output is the average of only the first two  and so on  fading in the values while they arrive until size items are reached  It is also worth considering that this method  like any other for rolling average  is asymmetrical  if you stop at the end of the input array  because the same fading does not happen at the end  it can happen after the end of data  with the right calculations   That is correct  The rolling average of 100 elements with a buffer of 10 gives different results  10 fading in  90 perfectly rolling 10 elements  and finally 10 fading out  giving a total of 110 results for 100 numbers fed in  It s your choice to decide which ones to show  and if it s better going the straight way  old to recent  or backwards  recent to old   To fade out correctly after the end  you can go on adding zeroes one by one and reducing the count of items by one every time until you have reached size elements  still keeping track of correct position of old values   Usage is like this  int avg 0  reset     avg addValue 2      Rpeat for 100 times avg addValue 3      Use avg value       avg addValue -4   avg addValue 12      last numer  100th input      If you want to fade out repeat 10 times after the end of data   avg removeValue       Rpeat for last 10 times after data has finished avg removeValue       Use avg value     avg removeValue    avg removeValue

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You simply need a circular array  circular buffer  of 1000 elements  where you add the element to the previous element and store it   It becomes an increasing sum  where you can always get the sum between any two pairs of elements  and divide by the number of elements between them  to yield the average

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Simple class to calculate rolling average and also rolling standard deviation    define  stdev cnt  sum  ssq  sqrt    double  cnt   ssq-pow  double  sum  2       double  cnt    double  cnt -1     class moving average   private      boost  circular buffer lt int gt   q      double sum      double ssq  public      moving average int n             sum 0          ssq 0          q   new boost  circular buffer lt int gt  n              moving average             delete q            void push double v            if  q- gt size      q- gt capacity                  double t q- gt front                sum- t              ssq- t t              q- gt pop front                      q- gt push back v           sum  v          ssq  v v            double size             return q- gt size              double mean             return sum size              double stdev             return  stdev size    sum  ssq

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If your needs are simple  you might just try using an exponential moving average   http   en wikipedia org wiki Moving average Exponential moving average  Put simply  you make an accumulator variable  and as your code looks at each sample  the code updates the accumulator with the new value   You pick a constant  alpha  that is between 0 and 1  and compute this   accumulator    alpha   new value     1 0 - alpha    accumulator   You just need to find a value of  alpha  where the effect of a given sample only lasts for about 1000 samples   Hmm  I m not actually sure this is suitable for you  now that I ve put it here   The problem is that 1000 is a pretty long window for an exponential moving average  I m not sure there is an alpha that would spread the average over the last 1000 numbers  without underflow in the floating point calculation   But if you wanted a smaller average  like 30 numbers or so  this is a very easy and fast way to do it

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