GetStdDev is a math code snippet to calculate the standard deviation of the values in a container.


#include <cassert>

#include <cmath>

#include <functional>

#include <numeric>

#include <vector>



template  <class T> struct SquareAccumulator

  : public std::binary_function<T,T,T>

{

  const T operator()(const T& sum, const T& x) const

    { return sum+(x*x); }

};



//From http://www.richelbilderbeek.nl/CppGetStdDev.htm

double GetStdDev(const std::vector<double>& v)

{

  assert(v.size() > 1

    && "Can only calculate standard deviations from "

       "data sets with size 2 or larger");

  const double sum_x

    = std::accumulate(v.begin(),v.end(),0.0);

  const double sum_x_squared

    = std::accumulate(v.begin(),v.end(),

        0.0,SquareAccumulator<double>());

  const double sz = static_cast<double>(v.size());

  return std::sqrt(((sz*sum_x_squared)-(sum_x*sum_x))

    / (sz*(sz-1.0)));

}

GetStdDev test

GetStdDev was tested by a previous version of this code snippet.


#include <cassert>

#include <cmath>

#include <functional>

#include <numeric>

#include <vector>



template  <class T> struct SquareAccumulator

  : public std::binary_function<T,T,T>

{

  const T operator()(const T& sum, const T& x) const

    { return sum+(x*x); }

};



//From http://www.richelbilderbeek.nl/CppGetStdDev.htm

double GetStdDev(const std::vector<double>& v)

{

  assert(v.size() > 1

    && "Can only calculate standard deviations from "

       "data sets with size 2 or larger");

  const double sum_x

    = std::accumulate(v.begin(),v.end(),0.0);

  const double sum_x_squared

    = std::accumulate(v.begin(),v.end(),

        0.0,SquareAccumulator<double>());

  const double sz = static_cast<double>(v.size());

  return std::sqrt(((sz*sum_x_squared)-(sum_x*sum_x))

    / (sz*(sz-1.0)));

}



//From http://www.richelbilderbeek.nl/CppGetStdDev.htm

double GetStdDevOld(const std::vector<double>& v)

{

  const std::size_t sz = v.size();

  assert(sz>1);



  double sumX = 0.0;

  double sumXsquared = 0.0;

  for (std::size_t i=0; i!=sz; ++i)

  {

    const double x = v[i];

    sumX+=x;

    sumXsquared+=(x*x);

  }

  const double dSize = static_cast<double>(sz);

  return std::sqrt(((dSize*sumXsquared)

    -(sumX*sumX))/(dSize *(dSize-1.0)));

}



#include <cstdlib>



//From htpp://www.richelbilderbeek.nl/CppGetRandomUniform.htm

double GetRandomUniform()

{

  return static_cast<double>(std::rand())

    / static_cast<double>(RAND_MAX);

}



#include <iostream>



//From htpp://www.richelbilderbeek.nl/CppGetStdDev.htm

int main()

{

  std::vector<double> v;

  v.push_back(GetRandomUniform());

  v.push_back(GetRandomUniform());



  int max = 2;

  while (max != 33554432)

  {

    for (int i=0; i!=max; ++i)

    {

      v.push_back(GetRandomUniform());

    }

    std::cout << max << ":\t"

      << GetStdDev(v) << "\t"

      << GetStdDevOld(v) << std::endl;



    max*=2;

  }

}

Screen output:


Starting /MyFolder/MyProject...

2:	0.207834	0.207834

4:	0.273555	0.273555

8:	0.2501	0.2501

16:	0.295567	0.295567

32:	0.301386	0.301386

64:	0.28569	0.28569

128:	0.290935	0.290935

256:	0.283272	0.283272

512:	0.283464	0.283464

1024:	0.289154	0.289154

2048:	0.288763	0.288763

4096:	0.288992	0.288992

8192:	0.288068	0.288068

16384:	0.288728	0.288728

32768:	0.288723	0.288723

65536:	0.28853	0.28853

131072:	0.288398	0.288398

262144:	0.288527	0.288527

524288:	0.288621	0.288621

1048576:	0.288542	0.288542

2097152:	0.288646	0.288646

4194304:	0.288659	0.288659

8388608:	0.288658	0.288658

16777216:	0.288649	0.288649

/MyFolder/MyProject exited with code 0

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(C++) GetStdDev

GetStdDev test