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Writing efficient normal distribution function (for learning purposes).

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Dear all, I'm a beginner in C++ so I'm sorry if my question might seem silly.
I'm also new to the group so I just say hello to all the people in it.

I've written a function that computes the Normal Distribution, but when comparing the time to create 1000 vectors
each with 1000 points I've the same performance than using the analogous Matlab built-in function.
I'd like to improve my code for speed.
I'm doing this mainly to learn how to write efficient C++ code, so please just don't tell me 
that library X and Y do this faster than my code, but help me understanding why and how to improve
my code.

I need both a single value and a vector version of this function,
so this is how I have defined them.

// this is the single point version of the function:
double normdist(const double& px,const double& mu,const double& csigma){
  // evaluating the formula taken from http://en.wikipedia.org/wiki/Normal_distribution
  double  val = sqrt(2*M_PI)*csigma;
  val = 1/val; 
  val = val*exp(-pow(px-mu,2)/(2*pow(csigma,2)));    
  return val ;
}

//this is the vector version. It takes as input a vector of double and gives the vector of corresponding values as output:

vector<double> normdist(const vector<double>& vx,const double& mu,const double& csigma){
  vector<double> gv(vx.size()) ; //allocates the space for the vector gv.
  for (int i=0 ; i<vx.size() ; i++){
    gv[i]=normdist(vx[i],mu,csigma);
  }
  return gv ;
}

As I told I'm a beginner so I guess there is plenty of room for improving the speed and the quality of the code
(just writing to you I have realized that the initialization of gv might not be optimal, since I create values I don't need).

Thank you very much to all of you!
Luca

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Writing efficient normal distribution function (for learning purposes). Luca Cerone <luca.cerone@gmail.com> - 2012-02-17 07:41 -0800
  Re: Writing efficient normal distribution function (for learning purposes). "Asger Joergensen" <Junk@Asger-P.dk> - 2012-02-17 16:45 +0000
    Re: Writing efficient normal distribution function (for learning purposes). lucacerone <luca.cerone@gmail.com> - 2012-02-17 09:36 -0800
      Re: Writing efficient normal distribution function (for learning purposes). "Asger Joergensen" <Junk@Asger-P.dk> - 2012-02-17 17:50 +0000
        Re: Writing efficient normal distribution function (for learning purposes). lucacerone <luca.cerone@gmail.com> - 2012-02-19 01:59 -0800
          Re: Writing efficient normal distribution function (for learning purposes). lucacerone <luca.cerone@gmail.com> - 2012-02-19 02:49 -0800
            Re: Writing efficient normal distribution function (for learning purposes). "Asger Joergensen" <Junk@Asger-P.dk> - 2012-02-19 11:53 +0000
            Re: Writing efficient normal distribution function (for learning purposes). Miles Bader <miles@gnu.org> - 2012-02-19 23:09 +0900
              Re: Writing efficient normal distribution function (for learning purposes). Joshua Maurice <joshuamaurice@gmail.com> - 2012-02-19 13:34 -0800
                Re: Writing efficient normal distribution function (for learning purposes). Marc <marc.glisse@gmail.com> - 2012-02-19 22:10 +0000
                Re: Writing efficient normal distribution function (for learning purposes). Miles Bader <miles@gnu.org> - 2012-02-20 09:14 +0900
                Re: Writing efficient normal distribution function (for learning purposes). Juha Nieminen <nospam@thanks.invalid> - 2012-02-20 10:24 +0000
                Re: Writing efficient normal distribution function (for learning purposes). Miles Bader <miles@gnu.org> - 2012-02-20 19:57 +0900
                Re: Writing efficient normal distribution function (for learning purposes). Dombo <dombo@disposable.invalid> - 2012-02-20 21:07 +0100
                Re: Writing efficient normal distribution function (for learning purposes). Juha Nieminen <nospam@thanks.invalid> - 2012-02-21 08:41 +0000
                Re: Writing efficient normal distribution function (for learning purposes). 88888 Dihedral <dihedral88888@googlemail.com> - 2012-02-21 01:10 -0800
                Re: Writing efficient normal distribution function (for learning purposes). Miles Bader <miles@gnu.org> - 2012-02-20 09:04 +0900
              Re: Writing efficient normal distribution function (for learning purposes). lucacerone <luca.cerone@gmail.com> - 2012-02-20 02:26 -0800
    Re: Writing efficient normal distribution function (for learning purposes). Juha Nieminen <nospam@thanks.invalid> - 2012-02-17 20:42 +0000
      Re: Writing efficient normal distribution function (for learning purposes). "Asger Joergensen" <Junk@Asger-P.dk> - 2012-02-17 22:20 +0000
  Re: Writing efficient normal distribution function (for learning purposes). Juha Nieminen <nospam@thanks.invalid> - 2012-02-17 20:52 +0000
  Re: Writing efficient normal distribution function (for learning purposes). Victor Bazarov <v.bazarov@comcast.invalid> - 2012-02-17 15:57 -0500
  Re: Writing efficient normal distribution function (for learning purposes). Joshua Maurice <joshuamaurice@gmail.com> - 2012-02-17 15:01 -0800
    Re: Writing efficient normal distribution function (for learning purposes). Victor Bazarov <v.bazarov@comcast.invalid> - 2012-02-18 08:44 -0500
      Re: Writing efficient normal distribution function (for learning purposes). Paavo Helde <myfirstname@osa.pri.ee> - 2012-02-18 09:20 -0600
  Re: Writing efficient normal distribution function (for learning purposes). Paavo Helde <myfirstname@osa.pri.ee> - 2012-02-18 09:36 -0600
    Re: Writing efficient normal distribution function (for learning purposes). glen herrmannsfeldt <gah@ugcs.caltech.edu> - 2012-02-18 20:19 +0000
      Re: Writing efficient normal distribution function (for learning purposes). Miles Bader <miles@gnu.org> - 2012-02-19 10:32 +0900
  Re: Writing efficient normal distribution function (for learning purposes). lucacerone <luca.cerone@gmail.com> - 2012-02-20 02:36 -0800
  Re: Writing efficient normal distribution function (for learning purposes). gwowen <gwowen@gmail.com> - 2012-02-20 06:48 -0800
    Re: Writing efficient normal distribution function (for learning purposes). lucacerone <luca.cerone@gmail.com> - 2012-02-21 04:32 -0800

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