C language produces a standard normal or Gaussian distribution random number

C language produces a standard normal or Gaussian distribution random number

Three ways to produce a normal or Gaussian distribution:


1. Applying the central limit theorem (large number theorem)

1 #include2 #include3 4 #defineNSUM 255 6 DoubleGaussrand ()7 {8      Doublex =0;9      inti;Ten       for(i =0; i < NSUM; i++) One      { AX + = (Double) rand ()/Rand_max; -      } -  theX-= NSUM/2.0; -x/= sqrt (NSUM/12.0); -  -      returnx; +}

2. Using the methods provided by box and Muller, discussed on the Internet in Knuth (more commonly used methods) Box-muller, usually to get random numbers that obey a normal distribution, The basic idea is to get the random numbers that obey the uniform distribution first; Then, the random number subjected to uniform distribution is changed to obey the normal distribution. Box-muller is a method of generating random numbers. The implicit principle of the box-muller algorithm is very esoteric, but the result is quite simple.  If there are two consistent random numbers U1 and U2 within the (0,1] range, 

You can use either of the following two equations to calculate the random number Z for a normal distribution:

z = R * cos (θ) or z = R * sin (θ)

wherein, R = sqrt ( -2 * ln (U2)), θ= 2 *π* U1

The normal value Z has a mean of equal to 0 and a standard deviation equal to 1, which can be mapped to a statistic X with a mean of M and a standard deviation of SD using the following equation:

X = m + (Z * SD)

C Code: (in computer programming, the log function ==ln () function, with e as the base of the natural logarithm, log10 is the base of the 10 function)

1#include <stdlib.h>2#include <stdio.h>3 #definePI 3.141592654double
 　　 Double Gaussrand ()4 {5     Static DoubleU, V;6     Static intPhase =0;7     DoubleZ;8 9     if(Phase = =0)Ten     { OneU = rand ()/(Rand_max + 1. 0); AV = rand ()/(Rand_max +1.0); -         Z = sqrt ( -2.0 * log (U)) * Sin (2.0 * PI *) V); -     } the     Else -     { -          Z = sqrt (-2.0 * log(U)) * cos (2.0 * PI * V);  -     } +  -Phase =1-phase; + retrn Z; A }

C + + code:

1#include <cstdlib>2#include <cmath>3#include <limits>4 DoubleGenerategaussiannoise (DoubleMuDoubleSigma)5 {6     Const DoubleEpsilon = std::numeric_limits<Double>:: Min ();7     Const DoubleTWO_PI =2.0*3.14159265358979323846;8 9     Static Doublez0, Z1;Ten     Static BOOLgenerate; OneGenerate =!generate; A  -     if(!generate) -        returnZ1 * Sigma +mu; the  -     DoubleU1, U2; -      Do -      { +u1 = rand () * (1.0/Rand_max); -U2 = rand () * (1.0/Rand_max); +      } A      while(U1 <=Epsilon); at  -Z0 = sqrt (-2.0* Log (u1)) * COS (TWO_PI *U2); -Z1 = sqrt (-2.0* Log (u1)) * Sin (TWO_PI *U2); -     returnZ0 * Sigma +mu; -}

3 Using methods originally provided by Marsaglia

1#include <stdlib.h>2#include <stdio.h>3 DoubleGaussrand ()4 {5      Static DoubleV1, V2, S;6      Static intPhase =0;7      DoubleX;8 9      if(Phase = =0)Ten      { One          Do{ A               DoubleU1 = (Double) rand ()/Rand_max; -               DoubleU2 = (Double) rand ()/Rand_max; -                 theV1 =2* U1-1; -V2 =2* U2-1; -S = V1 * V1 + V2 *V2; -} while(S >=1|| S = =0) +       -X = V1 * SQRT (-2* LOG (S)/S); +      } A      Else at      { -X = V2 * SQRT (-2* LOG (S)/S); -      } -  -Phase =1-phase; -      returnX; in}

Reference: http://blog.chinaunix.net/uid-22666248-id-357093.html

Https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform

C language produces a standard normal or Gaussian distribution random number