// Return a number from a unit Gaussian distribution. The mean is 0 and the
// standard deviation is 1.0.
// First we generate two uniformly random variables inside the complex unit
// circle. Then we transform these into Gaussians using the Box-Muller
// transformation. This method is described in Numerical Recipes in C
// ISBN 0-521-43108-5 at http://world.std.com/~nr
// When we find a number, we also find its twin, so we cache that here so
// that every other call is a lookup rather than a calculation. (I think GNU
// does this in their implementations as well, but I don't remember for
// certain.)
double
GAUnitGaussian(){
static GABoolean cached=gaFalse;
static double cachevalue;
if(cached == gaTrue){
cached = gaFalse;
return cachevalue;
}
double rsquare, factor, var1, var2;
do{
var1 = 2.0 * GARandomDouble() - 1.0;
var2 = 2.0 * GARandomDouble() - 1.0;
rsquare = var1*var1 + var2*var2;
} while(rsquare >= 1.0 || rsquare == 0.0);
double val = -2.0 * log(rsquare) / rsquare;
if(val > 0.0) factor = sqrt(val);
else factor = 0.0; // should not happen, but might due to roundoff
cachevalue = var1 * factor;
cached = gaTrue;
return (var2 * factor);
}
// Return a number from gaussian distribution. This code was pinched from the
// GNU libg++ Normal.cc implementation of a normal distribution. That is, in
// turn, based on Simulation, Modelling & Analysis by Law & Kelton, pp259.
//
// My random number generator (actually just the system's) isn't as good as
// that in the libg++, but this should be OK for this purpose.
double
Gauss(double mean, double variance){
for(;;) {
double u1 = GARandomDouble();
double u2 = GARandomDouble();
double v1 = 2 * u1 - 1;
double v2 = 2 * u2 - 1;
double w = (v1 * v1) + (v2 * v2);
if (w <= 1) {
double y = sqrt( (-2 * log(w)) / w);
double x1 = v1 * y;
// double x2 = v2 * y; // we don't use this one
return(x1 * sqrt(variance) + mean);
}
}
}
