@brief Gaussian random number generator. @details This function returns a deviate of a Gaussian distribution @f$f_G(x;\mu,\sigma) = \frac{1}{\sigma\sqrt{2\pi}} \exp{\left( -(x-\mu)^2/2\sigma^2 \right)}@f$, with mean @f$\mu@f$, and standard deviation @f$\sigma@f$.
We use the Inverse Transform Sampling Method for sampling @f$x@f$. With this method we get @f$x = \sqrt{-2\log{(1-y)}}\cos(2\pi z)@f$, where @f$y@f$ and @f$z@f$ are uniform random numbers in the interval @f$[0,1]@f$.
@param[in] mu Mean value @f$\mu@f$ of the Gaussian distribution. @param[in] mu Standard deviation @f$\sigma@f$ of the Gaussian distribution. @param random_norm Sampled number @f$x@f$ from the Gaussian distribution @f$f_G(x;\mu,\sigma)@f$. @param rand1 Uniform random number in the interval @f$[0,1]@f$. @param rand2 Uniform random number in the interval @f$[0,1]@f$.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=rp), | intent(in) | :: | mean | |||
| real(kind=rp), | intent(in) | :: | sigma |
FUNCTION random_norm(mean,sigma)
REAL(rp), INTENT(IN) :: mean
REAL(rp), INTENT(IN) :: sigma
REAL(rp) :: random_norm
REAL(rp) :: rand1
REAL(rp) :: rand2
call RANDOM_NUMBER(rand1)
call RANDOM_NUMBER(rand2)
random_norm = SQRT(-2.0_rp*LOG(1.0_rp-rand1))*COS(2.0_rp*C_PI*rand2);
END FUNCTION random_norm