oneapi::mkl::rng::device::gaussian
¶
Generates normally distributed random numbers.
Syntax
template<typename RealType, typename Method> class gaussian { public: using method_type = Method; using result_type = RealType; gaussian(): gaussian((RealType)0.0, (RealType)1.0){} explicit gaussian(RealType mean, RealType stddev); explicit gaussian(const param_type& pt); RealType mean() const; RealType stddev() const; param_type param() const; void param(const param_type& pt); };Include Files
oneapi/mkl/rng/device.hpp
Description
The
oneapi::mkl::rng::device::gaussian
class object is used in theoneapi::mkl::rng::device::generate
function to provide random numbers with normal (Gaussian) distribution with mean (a
) and standard deviation (stddev, σ
), wherea
,σ ∈ R
;σ
> 0.The probability density function is given by:
f_{a, \sigma} (x) = \frac{1}{\sigma \sqrt{2 \pi}} \exp \left( - \frac{(y-a)^2}{2\sigma^2} \right) dy, - \infty < x < + \infty
The cumulative distribution function is as follows:
F_{a, \sigma} (x) = \int_{-\infty}^{x} \frac{1}{\sigma \sqrt{2 \pi}} \exp \left( - \frac{(y-a)^2}{2\sigma^2} \right) dy, - \infty < x < + \infty
The cumulative distribution function
Fa,σ(x)
can be expressed in terms of standard normal distributionΦ(x)
asF a,σ (x) = Φ((x - a)/σ)
Template Parameters
typename RealType
Type of the produced values. The specific values are as follows:
float
double
typename Method
Generation method. The specific values are as follows:
oneapi::mkl::rng::device::gaussian_method::box_muller2
Input Parameters
Name
Type
Description
mean
RealType (float, double)
Mean value
a
.stddev
RealType (float, double)
Standard deviation σ.