Distribution Generators

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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Date 6/24/2024

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Distribution Generators

oneMKLVS routines are used to generate random numbers with different types of distribution. Each function group is introduced below by the type of underlying distribution and contains a short description of its functionality, as well as specifications of the call sequence and the explanation of input and output parameters. Table "Continuous Distribution Generators" and Table "Discrete Distribution Generators" list the random number generator routines with data types and output distributions, and sets correspondence between data types of the generator routines and the basic random number generators.

Continuous Distribution Generators
Type of Distribution	Data Types	BRNG Data Type	Description
vRngUniform	s, d	s, d	Uniform continuous distribution on the interval [`a,b`)
vRngGaussian	s, d	s, d	Normal (Gaussian) distribution
vRngGaussianMV	s, d	s, d	Normal (Gaussian) multivariate distribution
vRngExponential	s, d	s, d	Exponential distribution
vRngLaplace	s, d	s, d	Laplace distribution (double exponential distribution)
vRngWeibull	s, d	s, d	Weibull distribution
vRngCauchy	s, d	s, d	Cauchy distribution
vRngRayleigh	s, d	s, d	Rayleigh distribution
vRngLognormal	s, d	s, d	Lognormal distribution
vRngGumbel	s, d	s, d	Gumbel (extreme value) distribution
vRngGamma	s, d	s, d	Gamma distribution
vRngBeta	s, d	s, d	Beta distribution
vRngChiSquare	s, d	s, d	Chi-Square distribution

Discrete Distribution Generators
Type of Distribution	Data Types	BRNG Data Type	Description
vRngUniform	i	d	Uniform discrete distribution on the interval [`a,b`)
vRngUniformBits	i	i	Underlying BRNG integer recurrence
vRngUniformBits32	i	i	Uniformly distributed bits in 32-bit chunks
vRngUniformBits64	i	i	Uniformly distributed bits in 64-bit chunks
vRngBernoulli	i	s	Bernoulli distribution
vRngGeometric	i	s	Geometric distribution
vRngBinomial	i	d	Binomial distribution
vRngHypergeometric	i	d	Hypergeometric distribution
vRngPoisson	i	s (for VSL_RNG_METHOD_POISSON_POISNORM) s (for distribution parameter λ≥ 27) and d (for λ < 27) (for VSL_RNG_METHOD_POISSON_PTPE)	Poisson distribution
vRngPoisson	i	s	Poisson distribution with varying mean
vRngNegBinomial	i	d	Negative binomial distribution, or Pascal distribution
vRngMultinomial	i	d	Multinomial distribution

Modes of random number generation

The library provides two modes of random number generation, accurate and fast. Accurate generation mode is intended for the applications that are highly demanding to accuracy of calculations. When used in this mode, the generators produce random numbers lying completely within definitional domain for all values of the distribution parameters. For example, random numbers obtained from the generator of continuous distribution that is uniform on interval [a,b] belong to this interval irrespective of what a and b values may be. Fast mode provides high performance of generation and also guarantees that generated random numbers belong to the definitional domain except for some specific values of distribution parameters. The generation mode is set by specifying relevant value of the method parameter in generator routines. List of distributions that support accurate mode of generation is given in the table below.

Distribution Generators Supporting Accurate Mode
Type of Distribution	Data Types
vRngUniform	s, d
vRngExponential	s, d
vRngWeibull	s, d
vRngRayleigh	s, d
vRngLognormal	s, d
vRngGamma	s, d
vRngBeta	s, d

See additional details about accurate and fast mode of random number generation in VS Notes.

New method names

The current version of oneMKL has a modified structure of VS RNG method names. (SeeRNG Naming Conventions for details.) The old names are kept for backward compatibility. The tables below set correspondence between the new and legacy method names for VS random number generators.

Method Names for Continuous Distribution Generators
RNG	Legacy Method Name	New Method Name
vRngUniform	VSL_METHOD_SUNIFORM_STD, VSL_METHOD_DUNIFORM_STD, VSL_METHOD_SUNIFORM_STD_ACCURATE, VSL_METHOD_DUNIFORM_STD_ACCURATE	VSL_RNG_METHOD_UNIFORM_STD, VSL_RNG_METHOD_UNIFORM_STD_ACCURATE
vRngGaussian	VSL_METHOD_SGAUSSIAN_BOXMULLER, VSL_METHOD_SGAUSSIAN_BOXMULLER2, VSL_METHOD_SGAUSSIAN_ICDF, VSL_METHOD_DGAUSSIAN_BOXMULLER, VSL_METHOD_DGAUSSIAN_BOXMULLER2, VSL_METHOD_DGAUSSIAN_ICDF	VSL_RNG_METHOD_GAUSSIAN_BOXMULLER, VSL_RNG_METHOD_GAUSSIAN_BOXMULLER2, VSL_RNG_METHOD_GAUSSIAN_ICDF
vRngGaussianMV	VSL_METHOD_SGAUSSIANMV_BOXMULLER, VSL_METHOD_SGAUSSIANMV_BOXMULLER2, VSL_METHOD_SGAUSSIANMV_ICDF, VSL_METHOD_DGAUSSIANMV_BOXMULLER, VSL_METHOD_DGAUSSIANMV_BOXMULLER2, VSL_METHOD_DGAUSSIANMV_ICDF	VSL_RNG_METHOD_GAUSSIANMV_BOXMULLER, VSL_RNG_METHOD_GAUSSIANMV_BOXMULLER2, VSL_RNG_METHOD_GAUSSIANMV_ICDF
vRngExponential	VSL_METHOD_SEXPONENTIAL_ICDF, VSL_METHOD_DEXPONENTIAL_ICDF, VSL_METHOD_SEXPONENTIAL_ICDF_ACCURATE, VSL_METHOD_DEXPONENTIAL_ICDF_ACCURATE	VSL_RNG_METHOD_EXPONENTIAL_ICDF, VSL_RNG_METHOD_EXPONENTIAL_ICDF_ACCURATE
vRngLaplace	VSL_METHOD_SLAPLACE_ICDF, VSL_METHOD_DLAPLACEL_ICDF	VSL_RNG_METHOD_LAPLACE_ICDF
vRngWeibull	VSL_METHOD_SWEIBULL_ICDF, VSL_METHOD_DWEIBULL_ICDF, VSL_METHOD_SWEIBULL_ICDF_ACCURATE, VSL_METHOD_DWEIBULL_ICDF_ACCURATE	VSL_RNG_METHOD_WEIBULL_ICDF, VSL_RNG_METHOD_WEIBULL_ICDF_ACCURATE
vRngCauchy	VSL_METHOD_SCAUCHY_ICDF, VSL_METHOD_DCAUCHY_ICDF	VSL_RNG_METHOD_CAUCHY_ICDF
vRngRayleigh	VSL_METHOD_SRAYLEIGH_ICDF, VSL_METHOD_DRAYLEIGH_ICDF, VSL_METHOD_SRAYLEIGH_ICDF_ACCURATE, VSL_METHOD_DRAYLEIGH_ICDF_ACCURATE	VSL_RNG_METHOD_RAYLEIGH_ICDF, VSL_RNG_METHOD_RAYLEIGH_ICDF_ACCURATE
vRngLognormal	VSL_METHOD_SLOGNORMAL_BOXMULLER2, VSL_METHOD_DLOGNORMAL_BOXMULLER2, VSL_METHOD_SLOGNORMAL_BOXMULLER2_ACCURATE, VSL_METHOD_DLOGNORMAL_BOXMULLER2_ACCURATE	VSL_RNG_METHOD_LOGNORMAL_BOXMULLER2, VSL_RNG_METHOD_LOGNORMAL_BOXMULLER2_ACCURATE
vRngLognormal	VSL_METHOD_SLOGNORMAL_ICDF, VSL_METHOD_DLOGNORMAL_ICDF, VSL_METHOD_SLOGNORMAL_ICDF_ACCURATE, VSL_METHOD_DLOGNORMAL_ICDF_ACCURATE	VSL_RNG_METHOD_LOGNORMAL_ICDF, VSL_RNG_METHOD_LOGNORMAL_ICDF_ACCURATE
vRngGumbel	VSL_METHOD_SGUMBEL_ICDF, VSL_METHOD_DGUMBEL_ICDF	VSL_RNG_METHOD_GUMBEL_ICDF
vRngGamma	VSL_METHOD_SGAMMA_GNORM, VSL_METHOD_DGAMMA_GNORM, VSL_METHOD_SGAMMA_GNORM_ACCURATE, VSL_METHOD_DGAMMA_GNORM_ACCURATE	VSL_RNG_METHOD_GAMMA_GNORM, VSL_RNG_METHOD_GAMMA_GNORM_ACCURATE
vRngBeta	VSL_METHOD_SBETA_CJA, VSL_METHOD_DBETA_CJA, VSL_METHOD_SBETA_CJA_ACCURATE, VSL_METHOD_DBETA_CJA_ACCURATE	VSL_RNG_METHOD_BETA_CJA, VSL_RNG_METHOD_BETA_CJA_ACCURATE

Method Names for Discrete Distribution Generators
RNG	Legacy Method Name	New Method Name
vRngUniform	VSL_METHOD_IUNIFORM_STD	VSL_RNG_METHOD_UNIFORM_STD
vRngUniformBits	VSL_METHOD_IUNIFORMBITS_STD	VSL_RNG_METHOD_UNIFORMBITS_STD
vRngBernoulli	VSL_METHOD_IBERNOULLI_ICDF	VSL_RNG_METHOD_BERNOULLI_ICDF
vRngGeometric	VSL_METHOD_IGEOMETRIC_ICDF	VSL_RNG_METHOD_GEOMETRIC_ICDF
vRngBinomial	VSL_METHOD_IBINOMIAL_BTPE	VSL_RNG_METHOD_BINOMIAL_BTPE
vRngHypergeometric	VSL_METHOD_IHYPERGEOMETRIC_H2PE	VSL_RNG_METHOD_HYPERGEOMETRIC_H2PE
vRngPoisson	VSL_METHOD_IPOISSON_PTPE, VSL_METHOD_IPOISSON_POISNORM	VSL_RNG_METHOD_POISSON_PTPE, VSL_RNG_METHOD_POISSON_POISNORM
vRngPoissonV	VSL_METHOD_IPOISSONV_POISNORM	VSL_RNG_METHOD_POISSONV_POISNORM
vRngNegBinomial	VSL_METHOD_INEGBINOMIAL_NBAR	VSL_RNG_METHOD_NEGBINOMIAL_NBAR

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

Distribution Generators

Modes of random number generation

New method names