vRngGaussian

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

vRngGaussian

Generates normally distributed random numbers.

Syntax

status = vsrnggaussian ( method , stream , n , r , a , sigma )

status = vdrnggaussian ( method , stream , n , r , a , sigma )

Include Files

mkl.fi , mkl_vsl.f90

Description

vsRngGaussian vdRngGaussian The vRngGaussian function generates random numbers with normal (Gaussian) distribution with mean value a and standard deviation σ , where a , σ ∈ R ; σ > 0.

The probability density function is given by:

The cumulative distribution function is as follows:

The cumulative distribution function F_{a,σ}(x) can be expressed in terms of standard normal distribution Φ(x) as F_a,σ ( x ) = Φ (( x - a )/ σ )

Product and Performance Information Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex . Notice revision #20201201

Input Parameters

Name	Type	Description
`method`	Fortran 90:`INTEGER, INTENT(IN)`	Generation method. The specific values are as follows: VSL_RNG_METHOD_GAUSSIAN_BOXMULLER VSL_RNG_METHOD_GAUSSIAN_BOXMULLER2 VSL_RNG_METHOD_GAUSSIAN_ICDF See brief description of the methods `BOXMULLER` , `BOXMULLER2` , and `ICDF` in Table “Values of
`stream`	`TYPE (VSL_STREAM_STATE), INTENT(IN)`	Descriptor of the stream state structure
`n`	`INTEGER, INTENT(IN)`	Number of random values to be generated.
`a`	Fortran 77:`DOUBLE PRECISION` for `vdrnggaussian`Fortran 90:`REAL (KIND=4), INTENT(IN)` for `vsrnggaussian`Fortran 90:`REAL (KIND=8), INTENT(IN)` for `vdrnggaussian`	Mean value `a` .
`sigma`	Fortran 77:`DOUBLE PRECISION` for `vdrnggaussian`Fortran 90:`REAL (KIND=4), INTENT(IN)` for `vsrnggaussian`Fortran 90:`REAL (KIND=8), INTENT(IN)` for `vdrnggaussian`	Standard deviation, `\(\sigma\)`.

Output Parameters

Name	Type	Description
`r`	Fortran 77:`DOUBLE PRECISION` for `vdrnggaussian`Fortran 90:`REAL (KIND=4), INTENT(OUT)` for `vsrnggaussian`Fortran 90:`REAL (KIND=8), INTENT(OUT)` for `vdrnggaussian`	Vector of `n` normally distributed random numbers.

Return Values

VSL_ERROR_OK, VSL_STATUS_OK: Indicates no error, execution is successful.
VSL_ERROR_NULL_PTR: stream is a NULL pointer.
VSL_RNG_ERROR_BAD_STREAM: stream is not a valid random stream.
VSL_RNG_ERROR_BAD_UPDATE: Callback function for an abstract BRNG returns an invalid number of updated entries in a buffer, that is, < 0 or > nmax .
VSL_RNG_ERROR_NO_NUMBERS: Callback function for an abstract BRNG returns 0 as the number of updated entries in a buffer.
VSL_RNG_ERROR_QRNG_PERIOD_ELAPSED: Period of the generator has been exceeded.
VSL_RNG_ERROR_NONDETERM_NRETRIES_EXCEEDED: Number of retries to generate a random number by using non-deterministic random number generator exceeds threshold.
VSL_RNG_ERROR_ARS5_NOT_SUPPORTED: ARS-5 random number generator is not supported on the CPU running the application.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

vRngGaussian

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values