vRngGaussian

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

Version

Public

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Generates normally distributed random numbers.

Syntax

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

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

Include Files

Description

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

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	`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 `<method>` in `method` parameter"
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	`DOUBLE PRECISION` for `vdrnggaussian` `REAL (KIND=4), INTENT(IN)` for `vsrnggaussian` `REAL (KIND=8), INTENT(IN)` for `vdrnggaussian`	Mean value `a`.
sigma	`DOUBLE PRECISION` for `vdrnggaussian` `REAL (KIND=4), INTENT(IN)` for `vsrnggaussian` `REAL (KIND=8), INTENT(IN)` for `vdrnggaussian`	Standard deviation σ.

Output Parameters

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

Name

Type

Description

DOUBLE PRECISION for vdrnggaussian

REAL (KIND=4), INTENT(OUT) for vsrnggaussian

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.

Parent topic: Continuous Distributions