Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 3/22/2024
Public

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vRngGaussianMV

Generates random numbers from multivariate normal distribution.

Syntax

status = vsrnggaussianmv( method, stream, n, r, dimen, mstorage, a, t )

status = vdrnggaussianmv( method, stream, n, r, dimen, mstorage, a, t )

Include Files

  • mkl.fi, mkl_vsl.f90

Input Parameters

Name

Type

Description

method

INTEGER, INTENT(IN)

Generation method. The specific values are as follows:

VSL_RNG_METHOD_GAUSSIANMV_BOXMULLER
VSL_RNG_METHOD_GAUSSIANMV_BOXMULLER2
VSL_RNG_METHOD_GAUSSIANMV_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 d-dimensional vectors to be generated

dimen

Fortran 90: INTEGER, INTENT(IN)

Dimension d ( d 1) of output random vectors

mstorage

INTEGER, INTENT(IN)

Matrix storage scheme for upper triangular matrix TT. The routine supports three matrix storage schemes:

  • VSL_MATRIX_STORAGE_FULL all d x d elements of the matrix TT are passed, however, only the upper triangle part is actually used in the routine.

  • VSL_MATRIX_STORAGE_PACKED upper triangle elements of TT are packed by rows into a one-dimensional array.

  • VSL_MATRIX_STORAGE_DIAGONAL only diagonal elements of TT are passed.

a

DOUBLE PRECISION for vdrnggaussianmv

REAL(KIND=4), INTENT(IN) for vsrnggaussianmv

REAL(KIND=8), INTENT(IN) for vdrnggaussianmv

Mean vector a of dimension d

t

DOUBLE PRECISION for vdrnggaussianmv

REAL(KIND=4), INTENT(IN) for vsrnggaussianmv

REAL(KIND=8), INTENT(IN) for vdrnggaussianmv

Elements of the upper triangular matrix passed according to the matrix TT storage scheme mstorage.

Output Parameters

Name

Type

Description

r

DOUBLE PRECISION for vdrnggaussianmv

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

REAL(KIND=8), INTENT(OUT) for vdrnggaussianmv

Array of n random vectors of dimension dimen

Description

The vRngGaussianMV function generates random numbers with d-variate normal (Gaussian) distribution with mean value a and variance-covariance matrix C, where aRd; C is a d×d symmetric positive-definite matrix.

The probability density function is given by:


Equation

where xRd .

Matrix C can be represented as C = TTT, where T is a lower triangular matrix - Cholesky factor of C.

Instead of variance-covariance matrix C the generation routines require Cholesky factor of C in input. To compute Cholesky factor of matrix C, the user may call Intel® oneAPI Math Kernel Library (oneMKL) LAPACK routines for matrix factorization:?potrf or ?pptrf for v?RngGaussianMV/v?rnggaussianmv routines (? means either s or d for single and double precision respectively). See Application Notes for more details.

Product and Performance Information

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.

Notice revision #20201201

Application Notes

Since matrices are stored in Fortran by columns, while in C they are stored by rows, the usage of Intel® oneAPI Math Kernel Library (oneMKL) factorization routines (assuming Fortran matrices storage) in combination with multivariate normal RNG (assuming C matrix storage) is slightly different in C and Fortran. The following tables help in using these routines in C and Fortran. For further information please refer to the appropriate VS example file.

Using Cholesky Factorization Routines in Fortran

Matrix Storage Scheme

Variance-Covariance Matrix Argument

Factorization Routine

UPLO Parameter in Factorization Routine

Result of Factorization as Input Argument for RNG

VSL_MATRIX_STORAGE_FULL

C in Fortran two-dimensional array

spotrf for vsrnggaussianmv

dpotrf for vdrnggaussianmv

‘U’

Upper triangle of TT. Lower triangle is not used.

VSL_MATRIX_STORAGE_PACKED

Lower triangle of C packed by columns into one-dimensional array

spptrf for vsrnggaussianmv

dpptrf for vdrnggaussianmv

‘L’

Upper triangle of TT packed by rows into a one-dimensional array.

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.