Intel® oneAPI Math Kernel Library Developer Reference - Fortran

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

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 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.

Optimization Notice

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804

This notice covers the following instruction sets: SSE2, SSE4.2, AVX2, AVX-512.

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 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.