Contents

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.h
Input Parameters
Name
Type
Description
method
const MKL_INT
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
VSLStreamStatePtr
Pointer to the stream state structure
n
const MKL_INT
Number of
d
-dimensional vectors to be generated
dimen
const MKL_INT
Dimension
d
(
d
1)
of output random vectors
mstorage
const MKL_INT
Matrix storage scheme for lower triangular matrix
T
. The routine supports three matrix storage schemes:
  • VSL_MATRIX_STORAGE_FULL
    all
    d
    x
    d
    elements of the matrix
    T
    are passed, however, only the lower triangle part is actually used in the routine.
  • VSL_MATRIX_STORAGE_PACKED
    lower triangle elements of
    T
    are packed by rows into a one-dimensional array.
  • VSL_MATRIX_STORAGE_DIAGONAL
    only diagonal elements of
    T
    are passed.
a
const float*
for
vsRngGaussianMV
const double*
for
vdRngGaussianMV
Mean vector
a
of dimension
d
t
const float*
for
vsRngGaussianMV
const double*
for
vdRngGaussianMV
Elements of the lower triangular matrix passed according to the matrix
T
storage scheme
mstorage
.
Output Parameters
Name
Type
Description
r
float*
for
vsRngGaussianMV
double*
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
a
R
d
;
C
is a
d
×
d
symmetric positive-definite matrix.
The probability density function is given by:
Equation
where
x
R
d
.
Matrix
C
can be represented as
C
=
TT
T
, 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® MKL
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® MKL
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 C
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 C two-dimensional array
spotrf
for
vsRngGaussianMV
dpotrf
for
vdRngGaussianMV
‘U’
Lower triangle of
T
. Upper 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’
Lower triangle of
T
packed by columns 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.
1

Product and Performance Information

1

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 reservered 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