NAG Library Function Document
nag_quasi_rand_normal (g05yjc)
1
Purpose
nag_quasi_rand_normal (g05yjc) generates a quasi-random sequence from a Normal (Gaussian) distribution. It must be preceded by a call to one of the initialization functions
nag_quasi_init (g05ylc) or
nag_quasi_init_scrambled (g05ync).
2
Specification
#include <nag.h> |
#include <nagg05.h> |
void |
nag_quasi_rand_normal (Nag_OrderType order,
const double xmean[],
const double std[],
Integer n,
double quas[],
Integer pdquas,
Integer iref[],
NagError *fail) |
|
3
Description
nag_quasi_rand_normal (g05yjc) generates a quasi-random sequence from a Normal distribution by first generating a uniform quasi-random sequence which is then transformed into a Normal sequence using the inverse of the Normal CDF. The type of uniform sequence used depends on the initialization function called and can include the low-discrepancy sequences proposed by Sobol, Faure or Niederreiter. If the initialization function
nag_quasi_init_scrambled (g05ync) was used then the underlying uniform sequence is first scrambled prior to being transformed (see
Section 3 in
nag_quasi_init_scrambled (g05ync) for details).
4
References
Bratley P and Fox B L (1988) Algorithm 659: implementing Sobol's quasirandom sequence generator ACM Trans. Math. Software 14(1) 88–100
Fox B L (1986) Algorithm 647: implementation and relative efficiency of quasirandom sequence generators ACM Trans. Math. Software 12(4) 362–376
Wichura (1988) Algorithm AS 241: the percentage points of the Normal distribution Appl. Statist. 37 477–484
5
Arguments
Note: the following variables are used in the parameter descriptions:
- 1:
– Nag_OrderTypeInput
-
On entry: the
order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by
. See
Section 3.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.
Constraint:
or .
- 2:
– const doubleInput
-
On entry: specifies, for each dimension, the mean of the Normal distribution.
- 3:
– const doubleInput
-
On entry: specifies, for each dimension, the standard deviation of the Normal distribution.
Constraint:
, for .
- 4:
– IntegerInput
-
On entry: the number of quasi-random numbers required.
Constraint:
and .
- 5:
– doubleOutput
Note: the dimension,
dim, of the array
quas
must be at least
.
The dimension,
dim, of the array
quas
must be at least
- when ;
- when .
Where
appears in this document, it refers to the array element
- when ;
- when .
On exit: contains the
n quasi-random numbers of dimension
idim,
holds the
th value for the
th dimension.
- 6:
– IntegerInput
-
On entry: the stride separating row or column elements (depending on the value of
order) in the array
quas.
Constraints:
- if ,
;
- if , .
- 7:
– IntegerCommunication Array
-
On entry: contains information on the current state of the sequence.
On exit: contains updated information on the state of the sequence.
- 8:
– NagError *Input/Output
-
The NAG error argument (see
Section 3.7 in How to Use the NAG Library and its Documentation).
6
Error Indicators and Warnings
- NE_ALLOC_FAIL
-
Dynamic memory allocation failed.
See
Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
- NE_BAD_PARAM
-
On entry, argument had an illegal value.
- NE_INITIALIZATION
-
On entry,
iref has either not been initialized or has been corrupted.
- NE_INT
-
On entry, .
Constraint: .
- NE_INT_2
-
On entry, and .
Constraint: .
On entry, and .
Constraint: .
- NE_INTERNAL_ERROR
-
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact
NAG for assistance.
See
Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
- NE_NO_LICENCE
-
Your licence key may have expired or may not have been installed correctly.
See
Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
- NE_REAL_ARRAY
-
On entry, .
Constraint: .
- NE_TOO_MANY_CALLS
-
There have been too many calls to the generator.
7
Accuracy
Not applicable.
8
Parallelism and Performance
nag_quasi_rand_normal (g05yjc) is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
nag_quasi_rand_normal (g05yjc) makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the
x06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
The Sobol, Sobol (A659) and Niederreiter quasi-random number generators in nag_quasi_rand_normal (g05yjc) have been parallelized, but require quite large problem sizes to see any significant performance gain. Parallelism is only enabled when . The Faure generator is serial.
None.
10
Example
This example calls
nag_quasi_init (g05ylc) to initialize the generator and then
nag_quasi_rand_normal (g05yjc) to generate a sequence of five four-dimensional variates.
10.1
Program Text
Program Text (g05yjce.c)
10.2
Program Data
None.
10.3
Program Results
Program Results (g05yjce.r)