nag_quasi_rand_lognormal (g05ykc) generates a quasi-random sequence from a log-normal distribution. It must be preceded by a call to one of the initialization functions
nag_quasi_init (g05ylc) or
nag_quasi_init_scrambled (g05ync).
nag_quasi_rand_lognormal (g05ykc) generates a quasi-random sequence from a log-normal distribution by first generating a uniform quasi-random sequence which is then transformed into a log-normal sequence using the exponential of 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).
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
Note: the following variables are used in the parameter descriptions:
- 1:
order – 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 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.
Constraint:
or .
- 2:
xmean[] – const doubleInput
On entry: specifies, for each dimension, the mean of the underlying Normal distribution.
Constraint:
, for .
- 3:
std[] – const doubleInput
On entry: specifies, for each dimension, the standard deviation of the underlying Normal distribution.
Constraint:
, for .
- 4:
n – IntegerInput
On entry: the number of quasi-random numbers required.
Constraint:
and .
- 5:
quas[] – 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: holds the th value for the th dimension.
- 6:
pdquas – IntegerInput
-
On entry: the stride separating row or column elements (depending on the value of
order) in the array
quas.
Constraints:
- if ,
;
- if , .
- 7:
iref[] – 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:
fail – NagError *Input/Output
-
The NAG error argument (see
Section 3.6 in the Essential Introduction).
Not applicable.
nag_quasi_rand_lognormal (g05ykc) is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
nag_quasi_rand_lognormal (g05ykc) 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
Users' Note for your implementation for any additional implementation-specific information.
The Sobol, Sobol (A659) and Niederreiter quasi-random number generators in g05ykc 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.
This example calls
nag_quasi_init (g05ylc) to initialize the generator and then nag_quasi_rand_lognormal (g05ykc) to produce a sequence of five four-dimensional quasi-random numbers variates.
None.