Contents

Gaussian (VSL_RNG_METHOD_GAUSSIAN_BOXMULLER2)

Random number generator of normal (Gaussian) distribution with parameters
a
and
s
. You can produce a successive pair of the random numbers
x
1
, x
2
of the standard normal distribution according to the formula
where
u
1
,
u
2
are a pair of successive random numbers uniformly distributed over the interval (0, 1). For details, see [Box58].
The normal distribution with the parameters
a
and
s
is transformed to the random number
y
by scaling and the shift
y = sx+a
.
You can safely call this VS method even when the random numbers are generated in blocks with the size aliquant to 2.
For example, you use the VSL_METHOD_DGAUSSIAN_BOXMULLER2 method to generate a pair of random numbers of the standard normal distribution.
Option 1
Single call of method VSL_METHOD_DGAUSSIAN_BOXMULLER2 with the vector length equal to 2:
```
...
double x[2];
...
vdRngGaussian(VSL_RNG_METHOD_GAUSSIAN_BOXMULLER2, stream, 2, x, 0.0, 1.0);
...
```
In this case, you generate the random numbers
x
[0],
x
[1] by the formula:
Option 2
Double call of the method VSL_METHOD_DGAUSSIAN_BOXMULLER2 with the vector length equal to 1:

```
...
double x[2];
...
vdRngGaussian(VSL_RNG_METHOD_GAUSSIAN_BOXMULLER2, stream, 1, &x[0], 0.0, 1.0);
vdRngGaussian(VSL_RNG_METHOD_GAUSSIAN_BOXMULLER2, stream, 1, &x[1], 0.0, 1.0);
...
```
At the first call of vdRngGaussian you produce the random number
x
[0] by the formula:
At the second call of
vdRngGaussian
the vector length, over which you initially called the function to generate the random stream, is recognized as odd (equal to 1 in this case). Then the random number
x
[1] is generated by the formula:
and not by the formula:

Product and Performance Information

1

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Notice revision #20110804