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Appendix I / Utilities / General
_ _
C
:
65539 ⋅ S i −1
≥ 0 ⇒ Si
: = 65539 ⋅ S i −1
⎛
A ⋅ ⎜
⎜
⎝
⎡
12
= ⎢ ∑
i:
= 1
⎢⎣
⎤
−10
( S ⋅ 4.
656613⋅10
) ⎥ − 6 ⎟ + B
i
22.2-5
⎥⎦
Equation 22.2-24
⎞
⎟
⎠
Equation 22.2-25
GAUSS returns a Gaussian distributed random variable (C) from the pdf,
p
( C )
:
A ⋅
1 ⎛
⋅ exp ⎜ −
2 ⋅ π ⎜
⎝
( C − B )
= 2
2 ⋅ A
2
⎞
⎟
⎠
Equation 22.2-26
The exponential represents a scaling so that the cumulative probability, the
integral of p(C) over C ∈ [-∞,∞], is 1; the peak of p(C) being 1/√2π at (B).
The following special values are useful when analysing stochastic filters,
( C ∈ [ −1
, 1 ] ) : 0.
6837
p =
( C ∈ [ − 2 , 2 ] ) : 0.
9545
p =
( C ∈ [ − 3 , 3 ] ) : 0.
9973
p =
When initialising SIGNV the seed from GAUSS is used,
0
( 1 ) : S0
S =
[ 1(
1 ) 999 ] ⇒ S ( k + 1 ) : = S ( k )
k ∈
0
12
Equation 22.2-27
Equation 22.2-28
Equation 22.2-29
Equation 22.2-30
Equation 22.2-31
GAUSS uses integer overflow to generate random numbers and must be
compiled with overflow checking disabled. Initialisation of the random
number generator is completed by taking S12(1000) and using it to seed
1000 sequences stored in vector IRAND. During this process the seeds
returned by GAUSS are manipulated as follows,
( 1001 ) : S ( 1000 )
S0 = 12
Equation 22.2-32