help needed for checking Faure sequences dim 2

[Ferdinando M. Ametrano-3]

Hi all

I wonder if somebody could help me check the first points of a Faure
sequence dimension 2. After this verification the final C++ code will be
available in Quantlib thanks to Gianni Piolanti.

thank you in advance

ciao -- Nando

1,  [ 0.50000 ; 0.50000 ]
2,  [ 0.75000 ; 0.25000 ]
3,  [ 0.25000 ; 0.75000 ]
4,  [ 0.37500 ; 0.37500 ]
5,  [ 0.87500 ; 0.87500 ]
6,  [ 0.62500 ; 0.12500 ]
7,  [ 0.12500 ; 0.62500 ]
8,  [ 0.18750 ; 0.31250 ]
9,  [ 0.68750 ; 0.81250 ]
10, [ 0.93750 ; 0.06250 ]
11, [ 0.43750 ; 0.56250 ]
12, [ 0.31250 ; 0.18750 ]
13, [ 0.81250 ; 0.68750 ]
14, [ 0.56250 ; 0.43750 ]
15, [ 0.06250 ; 0.93750 ]
16, [ 0.09375 ; 0.46875 ]
17, [ 0.59375 ; 0.96875 ]
18, [ 0.84375 ; 0.21875 ]
19, [ 0.34375 ; 0.71875 ]
20, [ 0.46875 ; 0.09375 ]
21, [ 0.96875 ; 0.59375 ]
22, [ 0.71875 ; 0.34375 ]
23, [ 0.21875 ; 0.84375 ]
24, [ 0.15625 ; 0.15625 ]
25, [ 0.65625 ; 0.65625 ]
26, [ 0.90625 ; 0.40625 ]
27, [ 0.40625 ; 0.90625 ]
28, [ 0.28125 ; 0.28125 ]
29, [ 0.78125 ; 0.78125 ]
30, [ 0.53125 ; 0.03125 ]
31, [ 0.03125 ; 0.53125 ]

[Gianni Piolanti]

Hi ,

I'm a newbie to this list and I wish to do a remark about a test
proposed by Ferdinando. A Faure sequence generated by the code released doesn't match
the order of the original Faure algorithm because a Gray code transform must be
performed before applying the algorithm.
Gray code matrix B:

 |1 -1  0  0  0...|
 |0  1 -1  0  0...|
 |0  0  1 -1  0...|
 |0  0  0  1 -1...|
 |0  0  0  0  1...|

For example if we are doing a binary expansion of a number n>0 we have
n=sum(x(i)*2^i) Then applying the transformation we get G(n) = B*x as new
number to which apply the Faure algorithm.

Best regards.

Gianni.

>From: Ferdinando Ametrano <[hidden email]>

>To: QuantLib-users <[hidden email]>

>Subject: [Quantlib-users] help needed for checking Faure sequences dim 2

>Date: Tue, 24 Aug 2004 20:14:28 +0200

>

>Hi all

>

>I wonder if somebody could help me check the first points of a Faure

>sequence dimension 2. After this verification the final C++ code

>will be available in Quantlib thanks to Gianni Piolanti.

>

>thank you in advance

>

>ciao -- Nando

>

>1,  [ 0.50000 ; 0.50000 ]

>2,  [ 0.75000 ; 0.25000 ]

>3,  [ 0.25000 ; 0.75000 ]

>4,  [ 0.37500 ; 0.37500 ]

>5,  [ 0.87500 ; 0.87500 ]

>6,  [ 0.62500 ; 0.12500 ]

>7,  [ 0.12500 ; 0.62500 ]

>8,  [ 0.18750 ; 0.31250 ]

>9,  [ 0.68750 ; 0.81250 ]

>10, [ 0.93750 ; 0.06250 ]

>11, [ 0.43750 ; 0.56250 ]

>12, [ 0.31250 ; 0.18750 ]

>13, [ 0.81250 ; 0.68750 ]

>14, [ 0.56250 ; 0.43750 ]

>15, [ 0.06250 ; 0.93750 ]

>16, [ 0.09375 ; 0.46875 ]

>17, [ 0.59375 ; 0.96875 ]

>18, [ 0.84375 ; 0.21875 ]

>19, [ 0.34375 ; 0.71875 ]

>20, [ 0.46875 ; 0.09375 ]

>21, [ 0.96875 ; 0.59375 ]

>22, [ 0.71875 ; 0.34375 ]

>23, [ 0.21875 ; 0.84375 ]

>24, [ 0.15625 ; 0.15625 ]

>25, [ 0.65625 ; 0.65625 ]

>26, [ 0.90625 ; 0.40625 ]

>27, [ 0.40625 ; 0.90625 ]

>28, [ 0.28125 ; 0.28125 ]

>29, [ 0.78125 ; 0.78125 ]

>30, [ 0.53125 ; 0.03125 ]

>31, [ 0.03125 ; 0.53125 ]

>

>

>

>

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[Luigi Ballabio-2]

On 2004.08.24 20:14, Ferdinando Ametrano wrote:
> I wonder if somebody could help me check the first points of a Faure  
> sequence dimension 2. After this verification the final C++ code will  
> be available in Quantlib thanks to Gianni Piolanti.

Nando and Gianni,
        a wrong sequence is generated under Debian and gcc 3.3.
Is there any assumption in the code with regard to type sizes or  
something?

More data later,
        Luigi

[Luigi Ballabio-2]

On 2004.08.26 12:28, Luigi Ballabio wrote:
> Nando and Gianni,
> a wrong sequence is generated under Debian and gcc 3.3.
> Is there any assumption in the code with regard to type sizes or  
> something?

I (partially) take it back. Forget about Debian and gcc. The same  
(wrong) sequence is generated under VC6. Gianni, is it related to the  
Gray-code transform you mentioned?  Note that it's not a problem of  
just reordering--I'm getting random numbers outside the (0,1) range...

Later,
        Luigi

[Luigi Ballabio-2]

On 2004.08.26 12:28, Luigi Ballabio wrote:
> Nando and Gianni,
> a wrong sequence is generated under Debian and gcc 3.3.
> Is there any assumption in the code with regard to type sizes or  
> something?

P.S. The above applies to the 1-dimensional generation

[ML-21]

This website contains a number of Faure datasets (and other interesting
stuff about quasirandom sequences). Hopefully helpful:

http://www.csit.fsu.edu/~burkardt/datasets/faure/faure.html

-Mario


----- Original Message -----
From: "Ferdinando Ametrano" <[hidden email]>
To: "QuantLib-users" <[hidden email]>
Sent: Tuesday, August 24, 2004 8:14 PM
Subject: [Quantlib-users] help needed for checking Faure sequences dim 2

> Hi all
>
> I wonder if somebody could help me check the first points of a Faure
> sequence dimension 2. After this verification the final C++ code will be
> available in Quantlib thanks to Gianni Piolanti.
>
> thank you in advance
>
> ciao -- Nando
>
> 1,  [ 0.50000 ; 0.50000 ]
> 2,  [ 0.75000 ; 0.25000 ]
> 3,  [ 0.25000 ; 0.75000 ]
> 4,  [ 0.37500 ; 0.37500 ]
> 5,  [ 0.87500 ; 0.87500 ]
> 6,  [ 0.62500 ; 0.12500 ]
> 7,  [ 0.12500 ; 0.62500 ]
> 8,  [ 0.18750 ; 0.31250 ]
> 9,  [ 0.68750 ; 0.81250 ]
> 10, [ 0.93750 ; 0.06250 ]
> 11, [ 0.43750 ; 0.56250 ]
> 12, [ 0.31250 ; 0.18750 ]
> 13, [ 0.81250 ; 0.68750 ]
> 14, [ 0.56250 ; 0.43750 ]
> 15, [ 0.06250 ; 0.93750 ]
> 16, [ 0.09375 ; 0.46875 ]
> 17, [ 0.59375 ; 0.96875 ]
> 18, [ 0.84375 ; 0.21875 ]
> 19, [ 0.34375 ; 0.71875 ]
> 20, [ 0.46875 ; 0.09375 ]
> 21, [ 0.96875 ; 0.59375 ]
> 22, [ 0.71875 ; 0.34375 ]
> 23, [ 0.21875 ; 0.84375 ]
> 24, [ 0.15625 ; 0.15625 ]
> 25, [ 0.65625 ; 0.65625 ]
> 26, [ 0.90625 ; 0.40625 ]
> 27, [ 0.40625 ; 0.90625 ]
> 28, [ 0.28125 ; 0.28125 ]
> 29, [ 0.78125 ; 0.78125 ]
> 30, [ 0.53125 ; 0.03125 ]
> 31, [ 0.03125 ; 0.53125 ]
>
>
>
>
> -------------------------------------------------------
> SF.Net email is sponsored by Shop4tech.com-Lowest price on Blank Media
> 100pk Sonic DVD-R 4x for only $29 -100pk Sonic DVD+R for only $33
> Save 50% off Retail on Ink & Toner - Free Shipping and Free Gift.
> http://www.shop4tech.com/z/Inkjet_Cartridges/9_108_r285
> _______________________________________________
> Quantlib-users mailing list
> [hidden email]
> https://lists.sourceforge.net/lists/listinfo/quantlib-users