The Fast Linear Algorithm N dimensional sphere radius=1

N components: S=(Sx,Sy,Sz,Su,...) Norm S=1 P(x)=sinN-2(a).da.sinN-3(b).db ... dp    =(1-z2)(N-3)/2.dz.(1-y2)(N-4)/2.dy ... dw

Example N=5 The Fast Linear Algorithm (FLA) uses the rejection method with a function consisting of n steps (see the figure and article for more details)

Download the Fast Linear Algorithm:

	1.	To use the Fast Linear Algorithm you must have :
		sphere.c   (in C)
	2.	AND you must have the tables in the file "sphere.res". Two choices: . You can choose to download the file sphere.res already done or make one with create_sphere.out (.exe for windows), run it, and follow the instructions.
		sphere.res   (380 Ko) h → [0,100[ with rate=95% or For LINUX, only one executable create_sphere.out   (For LINUX, 450 Ko) For WINDOWS copy these two programs in the same directory 1. create_sphere.exe   (For WINDOWS, 34 Ko) 2. cygwin1.dll   (For WINDOWS, 950 Ko)

Download the Article:

Article.pdf (440 Ko)

Probabilities and Performances :

Figure: comparison of the time of simulation for various algorithms as function of the number of components N. The Fast Linear Algorithm (FLA) is the fastest of all algorithms proposed We can show more generally that another algorithm cannot be faster (see article). More...

Other Algorithms in C

• Other algorithms for O(N) sphere
  • Uniform_Sinus= using sinus (d(cos)<=> choose uniform cos) and rejection method
  • Gaussian= using Gaussian random number
  • Banerjia

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